Merge pull request 'CLI tweaks' (#22) from fix/cli-tweaks into main

Reviewed-on: #22

README.md

@@ -1,4 +1,4 @@
-# Midas
+<h1>Midas</h1>
 
 *Midas* is a type system to _Maintain Integrity of Data with Annotated Structures_. In Greek mythology, [Midas](https://en.wikipedia.org/wiki/Midas) was a Phrygian king who was blessed with the gift of turning everything he touched into gold.
 
@@ -6,6 +6,25 @@
 
 This framework is being developed as part of a Bachelor's Thesis by Louis Heredero at HEI Sion.
 
+<details>
+<summary><strong>Table of Contents</strong></summary>
+
+- [Requirements](#requirements)
+- [Installation](#installation)
+- [Commands](#commands)
+  - [Type Checking](#type-checking)
+  - [Compiling](#compiling)
+  - [Formatting](#formatting)
+  - [Highlighting](#highlighting)
+  - [Dumping the AST](#dumping-the-ast)
+  - [Dumping the Registry](#dumping-the-registry)
+  - [Generating Stubs](#generating-stubs)
+  - [Showing Type Judgements](#showing-type-judgements)
+  - [Validating Definitions](#validating-definitions)
+- [Tests](#tests)
+</details>
+
+
 ## Requirements
 
 - Python 3.11+
@@ -32,10 +51,26 @@ This framework is being developed as part of a Bachelor's Thesis by Louis Herede
 
 ## Commands
 
-### Compiling
+<!--
+check
+compile
+format
+highlight
+parse
+dump_registry
+types
+validate
+-->
 
-> [!NOTE]
-> In the current state of the project, the `compile` command doesn't generate any runnable code, it only runs the parsers and type checker on the provided files
+### Type Checking
+
+```shell
+midas check -t types.midas source.py
+```
+
+This command parses the given files and run the type checkers against the Midas definitions and Python program. Diagnostics are then printed showing warnings and errors.
+
+### Compiling
 
 ```shell
 midas compile -t types.midas source.py
@@ -43,14 +78,22 @@ midas compile -t types.midas source.py
 
 With the `compile` command, you can process a source Python file, with any number of custom type definition files (`-t FILE` option), and the type checker will verify the coherence of your program and generate the runnable code with valid syntax and runtime assertions.
 
-The optional `-l FILE` option lets you produce a highlighted version of the source code showing diagnostics from the type checker (see [Highlighting](#highlighting))
+### Formatting
+
+```shell
+midas format types.midas
+midas format types.midas -o formatted.midas
+```
+
+This command parses the given Midas file and outputs a pretty printed file from the AST.
 
 ### Highlighting
 
 ```shell
-midas utils highlight source.py
-# or
-midas utils highlight types.midas
+midas highlight source.py
+midas highlight source.py -o highlighted.html
+midas highlight types.midas
+midas highlight types.midas -o highlighted.html
 ```
 
 The `highlight` command takes in a source file (Python or Midas), runs the appropriate parser and outputs an HTML file containing the source code with added highlighting. This highlighting takes the form of hoverable annotations showing some of the parsed structures (e.g. a function definition, an assignment, a generic type, etc.)
@@ -60,14 +103,43 @@ The optional `-o FILE` option can be used to specify an output path. By default,
 ### Dumping the AST
 
 ```shell
-midas utils dump-ast source.py
-# or
-midas utils dump-ast types.midas
+midas parse source.py
+midas parse types.midas
 ```
 
-For debugging purposes, you can output the AST parsed from a Python or Midas file. For Python files, the `-p` flags lets you toggle the custom AST parsing. Without `-p`, the raw AST is returned, as produced by the builtin `ast` module. This flag has no effect on Midas files.
+For debugging purposes, you can output the AST parsed from a Python or Midas file. For Python files, the `--raw` flags lets you toggle the custom AST parsing. With `--raw`, the raw AST is returned, as produced by the builtin `ast` module. This flag has no effect on Midas files.
 
-The optional `-o FILE` option can be used to specify an output path. By default, the file is printed in stdout (equivalent to `-o -`).
+### Dumping the Registry
+
+```shell
+midas dump-registry -t types.midas
+```
+
+This command processes the given Midas definitions and dumps the contents of the types registry.
+
+### Generating Stubs
+
+```shell
+midas stubs types.midas -o stubs.pyi
+```
+
+This command generate Python stubs from a Midas definition file
+
+### Showing Type Judgements
+
+```shell
+midas types -t types.midas source.py
+```
+
+This command type checks the given Python source file and logs all typing judgements made by the type checker.
+
+### Validating Definitions
+
+```shell
+midas validate types.midas
+```
+
+This command lets you validate a Midas definition file by running the parser and type checker, verifying syntax and references.
 
 ## Tests
 
@@ -77,6 +149,7 @@ Several snapshot tests are available to assert the good behaviour of the parsers
 uv run -m tests.midas run -a
 uv run -m tests.python run -a
 uv run -m tests.checker run -a
+uv run -m tests.generator run -a
 ```
 
 **Available subcommands:**

examples/02_demonstration/demo.midas

@@ -0,0 +1,15 @@
+predicate in_range(min: float, max: float)(v: float) = min <= v & v <= max
+predicate is_ratio = in_range(0, 1)
+
+type Currency = float
+type Price[T <: Currency] = T where _ >= 0
+
+extend Price[T <: Currency] {
+    def __add__: fn(Price[T], /) -> Price[T]
+}
+
+type EUR = Currency
+type USD = Currency
+type CHF = Currency
+
+type Discount = float where is_ratio(_)

examples/02_demonstration/demo.py

@@ -0,0 +1,35 @@
+from typing import TypeVar
+
+from demo_stubs import CHF, EUR, USD, Currency, Discount, Price
+
+from midas.typing import cast, unsafe_cast
+
+T = TypeVar("T", bound=Currency)
+
+
+def apply_discount(amount: Price[T], discount: Discount) -> Price[T]:
+    return cast(Price[T], (1.0 - discount) * amount)
+
+
+a1 = cast(Price[EUR], 3.2)
+a2 = cast(Price[USD], 10.4)
+r1 = cast(Discount, 0.2)
+
+print(apply_discount(a1, r1))
+print(apply_discount(a2, r1))
+
+a3 = a1 + a1
+a4 = a1 + a2  # cannot add euros and dollars
+a3 = a2  # cannot change variable type
+
+dyn_price = float(input("Price (CHF): "))
+dyn_discount = float(input("Discount (0.0-1.0): "))
+discounted = apply_discount(
+    cast(Price[CHF], dyn_price),
+    cast(Discount, dyn_discount),
+)
+
+print(f"Discounted: CHF {discounted}")
+
+large_data = [i * 10 for i in range(100)]
+prices = unsafe_cast(list[Price[EUR]], large_data)

examples/02_demonstration/demo_stubs.pyi

@@ -0,0 +1,14 @@
+from __future__ import annotations
+from typing import Generic, TypeVar
+
+class Currency(float): ...
+
+_T0 = TypeVar("_T0", bound=Currency, covariant=True)
+
+class Price(Currency, Generic[_T0]):
+    def __add__(self, _0: Price[_T0], /) -> Price[_T0]: ...
+
+class EUR(Currency): ...
+class USD(Currency): ...
+class CHF(Currency): ...
+class Discount(float): ...

gen/midas.py

@@ -26,6 +26,14 @@ class MemberKind(Enum):
     METHOD = auto()
 
 
+@dataclass(frozen=True, kw_only=True)
+class ParamSpec:
+    l_paren: Token
+    pos: list[FunctionType.Argument]
+    mixed: list[FunctionType.Argument]
+    kw: list[FunctionType.Argument]
+
+
 ###<
 
 
@@ -50,9 +58,8 @@ class ExtendStmt:
 
 class PredicateStmt:
     name: Token
-    subject: Token
-    type: Type
-    condition: Expr
+    params: list[ParamSpec]
+    body: Expr
 
 
 ###<
@@ -78,6 +85,12 @@ class UnaryExpr:
     right: Expr
 
 
+class CallExpr:
+    callee: Expr
+    arguments: list[Expr]
+    keywords: dict[str, Expr]
+
+
 class GetExpr:
     expr: Expr
     name: Token
@@ -128,9 +141,7 @@ class ExtensionType:
 
 
 class FunctionType:
-    pos_args: list[Argument]
-    args: list[Argument]
-    kw_args: list[Argument]
+    params: ParamSpec
     returns: Type
 
     @dataclass(frozen=True, kw_only=True)

gen/python.py

@@ -145,6 +145,7 @@ class LogicalExpr:
 class CastExpr:
     type: MidasType
     expr: Expr
+    unsafe: bool
 
 
 class TernaryExpr:

midas/ast/midas.py

@@ -27,6 +27,14 @@ class MemberKind(Enum):
     METHOD = auto()
 
 
+@dataclass(frozen=True, kw_only=True)
+class ParamSpec:
+    l_paren: Token
+    pos: list[FunctionType.Argument]
+    mixed: list[FunctionType.Argument]
+    kw: list[FunctionType.Argument]
+
+
 ##############
 # Statements #
 ##############
@@ -86,9 +94,8 @@ class ExtendStmt(Stmt):
 @dataclass(frozen=True)
 class PredicateStmt(Stmt):
     name: Token
-    subject: Token
-    type: Type
-    condition: Expr
+    params: list[ParamSpec]
+    body: Expr
 
     def accept(self, visitor: Stmt.Visitor[T]) -> T:
         return visitor.visit_predicate_stmt(self)
@@ -116,6 +123,9 @@ class Expr(ABC):
         @abstractmethod
         def visit_unary_expr(self, expr: UnaryExpr) -> T: ...
 
+        @abstractmethod
+        def visit_call_expr(self, expr: CallExpr) -> T: ...
+
         @abstractmethod
         def visit_get_expr(self, expr: GetExpr) -> T: ...
 
@@ -161,6 +171,16 @@ class UnaryExpr(Expr):
         return visitor.visit_unary_expr(self)
 
 
+@dataclass(frozen=True)
+class CallExpr(Expr):
+    callee: Expr
+    arguments: list[Expr]
+    keywords: dict[str, Expr]
+
+    def accept(self, visitor: Expr.Visitor[T]) -> T:
+        return visitor.visit_call_expr(self)
+
+
 @dataclass(frozen=True)
 class GetExpr(Expr):
     expr: Expr
@@ -279,9 +299,7 @@ class ExtensionType(Type):
 
 @dataclass(frozen=True)
 class FunctionType(Type):
-    pos_args: list[Argument]
-    args: list[Argument]
-    kw_args: list[Argument]
+    params: ParamSpec
     returns: Type
 
     @dataclass(frozen=True, kw_only=True)

midas/ast/printer.py

@@ -150,13 +150,17 @@ class MidasAstPrinter(
         self._write_line("PredicateStmt")
         with self._child_level():
             self._write_line(f'name: "{stmt.name.lexeme}"')
-            self._write_line(f'subject: "{stmt.subject.lexeme}"')
-            self._write_line("type")
+            self._write_line("params")
+            with self._child_level():
+                for i, spec in enumerate(stmt.params):
+                    self._idx = i
+                    if i == len(stmt.params) - 1:
+                        self._mark_last()
+                    self._visit_param_spec(spec)
+
+            self._write_line("body", last=True)
             with self._child_level(single=True):
-                stmt.type.accept(self)
-            self._write_line("condition", last=True)
-            with self._child_level(single=True):
-                stmt.condition.accept(self)
+                stmt.body.accept(self)
 
     # Expressions
 
@@ -195,6 +199,29 @@ class MidasAstPrinter(
             with self._child_level(single=True):
                 expr.right.accept(self)
 
+    def visit_call_expr(self, expr: m.CallExpr) -> None:
+        self._write_line("CallExpr")
+        with self._child_level():
+            self._write_line("callee")
+            with self._child_level(single=True):
+                expr.callee.accept(self)
+            self._write_line("arguments")
+            with self._child_level():
+                for i, arg in enumerate(expr.arguments):
+                    self._idx = i
+                    if i == len(expr.arguments) - 1:
+                        self._mark_last()
+                    arg.accept(self)
+            self._write_line("keywords", last=True)
+            with self._child_level():
+                for i, (name, arg) in enumerate(expr.keywords.items()):
+                    self._idx = i
+                    if i == len(expr.keywords) - 1:
+                        self._mark_last()
+                    self._write_line(name)
+                    with self._child_level(single=True):
+                        arg.accept(self)
+
     def visit_get_expr(self, expr: m.GetExpr):
         self._write_line("GetExpr")
         with self._child_level():
@@ -276,34 +303,41 @@ class MidasAstPrinter(
     def visit_function_type(self, type: m.FunctionType) -> None:
         self._write_line("FunctionType")
         with self._child_level():
-            self._write_line("pos_args")
-            with self._child_level():
-                for i, arg in enumerate(type.pos_args):
-                    self._idx = i
-                    if i == len(type.pos_args) - 1:
-                        self._mark_last()
-                    self._print_function_arg(arg)
-
-            self._write_line("args")
-            with self._child_level():
-                for i, arg in enumerate(type.args):
-                    self._idx = i
-                    if i == len(type.args) - 1:
-                        self._mark_last()
-                    self._print_function_arg(arg)
-
-            self._write_line("kw_args")
-            with self._child_level():
-                for i, arg in enumerate(type.kw_args):
-                    self._idx = i
-                    if i == len(type.kw_args) - 1:
-                        self._mark_last()
-                    self._print_function_arg(arg)
+            self._write_line("params")
+            with self._child_level(single=True):
+                self._visit_param_spec(type.params)
 
             self._write_line("returns", last=True)
             with self._child_level(single=True):
                 type.returns.accept(self)
 
+    def _visit_param_spec(self, spec: m.ParamSpec) -> None:
+        self._write_line("ParamSpec")
+        with self._child_level():
+            self._write_line("pos")
+            with self._child_level():
+                for i, arg in enumerate(spec.pos):
+                    self._idx = i
+                    if i == len(spec.pos) - 1:
+                        self._mark_last()
+                    self._print_function_arg(arg)
+
+            self._write_line("mixed")
+            with self._child_level():
+                for i, arg in enumerate(spec.mixed):
+                    self._idx = i
+                    if i == len(spec.mixed) - 1:
+                        self._mark_last()
+                    self._print_function_arg(arg)
+
+            self._write_line("kw", last=True)
+            with self._child_level():
+                for i, arg in enumerate(spec.kw):
+                    self._idx = i
+                    if i == len(spec.kw) - 1:
+                        self._mark_last()
+                    self._print_function_arg(arg)
+
     def _print_function_arg(self, arg: m.FunctionType.Argument) -> None:
         self._write_line("Argument")
         with self._child_level():
@@ -367,10 +401,9 @@ class MidasPrinter(m.Expr.Visitor[str], m.Stmt.Visitor[str], m.Type.Visitor[str]
 
     def visit_predicate_stmt(self, stmt: m.PredicateStmt):
         name: str = stmt.name.lexeme
-        subject: str = stmt.subject.lexeme
-        type: str = stmt.type.accept(self)
-        condition: str = stmt.condition.accept(self)
-        return self.indented(f"predicate {name}({subject}: {type}) = {condition}")
+        sig: str = "".join(self._visit_param_spec(spec) for spec in stmt.params)
+        body: str = stmt.body.accept(self)
+        return self.indented(f"predicate {name}{sig} = {body}")
 
     def visit_logical_expr(self, expr: m.LogicalExpr):
         left: str = expr.left.accept(self)
@@ -389,6 +422,12 @@ class MidasPrinter(m.Expr.Visitor[str], m.Stmt.Visitor[str], m.Type.Visitor[str]
         right: str = expr.right.accept(self)
         return f"{operator}{right}"
 
+    def visit_call_expr(self, expr: m.CallExpr) -> str:
+        args: list[str] = [arg.accept(self) for arg in expr.arguments] + [
+            f"{name}={arg.accept(self)}" for name, arg in expr.keywords.items()
+        ]
+        return f"{expr.callee.accept(self)}({', '.join(args)})"
+
     def visit_get_expr(self, expr: m.GetExpr):
         expr_: str = expr.expr.accept(self)
         name: str = expr.name.lexeme
@@ -436,9 +475,13 @@ class MidasPrinter(m.Expr.Visitor[str], m.Stmt.Visitor[str], m.Type.Visitor[str]
         return f"{type.base.accept(self)} & {type.extension.accept(self)}"
 
     def visit_function_type(self, type: m.FunctionType) -> str:
-        pos_args: list[str] = [self._print_arg(arg) for arg in type.pos_args]
-        mixed_args: list[str] = [self._print_arg(arg) for arg in type.args]
-        kw_args: list[str] = [self._print_arg(arg) for arg in type.kw_args]
+        spec: str = self._visit_param_spec(type.params)
+        return f"fn {spec} -> {type.returns.accept(self)}"
+
+    def _visit_param_spec(self, spec: m.ParamSpec) -> str:
+        pos_args: list[str] = [self._print_arg(arg) for arg in spec.pos]
+        mixed_args: list[str] = [self._print_arg(arg) for arg in spec.mixed]
+        kw_args: list[str] = [self._print_arg(arg) for arg in spec.kw]
         args: list[str] = pos_args
 
         if len(pos_args) != 0:
@@ -447,8 +490,7 @@ class MidasPrinter(m.Expr.Visitor[str], m.Stmt.Visitor[str], m.Type.Visitor[str]
         if len(kw_args) != 0:
             args.append("*")
         args += kw_args
-
-        return f"fn ({', '.join(args)}) -> {type.returns.accept(self)}"
+        return f"({', '.join(args)})"
 
     def _print_arg(self, arg: m.FunctionType.Argument) -> str:
         res: str = ""
@@ -715,9 +757,10 @@ class PythonAstPrinter(
             self._write_line("type")
             with self._child_level(single=True):
                 expr.type.accept(self)
-            self._write_line("expr", last=True)
+            self._write_line("expr")
             with self._child_level(single=True):
                 expr.expr.accept(self)
+            self._write_line(f"unsafe: {expr.unsafe}", last=True)
 
     def visit_ternary_expr(self, expr: p.TernaryExpr) -> None:
         self._write_line("TernaryExpr")

midas/ast/python.py

@@ -350,6 +350,7 @@ class LogicalExpr(Expr):
 class CastExpr(Expr):
     type: MidasType
     expr: Expr
+    unsafe: bool
 
     def accept(self, visitor: Expr.Visitor[T]) -> T:
         return visitor.visit_cast_expr(self)

midas/checker/builtins.py

@@ -15,6 +15,7 @@ if TYPE_CHECKING:
 
 
 BUILTIN_SUBTYPES: dict[str, set[str]] = {
+    "object": {"float", "list", "dict", "str"},
     "float": {"int"},
     "int": {"bool"},
 }

midas/checker/diagnostic.py

@@ -9,6 +9,7 @@ class DiagnosticType(StrEnum):
     ERROR = "Error"
     WARNING = "Warning"
     INFO = "Info"
+    DEBUG = "Debug"
 
 
 @dataclass(frozen=True)

midas/checker/evaluator.py

@@ -0,0 +1,172 @@
+from dataclasses import dataclass
+from typing import Any, Callable, Optional
+
+import midas.ast.midas as m
+from midas.checker.preamble import Preamble
+from midas.checker.registry import TypesRegistry
+from midas.checker.reporter import FileReporter
+from midas.checker.types import Function, Predicate
+from midas.lexer.token import TokenType
+
+
+@dataclass(frozen=True, kw_only=True)
+class PartialPredicate(Predicate):
+    scope: dict[str, Any]
+
+
+class Evaluator(m.Expr.Visitor[Any]):
+    def __init__(self, types: TypesRegistry, reporter: Optional[FileReporter] = None):
+        self.types: TypesRegistry = types
+        self.reporter: Optional[FileReporter] = reporter
+        self.preamble: Preamble = Preamble(self.types)
+        self.scopes: list[dict[str, Any]] = [{}]
+
+    def evaluate(self, expr: m.Expr) -> Any:
+        value: Any = expr.accept(self)
+        if self.reporter is not None:
+            self.reporter.debug(expr.location, f"Value: {value}")
+        return value
+
+    def get_value(self, name: str) -> Any:
+        scope: dict[str, Any] = self.scopes[-1]
+        return scope[name]
+
+    def set_value(self, name: str, value: Any, force_declare: bool = False):
+        if not force_declare:
+            for scope in reversed(self.scopes):
+                if name in scope:
+                    scope[name] = value
+                    return
+        self.scopes[-1][name] = value
+
+    def visit_logical_expr(self, expr: m.LogicalExpr) -> Any:
+        def left():
+            return self.evaluate(expr.left)
+
+        def right():
+            return self.evaluate(expr.right)
+
+        match expr.operator.type:
+            case TokenType.AND:
+                return left() and right()
+            case _:
+                raise NotImplementedError
+
+    def visit_binary_expr(self, expr: m.BinaryExpr) -> Any:
+        left: Any = self.evaluate(expr.left)
+        right: Any = self.evaluate(expr.right)
+        match expr.operator.type:
+            case TokenType.MINUS:
+                return left - right
+            case TokenType.STAR:
+                return left * right
+            case TokenType.SLASH:
+                return left / right
+            case TokenType.GREATER:
+                return left > right
+            case TokenType.GREATER_EQUAL:
+                return left >= right
+            case TokenType.LESS:
+                return left < right
+            case TokenType.LESS_EQUAL:
+                return left <= right
+            case TokenType.EQUAL_EQUAL:
+                return left == right
+            case TokenType.BANG_EQUAL:
+                return left != right
+            case _:
+                raise NotImplementedError
+
+    def visit_unary_expr(self, expr: m.UnaryExpr) -> Any:
+        right: Any = self.evaluate(expr.right)
+        match expr.operator.type:
+            case TokenType.MINUS:
+                return -right
+            case _:
+                raise NotImplementedError
+
+    def visit_call_expr(self, expr: m.CallExpr) -> Any:
+        callee: Any = self.evaluate(expr.callee)
+        args: list[Any] = [self.evaluate(arg) for arg in expr.arguments]
+        kwargs: dict[str, Any] = {
+            name: self.evaluate(arg) for name, arg in expr.keywords.items()
+        }
+
+        match callee:
+            case Predicate():
+                return self._evaluate_predicate(callee, args, kwargs)
+            case _ if callable(callee):
+                return callee(*args, **kwargs)
+            case _:
+                return NotImplementedError
+
+    def visit_get_expr(self, expr: m.GetExpr) -> Any:
+        obj: Any = self.evaluate(expr.expr)
+        return getattr(obj, expr.name.lexeme)
+
+    def visit_variable_expr(self, expr: m.VariableExpr) -> Any:
+        name: str = expr.name.lexeme
+        for scope in reversed(self.scopes):
+            if name in scope:
+                return scope[name]
+
+        predicate: Optional[Predicate] = self.types.lookup_predicate(name)
+        if predicate is not None:
+            if predicate.alias:
+                return self.evaluate(predicate.body)
+            return predicate
+
+        glob: Optional[Callable] = self.preamble.get_py_func(name)
+        if glob is not None:
+            return glob
+        raise NameError(f"Unknown variable '{name}'")
+
+    def visit_grouping_expr(self, expr: m.GroupingExpr) -> Any:
+        return self.evaluate(expr.expr)
+
+    def visit_literal_expr(self, expr: m.LiteralExpr) -> Any:
+        return expr.value
+
+    def visit_wildcard_expr(self, expr: m.WildcardExpr) -> Any:
+        return self.get_value("_")
+
+    def _evaluate_predicate(
+        self, predicate: Predicate, args: list[Any], kwargs: dict[str, Any]
+    ) -> Any:
+        res: Any = None
+        if isinstance(predicate, PartialPredicate):
+            self.scopes.append(predicate.scope)
+        else:
+            self.scopes.append({})
+        match predicate.type:
+            case Function(returns=Function() as inner):
+                self._map_args(predicate.type, args, kwargs)
+                res = PartialPredicate(
+                    type=inner,
+                    body=predicate.body,
+                    alias=False,
+                    scope=self.scopes[-1],
+                )
+
+            case Function():
+                self._map_args(predicate.type, args, kwargs)
+                res = self.evaluate(predicate.body)
+
+            case _:
+                raise NotImplementedError
+        self.scopes.pop()
+        return res
+
+    def _map_args(self, function: Function, args: list[Any], kwargs: dict[str, Any]):
+        positional: list[Function.Argument] = function.pos_args + function.args
+        keywords: dict[str, Function.Argument] = {
+            arg.name: arg for arg in function.args + function.kw_args
+        }
+
+        for i, arg in enumerate(args):
+            param: Function.Argument = positional[i]
+            self.set_value(param.name, arg)
+
+        for name, arg in kwargs.items():
+            param: Function.Argument = keywords[name]
+            self.set_value(param.name, arg)

midas/checker/midas.py

@@ -1,27 +1,65 @@
 import logging
+from dataclasses import dataclass
 from pathlib import Path
 from typing import Optional
 
 import midas.ast.midas as m
+from midas.ast.location import Location
 from midas.checker.builtins import define_builtins
+from midas.checker.environment import Environment
+from midas.checker.operators import MIDAS_BINARY_METHODS, MIDAS_UNARY_METHODS
+from midas.checker.preamble import Preamble
 from midas.checker.registry import TypesRegistry
 from midas.checker.reporter import FileReporter, Reporter
 from midas.checker.types import (
     AliasType,
+    AppliedType,
     ComplexType,
+    ConstraintType,
     ExtensionType,
     Function,
     GenericType,
+    OverloadedFunction,
+    Predicate,
     Type,
     TypeVar,
     UnknownType,
+    unfold_type,
 )
+from midas.checker.variance import VarianceInferrer
 from midas.lexer.midas import MidasLexer
 from midas.lexer.token import Token
 from midas.parser.midas import MidasParser
 
 
-class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type]):
+@dataclass(frozen=True, kw_only=True)
+class TypedParamSpec:
+    pos: list[Function.Argument]
+    mixed: list[Function.Argument]
+    kw: list[Function.Argument]
+
+
+TypedExpr = tuple[m.Expr, Type]
+
+
+class ReturnException(Exception):
+    pass
+
+
+@dataclass(frozen=True, kw_only=True)
+class MappedArgument:
+    expr: m.Expr
+    type: Type
+    argument: Function.Argument
+
+
+@dataclass(frozen=True, kw_only=True)
+class OverloadCandidate:
+    function: Function
+    mapped: list[MappedArgument]
+
+
+class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[Type], m.Type.Visitor[Type]):
     """A resolver which evaluates Midas type definitions and build a registry"""
 
     def __init__(self, types: TypesRegistry, reporter: Reporter) -> None:
@@ -31,12 +69,18 @@ class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type
         self.types: TypesRegistry = types
         self._local_variables: dict[str, TypeVar] = {}
 
+        self._predicate_params: dict[str, Type] = {}
+
         self._current_name: Optional[str] = None
 
         define_builtins(self.types)
         builtins_path: Path = (Path(__file__).parent / "builtins.midas").resolve()
         self.process(builtins_path.read_text(), str(builtins_path))
 
+        self._bool: Type = self.get_type("bool")
+
+        self._preamble: Environment = Preamble(self.types)
+
     def process(self, source: str, path: Optional[str]):
         self.reporter = self.reporter.for_file(path)
         lexer: MidasLexer = MidasLexer(source)
@@ -47,6 +91,10 @@ class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type
             self.reporter.error(error.token.get_location(), error.message)
         self.resolve(stmts)
 
+    def type_of(self, expr: m.Expr) -> Type:
+        type: Type = expr.accept(self)
+        return type
+
     def get_type(self, name: str) -> Type:
         """Get a type from its name
 
@@ -63,6 +111,19 @@ class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type
             return self._local_variables[name]
         return self.types.get_type(name)
 
+    def get_variable(self, name: str) -> Type:
+        if name in self._predicate_params:
+            return self._predicate_params[name]
+        predicate: Optional[Predicate] = self.types.lookup_predicate(name)
+        if predicate is not None:
+            return predicate.type
+
+        global_: Optional[Type] = self._preamble.get(name)
+        if global_ is not None:
+            return global_
+
+        raise NameError(f"Unknown variable '{name}'")
+
     def resolve(self, stmts: list[m.Stmt]):
         """Process a sequence of statements
 
@@ -72,6 +133,16 @@ class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type
         for stmt in stmts:
             stmt.accept(self)
 
+        for name, type in self.types._types.items():
+            if isinstance(type, GenericType):
+                inferrer = VarianceInferrer(self.types)
+                self.types._types[name] = inferrer.infer(type)
+
+    def assert_bool(self, expr: m.Expr):
+        type: Type = self.type_of(expr)
+        if not self.types.is_subtype(type, self._bool):
+            self.reporter.error(expr.location, f"Must be a boolean but is {type}")
+
     def visit_type_stmt(self, stmt: m.TypeStmt) -> None:
         name: str = stmt.name.lexeme
         self._current_name = name
@@ -106,31 +177,163 @@ class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type
             )
 
     def visit_predicate_stmt(self, stmt: m.PredicateStmt) -> None:
-        self.reporter.warning(stmt.location, "PredicateStmt not yet supported")
+        for spec in stmt.params:
+            for param in spec.mixed:
+                assert param.name is not None
+                self._predicate_params[param.name.lexeme] = param.type.accept(self)
 
-    def visit_logical_expr(self, expr: m.LogicalExpr) -> None:
-        self.reporter.warning(expr.location, "LogicalExpr not yet supported")
+        type: Type = self.type_of(stmt.body)
+        params: list[TypedParamSpec] = [
+            self._visit_param_spec(spec) for spec in stmt.params
+        ]
 
-    def visit_binary_expr(self, expr: m.BinaryExpr) -> None:
-        self.reporter.warning(expr.location, "BinaryExpr not yet supported")
+        if not self._is_valid_predicate(type):
+            self.reporter.error(
+                stmt.body.location,
+                f"Predicate function body must evaluate to a boolean, got {type}",
+            )
+        if len(params) != 0:
+            type = self._bool
+            for spec in reversed(params):
+                type = Function(
+                    pos_args=spec.pos,
+                    args=spec.mixed,
+                    kw_args=spec.kw,
+                    returns=type,
+                )
+        self._predicate_params = {}
+        self.types.define_predicate(
+            stmt.name.lexeme,
+            Predicate(
+                type=type,
+                body=stmt.body,
+                alias=len(params) == 0,
+            ),
+        )
 
-    def visit_unary_expr(self, expr: m.UnaryExpr) -> None:
-        self.reporter.warning(expr.location, "UnaryExpr not yet supported")
+    def _is_valid_predicate(self, body: Type) -> bool:
+        match body:
+            case Function(returns=returns):
+                return self._is_valid_predicate(returns)
+            case _ if self.types.is_subtype(body, self._bool):
+                return True
+            case _:
+                return False
 
-    def visit_get_expr(self, expr: m.GetExpr) -> None:
-        self.reporter.warning(expr.location, "GetExpr not yet supported")
+    def visit_logical_expr(self, expr: m.LogicalExpr) -> Type:
+        self.assert_bool(expr.left)
+        self.assert_bool(expr.right)
+        return self._bool
 
-    def visit_variable_expr(self, expr: m.VariableExpr) -> None:
-        self.reporter.warning(expr.location, "VariableExpr not yet supported")
+    def visit_binary_expr(self, expr: m.BinaryExpr) -> Type:
+        method: Optional[str] = MIDAS_BINARY_METHODS.get(expr.operator.type)
+        if method is None:
+            self.logger.warning(f"Unsupported operator {expr.operator.lexeme}")
+            self.reporter.warning(
+                expr.location, f"Unsupported operator {expr.operator.lexeme}"
+            )
+            return UnknownType()
 
-    def visit_grouping_expr(self, expr: m.GroupingExpr) -> None:
+        return self._visit_binary_expr(expr.location, expr.left, expr.right, method)
+
+    def _visit_binary_expr(
+        self, location: Location, left_expr: m.Expr, right_expr: m.Expr, method: str
+    ) -> Type:
+        left: Type = self.type_of(left_expr)
+        right: Type = self.type_of(right_expr)
+
+        operation: Optional[Type] = self.types.lookup_member(left, method)
+        if operation is None:
+            self.reporter.error(
+                location,
+                f"Undefined operation {method} between {left} and {right}",
+            )
+            return UnknownType()
+
+        result: Optional[Type] = self._get_call_result(
+            location,
+            operation,
+            [(right_expr, right)],
+            {},
+        )
+        return result or UnknownType()
+
+    def visit_unary_expr(self, expr: m.UnaryExpr) -> Type:
+        method: Optional[str] = MIDAS_UNARY_METHODS.get(expr.operator.type)
+        if method is None:
+            self.logger.warning(f"Unsupported operator {expr.operator.lexeme}")
+            self.reporter.warning(
+                expr.location, f"Unsupported operator {expr.operator.lexeme}"
+            )
+            return UnknownType()
+
+        operand: Type = self.type_of(expr.right)
+        operation: Optional[Type] = self.types.lookup_member(operand, method)
+        if operation is None:
+            self.reporter.error(
+                expr.location,
+                f"Undefined operation {method} for {operand}",
+            )
+            return UnknownType()
+
+        result: Optional[Type] = self._get_call_result(
+            expr.location,
+            operation,
+            [],
+            {},
+        )
+        return result or UnknownType()
+
+    def visit_call_expr(self, expr: m.CallExpr) -> Type:
+        callee: Type = expr.callee.accept(self)
+        positional: list[TypedExpr] = [
+            (arg, self.type_of(arg)) for arg in expr.arguments
+        ]
+        keywords: dict[str, TypedExpr] = {
+            name: (arg, self.type_of(arg)) for name, arg in expr.keywords.items()
+        }
+        return (
+            self._get_call_result(
+                expr.location,
+                callee,
+                positional,
+                keywords,
+            )
+            or UnknownType()
+        )
+
+    def visit_get_expr(self, expr: m.GetExpr) -> Type:
+        object: Type = expr.expr.accept(self)
+        member: Optional[Type] = self.types.lookup_member(object, expr.name.lexeme)
+        if member is None:
+            self.reporter.error(
+                expr.location, f"Unknown member '{expr.name.lexeme}' of {object}"
+            )
+            return UnknownType()
+        return member
+
+    def visit_variable_expr(self, expr: m.VariableExpr) -> Type:
+        return self.get_variable(expr.name.lexeme)
+
+    def visit_grouping_expr(self, expr: m.GroupingExpr) -> Type:
         return expr.expr.accept(self)
 
-    def visit_literal_expr(self, expr: m.LiteralExpr) -> None:
-        self.reporter.warning(expr.location, "LiteralExpr not yet supported")
+    def visit_literal_expr(self, expr: m.LiteralExpr) -> Type:
+        match expr.value:
+            case bool():  # Must be before int
+                return self.types.get_type("bool")
+            case int():
+                return self.types.get_type("int")
+            case float():
+                return self.types.get_type("float")
+            case str():
+                return self.types.get_type("str")
+            case _:
+                self.reporter.warning(expr.location, f"Unknown literal {expr}")
+                return UnknownType()
 
-    def visit_wildcard_expr(self, expr: m.WildcardExpr) -> None:
-        self.reporter.warning(expr.location, "WildcardExpr not yet supported")
+    def visit_wildcard_expr(self, expr: m.WildcardExpr) -> Type:
+        return self.get_variable("_")
 
     def visit_named_type(self, type: m.NamedType) -> Type:
         name: str = type.name.lexeme
@@ -153,10 +356,10 @@ class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type
             return UnknownType()
 
     def visit_constraint_type(self, type: m.ConstraintType) -> Type:
-        type_: Type = type.type.accept(self)
-        type.constraint.accept(self)
-        # TODO
-        return UnknownType()
+        return ConstraintType(
+            type=type.type.accept(self),
+            constraint=type.constraint,
+        )
 
     def visit_complex_type(self, type: m.ComplexType) -> ComplexType:
         return ComplexType(
@@ -172,8 +375,17 @@ class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type
         )
 
     def visit_function_type(self, type: m.FunctionType) -> Type:
-        n_pos_args: int = len(type.pos_args)
-        n_args: int = len(type.args)
+        params: TypedParamSpec = self._visit_param_spec(type.params)
+        return Function(
+            pos_args=params.pos,
+            args=params.mixed,
+            kw_args=params.kw,
+            returns=type.returns.accept(self),
+        )
+
+    def _visit_param_spec(self, spec: m.ParamSpec) -> TypedParamSpec:
+        n_pos: int = len(spec.pos)
+        n_mixed: int = len(spec.mixed)
 
         def process_arg(arg: m.FunctionType.Argument, i: int) -> Function.Argument:
             return Function.Argument(
@@ -183,14 +395,10 @@ class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type
                 required=arg.required,
             )
 
-        return Function(
-            pos_args=[process_arg(arg, i) for i, arg in enumerate(type.pos_args)],
-            args=[process_arg(arg, i + n_pos_args) for i, arg in enumerate(type.args)],
-            kw_args=[
-                process_arg(arg, i + n_pos_args + n_args)
-                for i, arg in enumerate(type.kw_args)
-            ],
-            returns=type.returns.accept(self),
+        return TypedParamSpec(
+            pos=[process_arg(arg, i) for i, arg in enumerate(spec.pos)],
+            mixed=[process_arg(arg, i + n_pos) for i, arg in enumerate(spec.mixed)],
+            kw=[process_arg(arg, i + n_pos + n_mixed) for i, arg in enumerate(spec.kw)],
         )
 
     def _resolve_type_params(self, params: list[m.TypeParam]):
@@ -204,3 +412,343 @@ class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type
             self._local_variables[name] = var
             vars.append(var)
         return vars
+
+    def _get_call_result(
+        self,
+        location: Location,
+        callee: Type,
+        positional: list[TypedExpr],
+        keywords: dict[str, TypedExpr],
+        report_errors: bool = True,
+    ) -> Optional[Type]:
+        """Get the result type of a function call
+
+        If the function has overloads, the function will try to resolve the
+        appropriate signature.
+        Argument types are matched to the defined parameters.
+        The function doesn't take the raw expression as a parameter to accommodate
+        for desugared calls such as for operators.
+
+        Args:
+            location (Location): the call location
+            callee (Type): the called function
+            positional (list[TypedExpr]): the list positional arguments
+            keywords (dict[str, TypedExpr]): the map of keyword arguments
+            report_errors (bool, optional): whether type errors should be reported as diagnostics. Defaults to True.
+
+        Returns:
+            Type: the return type of the call, or `None` if either
+            the call is invalid or no overload matched the arguments uniquely
+        """
+        match callee:
+            case Function() as function:
+                valid: bool
+                mapped: list[MappedArgument]
+                valid, mapped = self.map_call_arguments(
+                    function, location, positional, keywords
+                )
+                valid = valid and self._are_arguments_valid(mapped, report_errors)
+                if not valid:
+                    return None
+                return function.returns
+
+            case OverloadedFunction(overloads=overloads):
+                function = self._match_overload(
+                    overloads, location, positional, keywords, report_errors
+                )
+                if function is None:
+                    return None
+                return function.returns
+
+            case AppliedType(body=body):
+                return self._get_call_result(
+                    location, body, positional, keywords, report_errors
+                )
+
+            case UnknownType():
+                return UnknownType()
+
+            case _:
+                if report_errors:
+                    self.reporter.error(location, f"{callee} is not callable")
+                return None
+
+    def _are_arguments_valid(
+        self,
+        arguments: list[MappedArgument],
+        report_errors: bool = True,
+    ) -> bool:
+        """Check whether the passed argument types correspond to their matched parameter definitions
+
+        Args:
+            arguments (list[MappedArgument]): the list of argument/parameter pairs
+            report_errors (bool, optional): whether type errors should be reported as diagnostics. Defaults to True.
+
+        Returns:
+            bool: True if all arguments fit the matching parameter definitions, False otherwise
+        """
+        valid: bool = True
+        for arg in arguments:
+            if not self.types.is_subtype(arg.type, arg.argument.type):
+                if report_errors:
+                    self.reporter.error(
+                        arg.expr.location,
+                        f"Wrong type for argument '{arg.argument.name}', expected {arg.argument.type}, got {arg.type}",
+                    )
+                valid = False
+        return valid
+
+    def _match_overload(
+        self,
+        overloads: list[Type],
+        location: Location,
+        positional: list[TypedExpr],
+        keywords: dict[str, TypedExpr],
+        report_errors: bool = True,
+    ) -> Optional[Function]:
+        """Try and resolve the appropriate overload for the given arguments
+
+        Args:
+            overloads (list[Type]): the list of possible overloads
+            location (Location): the call location
+            positional (list[TypedExpr]): the list of positional arguments
+            keywords (dict[str, TypedExpr]): the map of keywords arguments
+            report_errors (bool, optional): whether type errors should be reported as diagnostics. Defaults to True.
+
+        Returns:
+            Optional[Function]: the resolved function signature if it can be
+            determined unambiguously, or `None`.
+        """
+        candidates: list[OverloadCandidate] = []
+        for overload in overloads:
+            function: Type = unfold_type(overload)
+            if not isinstance(function, Function):
+                if report_errors:
+                    self.logger.error(
+                        f"Overload is not a function: {overload} is {function}"
+                    )
+                continue
+            valid, mapped = self.map_call_arguments(
+                function=function,
+                location=location,
+                positional=positional,
+                keywords=keywords,
+                report_errors=False,
+            )
+            if valid and self._are_arguments_valid(mapped, report_errors=False):
+                candidates.append(
+                    OverloadCandidate(
+                        function=function,
+                        mapped=mapped,
+                    )
+                )
+
+        pos_types: str = ", ".join(str(type) for _, type in positional)
+        kw_types: str = ", ".join(
+            f"{name}: {type}" for name, (_, type) in keywords.items()
+        )
+        for_args: str = f"for arguments pos=[{pos_types}] and kw={{{kw_types}}}"
+
+        n_candidates: int = len(candidates)
+
+        # Exactly 1 match -> return it
+        if n_candidates == 1:
+            return candidates[0].function
+
+        # No match -> invalid call
+        if n_candidates == 0:
+            overloads_str: str = ", ".join(map(str, overloads))
+            if report_errors:
+                self.reporter.error(
+                    location,
+                    f"No matching overload in [{overloads_str}] {for_args}",
+                )
+            return None
+
+        # Multiple matches -> see if one <: all others (more specific)
+        for i1, c1 in enumerate(candidates):
+            mapped1: list[MappedArgument] = c1.mapped
+            best_match: bool = True
+            for i2, c2 in enumerate(candidates):
+                if i1 == i2:
+                    continue
+                mapped2: list[MappedArgument] = c2.mapped
+                if not self._are_mapped_subtypes(mapped1, mapped2):
+                    best_match = False
+                    break
+                self.logger.debug(f"{c1.function} is a full overload of {c2.function}")
+            if best_match:
+                return c1.function
+
+        candidates_str: str = ", ".join(
+            str(candidate.function) for candidate in candidates
+        )
+        if report_errors:
+            self.reporter.error(
+                location,
+                f"Multiple matching overloads {for_args}: {candidates_str}",
+            )
+        return None
+
+    def map_call_arguments(
+        self,
+        function: Function,
+        location: Location,
+        positional: list[TypedExpr],
+        keywords: dict[str, TypedExpr],
+        report_errors: bool = True,
+    ) -> tuple[bool, list[MappedArgument]]:
+        """Map call arguments to a function's parameters as defined in its signature
+
+        This method maps positional-only, keyword-only and mixed parameter definitions
+        with the arguments passed at the call site
+
+        Any mismatched, missing or unexpected argument is reported as a diagnostic,
+        unless `report_errors` is set to `False`
+
+        Args:
+            function (Function): the function definition
+            location (Location): the call location
+            positional (list[TypedExpr]): the list of positional arguments
+            keywords (dict[str, TypedExpr]): the map of keyword arguments
+            report_errors (bool, optional): whether type errors should be reported as diagnostics. Defaults to True.
+
+        Returns:
+            tuple[bool, list[MappedArgument]]: a boolean reporting whether
+            the call is valid and the list of mapped arguments
+        """
+        set_args: set[str] = set()
+
+        required_positional: list[str] = [
+            arg.name for arg in function.pos_args + function.args if arg.required
+        ]
+        required_keyword: list[str] = [
+            arg.name for arg in function.kw_args if arg.required
+        ]
+
+        mapped: list[MappedArgument] = []
+
+        pos_params: list[Function.Argument] = list(function.pos_args)
+        mixed_params: list[Function.Argument] = list(function.args)
+        kw_params: dict[str, Function.Argument] = {
+            arg.name: arg for arg in function.kw_args
+        }
+
+        valid_call: bool = True
+
+        # TODO: handle *args and **kwargs sinks
+        for arg in positional:
+            param: Function.Argument
+            if len(pos_params) != 0:
+                param = pos_params.pop(0)
+            elif len(mixed_params) != 0:
+                param = mixed_params.pop(0)
+            else:
+                if report_errors:
+                    self.reporter.error(
+                        arg[0].location, "Too many positional arguments"
+                    )
+                valid_call = False
+                break
+            name: str = param.name
+            if name in required_positional:
+                required_positional.remove(name)
+            if name in required_keyword:
+                required_keyword.remove(name)
+            set_args.add(name)
+            mapped.append(
+                MappedArgument(
+                    expr=arg[0],
+                    type=arg[1],
+                    argument=param,
+                )
+            )
+
+        kw_params.update({arg.name: arg for arg in mixed_params})
+        for name, arg in keywords.items():
+            param: Function.Argument
+            if name not in kw_params:
+                if report_errors:
+                    if name in set_args:
+                        self.reporter.error(
+                            arg[0].location, f"Multiple values for argument '{name}'"
+                        )
+                    else:
+                        self.reporter.error(
+                            arg[0].location, f"Unknown keyword argument '{name}'"
+                        )
+                valid_call = False
+                continue
+            param = kw_params.pop(name)
+            if name in required_positional:
+                required_positional.remove(name)
+            if name in required_keyword:
+                required_keyword.remove(name)
+            set_args.add(name)
+            mapped.append(
+                MappedArgument(
+                    expr=arg[0],
+                    type=arg[1],
+                    argument=param,
+                )
+            )
+
+        def join_args(args: list[str]) -> str:
+            args = list(map(lambda a: f"'{a}'", args))
+            if len(args) == 0:
+                return ""
+            if len(args) == 1:
+                return args[0]
+            return ", ".join(args[:-1]) + " and " + args[-1]
+
+        if len(required_positional) != 0:
+            plural: str = "" if len(required_positional) == 1 else "s"
+            args: str = join_args(required_positional)
+            if report_errors:
+                self.reporter.error(
+                    location,
+                    f"Missing required positional argument{plural}: {args}",
+                )
+            valid_call = False
+
+        if len(required_keyword) != 0:
+            plural: str = "" if len(required_keyword) == 1 else "s"
+            args: str = join_args(required_keyword)
+            if report_errors:
+                self.reporter.error(
+                    location,
+                    f"Missing required keyword argument{plural}: {args}",
+                )
+            valid_call = False
+
+        return valid_call, mapped
+
+    def _are_mapped_subtypes(
+        self, mapped1: list[MappedArgument], mapped2: list[MappedArgument]
+    ) -> bool:
+        """Check whether the given argument mappings are subtype/supertype of one another
+
+        This function checks whether the argument mappings `mapped1` are subtypes
+        of `mapped2`. If any of the parameter type in `mapped1` is not a subtype
+        of the corresponding parameter in `mapped2`, `False` is returned.
+
+        This is used to check whether a given overload is
+        a more specific function/ a subtype of another.
+
+        Args:
+            mapped1 (list[MappedArgument]): the first argument mappings (subtype)
+            mapped2 (list[MappedArgument]): the second argument mappings (supertype)
+
+        Returns:
+            bool: `True` if `mapped1` is a subtype of `mapped2`, `False` otherwise
+        """
+        by_expr: dict[m.Expr, Type] = {}
+        for arg in mapped1:
+            by_expr[arg.expr] = arg.argument.type
+
+        for arg in mapped2:
+            type2: Type = arg.argument.type
+            type1: Type = by_expr[arg.expr]
+            if not self.types.is_subtype(type1, type2):
+                return False
+        return True

midas/checker/operators.py

@@ -1,7 +1,9 @@
 import ast
 from typing import Type
 
-OPERATOR_METHODS: dict[Type[ast.operator], str] = {
+from midas.lexer.token import TokenType
+
+PY_OPERATOR_METHODS: dict[Type[ast.operator], str] = {
     ast.Add: "__add__",
     ast.Sub: "__sub__",
     ast.Mult: "__mul__",
@@ -17,9 +19,9 @@ OPERATOR_METHODS: dict[Type[ast.operator], str] = {
     ast.FloorDiv: "__floordiv__",
 }
 
-COMPARATOR_METHODS: dict[Type[ast.cmpop], str] = {
+PY_COMPARATOR_METHODS: dict[Type[ast.cmpop], str] = {
     ast.Eq: "__eq__",
-    # ast.NotEq: "__noteq__",
+    ast.NotEq: "__eq__",
     ast.Lt: "__lt__",
     ast.LtE: "__le__",
     ast.Gt: "__gt__",
@@ -30,9 +32,40 @@ COMPARATOR_METHODS: dict[Type[ast.cmpop], str] = {
     # ast.NotIn: "__notin__",
 }
 
-UNARY_METHODS: dict[Type[ast.unaryop], str] = {
+PY_UNARY_METHODS: dict[Type[ast.unaryop], str] = {
     ast.Invert: "__invert__",
     # ast.Not: "",
     ast.UAdd: "__pos__",
     ast.USub: "__neg__",
 }
+
+
+MIDAS_BINARY_METHODS: dict[TokenType, str] = {
+    # TokenType.PLUS: "__add__",
+    TokenType.MINUS: "__sub__",
+    TokenType.STAR: "__mul__",
+    TokenType.SLASH: "__truediv__",
+    # TokenType.MODULO: "__mod__",
+    # TokenType.POW: "__pow__",
+    # ast.BitOr: "__or__",
+    # ast.BitXor: "__xor__",
+    # ast.BitAnd: "__and__",
+    # ast.FloorDiv: "__floordiv__",
+    TokenType.EQUAL_EQUAL: "__eq__",
+    TokenType.BANG_EQUAL: "__eq__",
+    TokenType.LESS: "__lt__",
+    TokenType.LESS_EQUAL: "__le__",
+    TokenType.GREATER: "__gt__",
+    TokenType.GREATER_EQUAL: "__ge__",
+    # ast.Is: "__is__",
+    # ast.IsNot: "__isnot__",
+    # ast.In: "__in__",
+    # ast.NotIn: "__notin__",
+}
+
+MIDAS_UNARY_METHODS: dict[TokenType, str] = {
+    # ast.Invert: "__invert__",
+    # ast.Not: "",
+    # TokenType.PLUS: "__pos__",
+    TokenType.MINUS: "__neg__",
+}

midas/checker/preamble.py

@@ -1,4 +1,5 @@
 from dataclasses import dataclass
+from typing import Callable, Optional
 
 from midas.checker.environment import Environment
 from midas.checker.registry import TypesRegistry
@@ -16,16 +17,18 @@ class Preamble(Environment):
     def __init__(self, types: TypesRegistry) -> None:
         super().__init__()
         self._types: TypesRegistry = types
+        self._python_funcs: dict[str, Callable] = {}
 
-        self._def_type_constructor("object")
-        self._def_type_constructor("float")
-        self._def_type_constructor("int")
-        self._def_type_constructor("bool")
-        self._def_type_constructor("str")
+        self._def_type_constructor("object", object)
+        self._def_type_constructor("float", float)
+        self._def_type_constructor("int", int)
+        self._def_type_constructor("bool", bool)
+        self._def_type_constructor("str", str)
         self._def_function(
             name="list",
             pos=[Param("object", TopType())],
             returns=self._list_of(TopType()),
+            py_function=list,
         )
 
         # TODO: use sink
@@ -33,6 +36,7 @@ class Preamble(Environment):
             name="print",
             pos=[Param("object", TopType())],
             returns=UnitType(),
+            py_function=print,
         )
 
         map_in = TypeVar(name="T", bound=None)
@@ -52,17 +56,25 @@ class Preamble(Environment):
                 ),
             ],
             returns=self._list_of(map_out),  # TODO: replace with Iterable[U]
+            type_vars=[map_in, map_out],
+            py_function=map,
+        )
+        self._def_function(
+            name="input",
+            pos=[Param("prompt", TopType(), required=False)],
+            returns=self._types.get_type("str"),
         )
 
     def _list_of(self, item_type: Type) -> Type:
         return self._types.apply_generic(self._types.get_type("list"), [item_type])
 
-    def _def_type_constructor(self, name: str):
+    def _def_type_constructor(self, name: str, py_function: Optional[Callable] = None):
         # TODO: more specific arg types
         self._def_function(
             name=name,
             pos=[Param("object", TopType(), required=False)],
             returns=self._types.get_type(name),
+            py_function=py_function,
         )
 
     def _make_function(
@@ -109,6 +121,7 @@ class Preamble(Environment):
         kw: list[Param] = [],
         returns: Type = UnitType(),
         type_vars: list[TypeVar] = [],
+        py_function: Optional[Callable] = None,
     ):
         function: Type = self._make_function(
             name=name,
@@ -119,3 +132,8 @@ class Preamble(Environment):
             type_vars=type_vars,
         )
         self.define(name, function)
+        if py_function is not None:
+            self._python_funcs[name] = py_function
+
+    def get_py_func(self, name: str) -> Optional[Callable]:
+        return self._python_funcs.get(name)

midas/checker/python.py

@@ -1,12 +1,18 @@
 import ast
 import logging
 from dataclasses import dataclass
-from typing import Optional
+from typing import Any, Optional
 
 import midas.ast.python as p
 from midas.ast.location import Location
+from midas.ast.printer import MidasPrinter
 from midas.checker.environment import Environment
-from midas.checker.operators import COMPARATOR_METHODS, OPERATOR_METHODS, UNARY_METHODS
+from midas.checker.evaluator import Evaluator
+from midas.checker.operators import (
+    PY_COMPARATOR_METHODS,
+    PY_OPERATOR_METHODS,
+    PY_UNARY_METHODS,
+)
 from midas.checker.preamble import Preamble
 from midas.checker.registry import TypesRegistry
 from midas.checker.reporter import FileReporter, Reporter
@@ -14,13 +20,19 @@ from midas.checker.resolver import Resolver
 from midas.checker.types import (
     AliasType,
     AppliedType,
+    BaseType,
+    ConstraintType,
     Function,
+    GenericType,
     OverloadedFunction,
     Type,
+    TypeVar,
     UnitType,
     UnknownType,
+    Variance,
     unfold_type,
 )
+from midas.checker.unifier import Unifier
 from midas.parser.python import PythonParser
 from midas.utils import TypedAST
 
@@ -63,6 +75,7 @@ class PythonTyper(
         self.env: Environment = self.global_env
         self.locals: dict[p.Expr, int] = {}
         self.judgements: list[tuple[p.Expr, Type]] = []
+        self.evaluated_casts: list[p.CastExpr] = []
 
     def process(self, source: str, path: Optional[str]) -> TypedAST:
         self.reporter = self.reporter.for_file(path)
@@ -76,10 +89,15 @@ class PythonTyper(
         self.env = self.global_env
         self.locals = resolver.locals
         self.judgements = []
+        self.evaluated_casts = []
 
         self.check(stmts)
 
-        return TypedAST(stmts=stmts, judgements=self.judgements)
+        return TypedAST(
+            stmts=stmts,
+            judgements=self.judgements,
+            evaluated_casts=self.evaluated_casts,
+        )
 
     def judge(self, expr: p.Expr, type: Type):
         """Record a typing judgement
@@ -223,7 +241,8 @@ class PythonTyper(
             )
             pos += 1
 
-        for arg in pos_args + args + kw_args:
+        all_args: list[Function.Argument] = pos_args + args + kw_args
+        for arg in all_args:
             env.define(arg.name, arg.type)
 
         returns_hint: Optional[Type] = None
@@ -264,12 +283,25 @@ class PythonTyper(
             returns = inferred_return
 
         # TODO: handle *args and **kwargs sinks
-        function: Function = Function(
+        function: Type = Function(
             pos_args=pos_args,
             args=args,
             kw_args=kw_args,
             returns=returns,
         )
+        generic_params: list[TypeVar] = []
+        all_types: list[Type] = [arg.type for arg in all_args] + [returns]
+        for type in all_types:
+            if isinstance(type, TypeVar):
+                if type not in generic_params:
+                    generic_params.append(type)
+
+        if len(generic_params) != 0:
+            function = GenericType(
+                name=stmt.name,
+                params=generic_params,
+                body=function,
+            )
         self.env.define(stmt.name, function)
 
     def visit_type_assign(self, stmt: p.TypeAssign) -> None:
@@ -377,7 +409,7 @@ class PythonTyper(
         pass
 
     def visit_binary_expr(self, expr: p.BinaryExpr) -> Type:
-        method: Optional[str] = OPERATOR_METHODS.get(expr.operator.__class__)
+        method: Optional[str] = PY_OPERATOR_METHODS.get(expr.operator.__class__)
         if method is None:
             self.logger.warning(f"Unsupported operator {expr.operator}")
             self.reporter.warning(
@@ -388,7 +420,7 @@ class PythonTyper(
         return self._visit_binary_expr(expr.location, expr.left, expr.right, method)
 
     def visit_compare_expr(self, expr: p.CompareExpr) -> Type:
-        method: Optional[str] = COMPARATOR_METHODS.get(expr.operator.__class__)
+        method: Optional[str] = PY_COMPARATOR_METHODS.get(expr.operator.__class__)
         if method is None:
             self.logger.warning(f"Unsupported operator {expr.operator}")
             self.reporter.warning(
@@ -421,7 +453,7 @@ class PythonTyper(
         return result or UnknownType()
 
     def visit_unary_expr(self, expr: p.UnaryExpr) -> Type:
-        method: Optional[str] = UNARY_METHODS.get(expr.operator.__class__)
+        method: Optional[str] = PY_UNARY_METHODS.get(expr.operator.__class__)
         if method is None:
             self.logger.warning(f"Unsupported operator {expr.operator}")
             self.reporter.warning(
@@ -447,6 +479,10 @@ class PythonTyper(
         return result or UnknownType()
 
     def visit_call_expr(self, expr: p.CallExpr) -> Type:
+        match expr.callee:
+            case p.VariableExpr(name="TypeVar"):
+                return self.define_typevar(expr) or UnknownType()
+
         callee: Type = self.type_of(expr.callee)
         positional: list[TypedExpr] = [
             (arg, self.type_of(arg)) for arg in expr.arguments
@@ -512,7 +548,16 @@ class PythonTyper(
         return UnknownType()
 
     def visit_cast_expr(self, expr: p.CastExpr) -> Type:
-        return self.resolve_type_expr(expr.type)
+        subject_type: Type = self.type_of(expr.expr)
+        target_type: Type = self.resolve_type_expr(expr.type)
+        is_lit, lit_value = self._get_literal(expr.expr)
+        if is_lit:
+            evaluated: bool = self._evaluate_cast_statically(
+                expr, subject_type, target_type, lit_value
+            )
+            if evaluated:
+                self.evaluated_casts.append(expr)
+        return target_type
 
     def visit_ternary_expr(self, expr: p.TernaryExpr) -> Type:
         test_type: Type = self.type_of(expr.test)
@@ -653,7 +698,7 @@ class PythonTyper(
         If the function has overloads, the function will try to resolve the
         appropriate signature.
         Argument types are matched to the defined parameters.
-        The function doesn't take the raw expression as a parameter to accomodate
+        The function doesn't take the raw expression as a parameter to accommodate
         for desugared calls such as for operators.
 
         Args:
@@ -700,6 +745,28 @@ class PythonTyper(
                     location, base, positional, keywords, report_errors
                 )
 
+            case GenericType():
+                unifier: Unifier = Unifier(self.types)
+                pos: list[Type] = [a[1] for a in positional]
+                kw: dict[str, Type] = {k: v[1] for k, v in keywords.items()}
+                unified: Optional[Type] = unifier.unify_call(callee, pos, kw)
+                if unified is None:
+                    if report_errors:
+                        pos_str: str = ", ".join(str(t) for t in pos)
+                        kw_str: str = ", ".join(f"{k}: {v}" for k, v in kw.items())
+                        self.reporter.error(
+                            location,
+                            f"Could not unify {callee}={callee.body} with pos=[{pos_str}] and kw={{{kw_str}}}",
+                        )
+                    return None
+                return self._get_call_result(
+                    location,
+                    unified,
+                    positional,
+                    keywords,
+                    report_errors,
+                )
+
             case _:
                 if report_errors:
                     self.reporter.error(
@@ -752,7 +819,7 @@ class PythonTyper(
 
         Returns:
             Optional[Function]: the resolved function signature if it can be
-            determined unambigously, or `None`.
+            determined unambiguously, or `None`.
         """
         candidates: list[OverloadCandidate] = []
         for overload in overloads:
@@ -1005,3 +1072,147 @@ class PythonTyper(
             report_errors=False,
         )
         return result
+
+    def define_typevar(self, call: p.CallExpr) -> Optional[TypeVar]:
+        def is_kw_true(name: str) -> bool:
+            match call.keywords.get(name):
+                case p.LiteralExpr(value=True):
+                    return True
+                case _:
+                    return False
+
+        match call:
+            case p.CallExpr(
+                arguments=[p.LiteralExpr(value=str() as name)],
+            ):
+                bound: Optional[Type] = None
+                variance: Variance = Variance.INVARIANT
+                if "bound" in call.keywords:
+                    bound_type: p.MidasType = self._parse_type_from_expr(
+                        call.keywords["bound"]
+                    )
+                    bound = self.resolve_type_expr(bound_type)
+
+                if is_kw_true("covariant"):
+                    variance = Variance.COVARIANT
+
+                if is_kw_true("contravariant"):
+                    if variance == Variance.COVARIANT:
+                        self.reporter.warning(
+                            call.keywords["contravariant"].location,
+                            "TypeVar cannot be covariant and contravariant at the same time. Marked as invariant",
+                        )
+                        variance = Variance.INVARIANT
+                    else:
+                        variance = Variance.CONTRAVARIANT
+                var: TypeVar = TypeVar(name=name, bound=bound, variance=variance)
+                self.types.define_type(name, var)
+                return var
+
+            case _:
+                self.reporter.warning(
+                    call.location, "Invalid usage of 'TypeVar', skipping"
+                )
+                return None
+
+    def _parse_type_from_expr(self, expr: p.Expr) -> p.MidasType:
+        location: Location = expr.location
+        parser = PythonParser()
+        match expr:
+            case p.LiteralExpr(value=str() as value):
+                node: ast.Expression = ast.parse(value, mode="eval")
+                return parser._parse_type(node.body)
+            case p.VariableExpr(name=name):
+                return p.BaseType(location=location, base=name, param=None)
+            case _:
+                raise NotImplementedError
+
+    def _get_literal(self, expr: p.Expr) -> tuple[bool, Any]:
+        match expr:
+            case p.LiteralExpr(value=value):
+                return True, value
+
+            case p.ListExpr(items=items):
+                values: list[Any] = []
+                for item in items:
+                    is_lit, value = self._get_literal(item)
+                    if not is_lit:
+                        return False, None
+                    values.append(value)
+                return True, values
+
+            case p.DictExpr(keys=keys, values=values):
+                pairs: list[tuple[Any, Any]] = []
+                for key, value in zip(keys, values):
+                    key_val = None
+                    if key is not None:
+                        is_lit, key_val = self._get_literal(key)
+                        if not is_lit:
+                            return False, None
+
+                    is_lit, value_val = self._get_literal(value)
+                    if not is_lit:
+                        return False, None
+
+                    if key is None:
+                        # TODO: check that value is always a dict
+                        assert isinstance(value_val, dict)
+                        pairs.extend(value_val.items())
+                    else:
+                        pairs.append((key_val, value_val))
+                return True, dict(pairs)
+
+            case _:
+                return False, None
+
+    def _evaluate_cast_statically(
+        self, expr: p.CastExpr, subject_type: Type, target_type: Type, lit_value: Any
+    ) -> bool:
+        match target_type:
+            case AliasType(type=base):
+                return self._evaluate_cast_statically(
+                    expr, subject_type, base, lit_value
+                )
+
+            case AppliedType(body=body):
+                return self._evaluate_cast_statically(
+                    expr, subject_type, body, lit_value
+                )
+
+            case ConstraintType(type=base, constraint=constraint):
+                evaluated: bool = True
+                if not self._evaluate_cast_statically(
+                    expr, subject_type, base, lit_value
+                ):
+                    evaluated = False
+
+                evaluator = Evaluator(self.types)
+                evaluator.set_value("_", lit_value)
+                res = evaluator.evaluate(constraint)
+                if not res:
+                    printer = MidasPrinter()
+                    constraint_str: str = printer.print(constraint)
+                    self.reporter.error(
+                        expr.location,
+                        f"Value {lit_value!r} does not fit constraint '{constraint_str}'",
+                    )
+                    evaluated = False
+                return evaluated
+
+            case BaseType():
+                # TODO: do we want to allow cast(float, int)? would require runtime conversion
+                if not self.types.is_subtype(
+                    subject_type, target_type
+                ) or not self.types.is_subtype(target_type, subject_type):
+                    self.reporter.error(
+                        expr.location,
+                        f"Value {lit_value!r} of type {subject_type} cannot be cast as {target_type}",
+                    )
+                    return False
+                return True
+
+            case _:
+                self.reporter.info(
+                    expr.location, f"Cannot evaluate cast to {target_type} statically"
+                )
+                return False

midas/checker/registry.py

@@ -9,14 +9,17 @@ from midas.checker.types import (
     AppliedType,
     BaseType,
     ComplexType,
+    ConstraintType,
     ExtensionType,
     Function,
     GenericType,
     OverloadedFunction,
+    Predicate,
     TopType,
     Type,
     TypeVar,
     UnknownType,
+    Variance,
     substitute_typevars,
 )
 
@@ -32,6 +35,7 @@ class TypesRegistry:
         self.logger: logging.Logger = logging.getLogger("TypesRegistry")
         self._types: dict[str, Type] = {}
         self._members: dict[str, dict[str, Member]] = {}
+        self._predicates: dict[str, Predicate] = {}
 
     def get_type(self, name: str) -> Type:
         """Get a type from its name
@@ -101,6 +105,11 @@ class TypesRegistry:
         else:
             members[member_name] = Member(kind=kind, type=member_type)
 
+    def define_predicate(self, name: str, predicate: Predicate):
+        if name in self._predicates:
+            raise ValueError(f"Predicate {name} already defined")
+        self._predicates[name] = predicate
+
     def is_subtype(self, type1: Type, type2: Type) -> bool:
         """Check whether `type1` is a subtype of `type2`
 
@@ -121,6 +130,19 @@ class TypesRegistry:
             case (_, TopType()):
                 return True
 
+            case (_, UnknownType()):
+                return True
+
+            case (TypeVar(bound=bound), _):
+                if bound is None:
+                    return False
+                return self.is_subtype(bound, type2)
+
+            case (_, TypeVar(bound=bound)):
+                if bound is None:
+                    return True
+                return self.is_subtype(type1, bound)
+
             case (AliasType(type=base1), _):
                 return self.is_subtype(base1, type2)
 
@@ -138,10 +160,30 @@ class TypesRegistry:
             case (Function(), Function()):
                 return self.is_func_subtype(type1, type2)
 
-            case (TypeVar(bound=bound), _):
-                if bound is None:
+            case (ConstraintType(type=base1), _):
+                return self.is_subtype(base1, type2)
+
+            case (
+                AppliedType(name=name1, args=args1),
+                AppliedType(name=name2, args=args2),
+            ) if (
+                name1 == name2
+            ):
+                generic: Type = self.get_type(name1)
+                assert isinstance(generic, GenericType)
+                for param, arg1, arg2 in zip(generic.params, args1, args2):
+                    variance: Variance = param.variance
+                    if variance in {Variance.INVARIANT, Variance.COVARIANT}:
+                        if not self.is_subtype(arg1, arg2):
                             return False
-                return self.is_subtype(bound, type2)
+                    if variance in {Variance.INVARIANT, Variance.CONTRAVARIANT}:
+                        if not self.is_subtype(arg2, arg1):
+                            return False
+                return True
+
+            # TODO: verify legitimacy
+            case (AppliedType(body=body), _):
+                return self.is_subtype(body, type2)
 
         return False
 
@@ -359,9 +401,18 @@ class TypesRegistry:
                 )
                 return self.lookup_member(base, member_name)
 
+            case ConstraintType(type=base):
+                return self.lookup_member(base, member_name)
+
+            case TypeVar(bound=bound) if bound is not None:
+                return self.lookup_member(bound, member_name)
+
             case UnknownType():
                 return UnknownType()
 
             case _:
                 self.logger.debug(f"Can't get member on {type}")
                 return None
+
+    def lookup_predicate(self, name: str) -> Optional[Predicate]:
+        return self._predicates.get(name)

midas/checker/reporter.py

@@ -61,3 +61,10 @@ class FileReporter:
             location=location,
             message=message,
         )
+
+    def debug(self, location: Location, message: str):
+        self.report(
+            type=DiagnosticType.DEBUG,
+            location=location,
+            message=message,
+        )

midas/checker/types.py

@@ -1,7 +1,11 @@
 from __future__ import annotations
 
 from dataclasses import dataclass, field
-from typing import Optional
+from enum import StrEnum
+from typing import Optional, assert_never
+
+import midas.ast.midas as m
+from midas.ast.printer import MidasPrinter
 
 
 @dataclass(frozen=True, kw_only=True)
@@ -99,15 +103,27 @@ class ExtensionType:
         return f"{self.base} & {self.extension}"
 
 
+class Variance(StrEnum):
+    INVARIANT = "INVARIANT"
+    COVARIANT = "COVARIANT"
+    CONTRAVARIANT = "CONTRAVARIANT"
+
+
 @dataclass(frozen=True, kw_only=True)
 class TypeVar:
     name: str
     bound: Optional[Type]
+    variance: Variance = Variance.INVARIANT
 
     def __str__(self) -> str:
+        variance: str = {
+            Variance.COVARIANT: "+",
+            Variance.CONTRAVARIANT: "-",
+        }.get(self.variance, "")
+        res: str = f"{variance}{self.name}"
         if self.bound is not None:
-            return f"{self.name} <: {self.bound}"
-        return self.name
+            res = f"{res} <: {self.bound}"
+        return res
 
 
 @dataclass(frozen=True, kw_only=True)
@@ -130,6 +146,16 @@ class AppliedType:
         return f"{self.name}[{', '.join(map(str, self.args))}]"
 
 
+@dataclass(frozen=True, kw_only=True)
+class ConstraintType:
+    type: Type
+    constraint: m.Expr
+
+    def __str__(self) -> str:
+        printer = MidasPrinter()
+        return f"{self.type} where {printer.print(self.constraint)}"
+
+
 def substitute_typevars(type: Type, substitutions: dict[str, Type]) -> Type:
     def sub_argument(arg: Function.Argument):
         return Function.Argument(
@@ -198,6 +224,12 @@ def substitute_typevars(type: Type, substitutions: dict[str, Type]) -> Type:
                 body=substitute_typevars(body, substitutions),
             )
 
+        case ConstraintType():
+            return ConstraintType(
+                type=substitute_typevars(type.type, substitutions),
+                constraint=type.constraint,
+            )
+
         case TypeVar(name=name):
             if name in substitutions:
                 return substitutions[name]
@@ -221,9 +253,13 @@ def substitute_typevars(type: Type, substitutions: dict[str, Type]) -> Type:
         case UnknownType() | UnitType():
             return type
 
-        case _:
+        case TopType() | GenericType():
             raise NotImplementedError(f"Unsupported type {type}")
 
+        # Ensure exhaustiveness
+        case _:
+            assert_never(type)
+
 
 def unfold_type(type: Type) -> Type:
     match type:
@@ -233,6 +269,65 @@ def unfold_type(type: Type) -> Type:
             return type
 
 
+def to_annotation(type: Type) -> str:
+    def _args_annotation(func: Function) -> str:
+        if len(func.kw_args) != 0:
+            return "..."
+
+        args: str = ", ".join(
+            to_annotation(arg.type) for arg in func.pos_args + func.args
+        )
+        return f"[{args}]"
+
+    match type:
+        case TopType():
+            return "Any"
+
+        case BaseType(name=name):
+            return name
+
+        case AliasType(name=name):
+            return name
+
+        case UnknownType():
+            return "Any"
+
+        case UnitType():
+            return "None"
+
+        case Function(returns=returns):
+            params_annot: str = _args_annotation(type)
+            return f"Callable[{params_annot}, {to_annotation(returns)}]"
+
+        case OverloadedFunction():
+            return "Callable"
+
+        case ComplexType() | ExtensionType():
+            raise NotImplementedError
+
+        case TypeVar(name=name):
+            return name
+
+        case GenericType(name=name, params=params):
+            return f"{name}[{', '.join(map(to_annotation, params))}]"
+
+        case AppliedType(name=name, args=args):
+            return f"{name}[{', '.join(map(to_annotation, args))}]"
+
+        case ConstraintType():
+            return str(type)
+
+        case _:
+            assert_never(type)
+
+
+@dataclass(frozen=True, kw_only=True)
+class Predicate:
+    type: Type
+    body: m.Expr
+    alias: bool
+
+
 Type = (
     TopType
     | BaseType
@@ -246,4 +341,5 @@ Type = (
     | TypeVar
     | GenericType
     | AppliedType
+    | ConstraintType
 )

midas/checker/unifier.py

@@ -0,0 +1,169 @@
+import logging
+from typing import Optional
+
+from midas.checker.registry import TypesRegistry
+from midas.checker.types import (
+    AppliedType,
+    Function,
+    GenericType,
+    TopType,
+    Type,
+    TypeVar,
+)
+
+
+class UnificationError(Exception): ...
+
+
+class Unifier:
+    def __init__(self, types: TypesRegistry) -> None:
+        self.types: TypesRegistry = types
+        self.logger: logging.Logger = logging.getLogger("Unifier")
+
+    def unify_call(
+        self,
+        type: GenericType,
+        positional: list[Type],
+        keywords: dict[str, Type],
+    ) -> Optional[Type]:
+        concrete_func: Function = Function(
+            pos_args=[
+                Function.Argument(
+                    pos=i,
+                    name=str(i),
+                    type=arg,
+                    required=True,
+                )
+                for i, arg in enumerate(positional)
+            ],
+            args=[],
+            kw_args=[
+                Function.Argument(
+                    pos=len(positional) + i,
+                    name=name,
+                    type=arg,
+                    required=True,
+                )
+                for i, (name, arg) in enumerate(keywords.items())
+            ],
+            returns=TopType(),  # TODO: use expected type
+        )
+        return self.unify_generic(type, concrete_func, match_return=False)
+
+    def unify_generic(
+        self,
+        template: GenericType,
+        concrete: Type,
+        match_return: bool = True,
+    ) -> Optional[Type]:
+        substitutions: dict[str, Type]
+        try:
+            substitutions = self.match(template.body, concrete, match_return)
+        except UnificationError:
+            return None
+
+        args: list[Type] = []
+        for param in template.params:
+            if param.name not in substitutions:
+                return None
+            args.append(substitutions[param.name])
+
+        applied: Type = self.types.apply_generic(template, args)
+        return applied
+
+    def match(
+        self,
+        template: Type,
+        concrete: Type,
+        match_return: bool = True,
+    ) -> dict[str, Type]:
+        # TODO: if concrete is Generic, record bound TypeVar. Then when merging
+        # substitutions, check that the constraint is respected
+        match (template, concrete):
+            case (TypeVar(name=name), _):
+                return {name: concrete}
+
+            case (
+                AppliedType(name=template_name, args=template_args),
+                AppliedType(name=concrete_name, args=concrete_args),
+            ) if template_name == concrete_name and len(template_args) == len(
+                concrete_args
+            ):
+                substitutions: dict[str, Type] = {}
+                for template_arg, concrete_arg in zip(template_args, concrete_args):
+                    new_substistutions: dict[str, Type] = self.match(
+                        template_arg, concrete_arg
+                    )
+                    substitutions = self.merge(substitutions, new_substistutions)
+
+                return substitutions
+
+            case (Function(), Function()):
+                mapped: list[tuple[Function.Argument, Function.Argument]] = (
+                    self.map_params(template, concrete)
+                )
+                substitutions: dict[str, Type] = {}
+                for template_arg, concrete_arg in mapped:
+                    arg_subs: dict[str, Type] = self.match(
+                        template_arg.type, concrete_arg.type
+                    )
+                    substitutions = self.merge(substitutions, arg_subs)
+
+                if match_return:
+                    return_subs: dict[str, Type] = self.match(
+                        template.returns, concrete.returns
+                    )
+                    substitutions = self.merge(substitutions, return_subs)
+
+                return substitutions
+
+            case _:
+                self.logger.debug(f"Can't match {concrete!r} with {template!r}")
+                return {}
+
+    def merge(self, subs1: dict[str, Type], subs2: dict[str, Type]) -> dict[str, Type]:
+        merged: dict[str, Type] = subs1.copy()
+
+        for k, v in subs2.items():
+            if k in merged and merged[k] != v:
+                self.logger.debug(
+                    f"Substitution already defined for {k} with type {merged[k]}, got {v}"
+                )
+                raise UnificationError
+            merged[k] = v
+        return merged
+
+    def map_params(
+        self, func1: Function, func2: Function
+    ) -> list[tuple[Function.Argument, Function.Argument]]:
+        pos1: list[Function.Argument] = func1.pos_args
+        mixed1: list[Function.Argument] = func1.args
+        kw1: list[Function.Argument] = func1.kw_args
+
+        pos2: list[Function.Argument] = func2.pos_args
+        mixed2: list[Function.Argument] = func2.args
+        kw2: list[Function.Argument] = func2.kw_args
+
+        mapped: list[tuple[Function.Argument, Function.Argument]] = []
+
+        by_pos2: dict[int, Function.Argument] = {arg.pos: arg for arg in pos2 + mixed2}
+        by_name2: dict[str, Function.Argument] = {arg.name: arg for arg in mixed2 + kw2}
+
+        for arg1 in pos1:
+            if (arg2 := by_pos2.get(arg1.pos)) is not None:
+                mapped.append((arg1, arg2))
+
+        for arg1 in mixed1:
+            # Match both positionally and by name, conflicts are caught
+            # when merging substitutions
+            if (arg2 := by_pos2.get(arg1.pos)) is not None:
+                mapped.append((arg1, arg2))
+
+            if (arg2 := by_name2.get(arg1.name)) is not None:
+                mapped.append((arg1, arg2))
+
+        for arg1 in kw1:
+            if (arg2 := by_name2.get(arg1.name)) is not None:
+                mapped.append((arg1, arg2))
+
+        return mapped

midas/checker/variance.py

@@ -0,0 +1,129 @@
+from typing import Literal, Optional, cast
+
+from midas.checker.registry import Member, TypesRegistry
+from midas.checker.types import (
+    AppliedType,
+    ConstraintType,
+    Function,
+    GenericType,
+    OverloadedFunction,
+    Type,
+    TypeVar,
+    Variance,
+)
+
+Polarity = Literal[-1, 0, 1]
+
+
+class Tracker:
+    def __init__(self, vars: list[TypeVar]) -> None:
+        self.vars: list[TypeVar] = vars
+        self.refs: dict[str, set[Polarity]] = {var.name: set() for var in self.vars}
+
+    def record(self, var: TypeVar, polarity: Polarity):
+        self.refs[var.name].add(polarity)
+
+    def get_updated_vars(self) -> list[TypeVar]:
+        return [
+            TypeVar(
+                name=var.name, bound=var.bound, variance=self.get_variance(var.name)
+            )
+            for var in self.vars
+        ]
+
+    def get_variance(self, name: str) -> Variance:
+        refs: set[Polarity] = self.refs[name]
+        if refs == {-1}:
+            return Variance.CONTRAVARIANT
+        if refs == {1}:
+            return Variance.COVARIANT
+        return Variance.INVARIANT
+
+    def __contains__(self, item: TypeVar | str):
+        if isinstance(item, TypeVar):
+            return item.name in self
+        return item in self.refs
+
+
+class VarianceInferrer:
+    def __init__(self, types: TypesRegistry) -> None:
+        self.types: TypesRegistry = types
+        self.tracker: Tracker = Tracker([])
+
+    def infer(self, type: GenericType) -> GenericType:
+        self.tracker = Tracker(type.params)
+
+        self.walk(type.body, 1, type.name)
+        members: dict[str, Member] = self.types._members.get(type.name, {})
+        for name, member in members.items():
+            self.walk(member.type, 1, type.name, [f"member:'{name}'"])
+
+        return GenericType(
+            name=type.name,
+            params=self.tracker.get_updated_vars(),
+            body=type.body,
+        )
+
+    def walk(
+        self,
+        type: Type,
+        polarity: Polarity,
+        base_name: str,
+        path: Optional[list[str]] = None,
+    ):
+        if path is None:
+            path = []
+
+        match type:
+            # Arguments are negative positions -> flip polarity
+            # Return is positive position -> keep polarity
+            case Function(pos_args=pos_args, args=mixed_args, kw_args=kw_args):
+                all_args: list[Function.Argument] = pos_args + mixed_args + kw_args
+                for arg in all_args:
+                    self.walk(
+                        arg.type,
+                        -polarity,
+                        base_name,
+                        path + [f"arg:'{arg.name}'"],
+                    )
+
+                self.walk(type.returns, polarity, base_name, path + ["return"])
+
+            # Walk all overloads
+            case OverloadedFunction(overloads=overloads):
+                for overload in overloads:
+                    self.walk(overload, polarity, base_name, path)
+
+            # If same name as root generic -> skip
+            # Get inferred variance of parameters and multiply with current
+            # polarity to recurse through arguments
+            case AppliedType(name=name, args=args):
+                # TODO: handle mutually recursive types
+                if name == base_name:
+                    return
+                generic: Type = self.types.get_type(name)
+                assert isinstance(generic, GenericType)
+                params: list[TypeVar] = generic.params
+                polarities: dict[Variance, Polarity] = {
+                    Variance.INVARIANT: 0,
+                    Variance.COVARIANT: 1,
+                    Variance.CONTRAVARIANT: -1,
+                }
+                for arg, param in zip(args, params):
+                    param_polarity: Polarity = polarities[param.variance]
+                    self.walk(
+                        arg,
+                        cast(Polarity, polarity * param_polarity),
+                        base_name,
+                        path + [f"applied:'{name}'"],
+                    )
+
+            # Walk base type
+            case ConstraintType(type=base):
+                self.walk(base, polarity, base_name, path + ["constraint"])
+
+            # Reached end
+            # If tracked, record polarity
+            case TypeVar():
+                if type in self.tracker:
+                    self.tracker.record(type, polarity)

midas/cli/commands/compile.py

@@ -19,9 +19,11 @@ from midas.utils import TypedAST
 @click.command(help="Compile source")
 @click.argument("file", type=click.File("r"))
 @click.option("-t", "--types", type=click.File("r"), multiple=True)
+@click.option("--ignore-errors", is_flag=True)
 def compile(
     file: TextIO,
     types: tuple[TextIO],
+    ignore_errors: bool,
 ):
     source: str = file.read()
     source_path: Path = Path(file.name).resolve()
@@ -35,8 +37,10 @@ def compile(
     printer = DiagnosticPrinter()
     printer.print_all(diagnostics)
 
-    if any(map(lambda d: d.type == DiagnosticType.ERROR, diagnostics)):
+    if not ignore_errors and any(
+        map(lambda d: d.type == DiagnosticType.ERROR, diagnostics)
+    ):
         sys.exit(1)
 
-    generator = Generator(workdir=source_path.parent)
+    generator = Generator(workdir=source_path.parent, types=checker.types)
     generator.generate(typed_ast, source_path)

midas/cli/commands/registry.py

@@ -8,7 +8,9 @@ from typing import TextIO
 
 import click
 
+from midas.ast.printer import MidasPrinter
 from midas.checker.checker import TypeChecker
+from midas.checker.registry import Member
 from midas.checker.types import AliasType, AppliedType, BaseType, GenericType, Type
 
 
@@ -35,10 +37,30 @@ def dump_registry(
     for types_file in types:
         checker.import_midas(Path(types_file.name).resolve())
 
+    print("##### Types #####")
     for name, type in checker.types._types.items():
-        members: dict[str, Type] = checker.types._members.get(name, {})
-        print(f"{name} = {base_type(type)}")
+        members: dict[str, Member] = checker.types._members.get(name, {})
+        params: str = ""
+        if isinstance(type, GenericType):
+            params = ", ".join(map(str, type.params))
+            params = f"[{params}]"
+        print(f"{name}{params} = {base_type(type)}")
         if len(members) != 0:
             print(" " * 4 + "Members:")
-            for member_name, member_type in members.items():
-                print(" " * 8 + f"{member_name}: {member_type}")
+            for member_name, member in members.items():
+                kind: str = member.kind.name
+                print(" " * 8 + f"({kind:8}) {member_name}: {member.type}")
+
+    print("##### Predicates #####")
+    printer = MidasPrinter()
+    for name, predicate in checker.types._predicates.items():
+        body: str = printer.print(predicate.body)
+        if predicate.alias:
+            print(f"{name}: {predicate.type} = {body}")
+        else:
+            print(f"{name}{predicate.type}:")
+            body = "\n".join(
+                "    " + ("return " if i == 0 else "") + line
+                for i, line in enumerate(body.split("\n"))
+            )
+            print(body)

midas/cli/commands/stubs.py

@@ -1,27 +1,64 @@
 import ast
+import time
 from pathlib import Path
 from typing import TextIO
 
+import black
 import click
+from watchdog.events import DirModifiedEvent, FileModifiedEvent, FileSystemEventHandler
+from watchdog.observers import Observer
 
 from midas.checker.checker import TypeChecker
 from midas.generator.stubs import StubsGenerator
 
 
-@click.command(help="Generate stubs from Midas definitions")
-@click.argument("file", type=click.File("r"))
-@click.option("-o", "--output", type=click.File("w"), default="-")
-def stubs(
-    file: TextIO,
-    output: TextIO,
-):
-    source_path: Path = Path(file.name).resolve()
-
+def generate_stubs(in_path: Path, out_path: Path):
     checker = TypeChecker()
-    checker.import_midas(source_path)
+    checker.import_midas(in_path)
 
     generator = StubsGenerator(checker.types)
     module: ast.Module = generator.generate_stubs()
     module = ast.fix_missing_locations(module)
 
-    output.write(ast.unparse(module))
+    output: str = ast.unparse(module)
+    output = black.format_str(output, mode=black.Mode(is_pyi=True))
+
+    out_path.write_text(output)
+
+
+class Handler(FileSystemEventHandler):
+    def __init__(self, in_path: Path, out_path: Path) -> None:
+        super().__init__()
+        self.in_path: Path = in_path
+        self.out_path: Path = out_path
+
+    def on_modified(self, event: DirModifiedEvent | FileModifiedEvent) -> None:
+        generate_stubs(self.in_path, self.out_path)
+
+
+@click.command(help="Generate stubs from Midas definitions")
+@click.argument("file", type=click.File("r"))
+@click.option("-o", "--output", type=click.File("w"), default="-")
+@click.option("-w", "--watch", is_flag=True)
+def stubs(
+    file: TextIO,
+    output: TextIO,
+    watch: bool,
+):
+    source_path: Path = Path(file.name).resolve()
+    out_path: Path = Path(output.name).resolve()
+    generate_stubs(source_path, out_path)
+
+    if watch:
+        print(f"Watching {source_path}...")
+        print("Press CTRL+C to stop")
+        handler = Handler(source_path, out_path)
+        observer = Observer()
+        observer.schedule(handler, str(source_path))
+        observer.start()
+        try:
+            while True:
+                time.sleep(1)
+        except KeyboardInterrupt:
+            observer.stop()
+        observer.join()

midas/cli/commands/types.py

@@ -41,6 +41,7 @@ def types(
                 message=f"Type: {type}",
             )
         )
+    diagnostics.extend(checker.diagnostics)
     printer = DiagnosticPrinter()
     printer.print_all(diagnostics)
 

midas/cli/highlighter.py

@@ -228,6 +228,13 @@ class PythonHighlighter(
         for item in expr.items:
             item.accept(self)
 
+    def visit_dict_expr(self, expr: p.DictExpr) -> None:
+        for key in expr.keys:
+            if key is not None:
+                key.accept(self)
+        for value in expr.values:
+            value.accept(self)
+
     def visit_subscript_expr(self, expr: p.SubscriptExpr) -> None:
         expr.object.accept(self)
         expr.index.accept(self)
@@ -240,6 +247,10 @@ class PythonHighlighter(
         if expr.step is not None:
             expr.step.accept(self)
 
+    def visit_raw_expr(self, expr: p.RawExpr) -> None: ...
+
+    def visit_raw_stmt(self, stmt: p.RawStmt) -> None: ...
+
 
 class MidasHighlighter(
     Highlighter, m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[None]
@@ -266,8 +277,9 @@ class MidasHighlighter(
     def visit_predicate_stmt(self, stmt: m.PredicateStmt) -> None:
         self.wrap(stmt, "predicate")
         self.wrap(LocatableToken(stmt.name), "predicate-name")
-        stmt.type.accept(self)
-        stmt.condition.accept(self)
+        for spec in stmt.params:
+            self._visit_param_spec(spec)
+        stmt.body.accept(self)
 
     def visit_logical_expr(self, expr: m.LogicalExpr) -> None:
         self.wrap(expr, "logical-expr")
@@ -283,6 +295,14 @@ class MidasHighlighter(
         self.wrap(expr, "unary-expr")
         expr.right.accept(self)
 
+    def visit_call_expr(self, expr: m.CallExpr) -> None:
+        self.wrap(expr, "call-expr")
+        expr.callee.accept(self)
+        for arg in expr.arguments:
+            arg.accept(self)
+        for arg in expr.keywords.values():
+            arg.accept(self)
+
     def visit_get_expr(self, expr: m.GetExpr) -> None:
         self.wrap(expr, "get-expr")
         expr.expr.accept(self)
@@ -318,8 +338,7 @@ class MidasHighlighter(
 
     def visit_function_type(self, type: m.FunctionType) -> None:
         self.wrap(type, "function")
-        for arg in type.pos_args + type.args + type.kw_args:
-            arg.type.accept(self)
+        self._visit_param_spec(type.params)
         type.returns.accept(self)
 
     def visit_extension_type(self, type: m.ExtensionType) -> None:
@@ -327,6 +346,10 @@ class MidasHighlighter(
         type.base.accept(self)
         type.extension.accept(self)
 
+    def _visit_param_spec(self, spec: m.ParamSpec) -> None:
+        for param in spec.pos + spec.mixed + spec.kw:
+            param.type.accept(self)
+
 
 class DiagnosticsHighlighter(Highlighter):
     EXTRA_CSS_PATH: Optional[Path] = Path(__file__).parent / "hl_diagnostic.css"

midas/cli/utils.py

@@ -1,3 +1,4 @@
+from collections import defaultdict
 from pathlib import Path
 from typing import Optional
 
@@ -7,6 +8,13 @@ from midas.cli.ansi import Ansi
 
 
 class DiagnosticPrinter:
+    COLORS: dict[DiagnosticType, int] = {
+        DiagnosticType.ERROR: Ansi.RED,
+        DiagnosticType.WARNING: Ansi.YELLOW,
+        DiagnosticType.INFO: Ansi.CYAN,
+        DiagnosticType.DEBUG: Ansi.MAGENTA,
+    }
+
     def __init__(self) -> None:
         self.files: dict[Optional[str], list[str]] = {}
 
@@ -22,10 +30,25 @@ class DiagnosticPrinter:
         return self.files[filename]
 
     def print_all(self, diagnostics: list[Diagnostic], indent: int = 4):
+        by_type: dict[DiagnosticType, int] = defaultdict(int)
         for diagnostic in diagnostics:
             filename: Optional[str] = diagnostic.file_path
             lines = self.get_lines(filename)
             self.print(lines, diagnostic, indent=indent)
+            by_type[diagnostic.type] += 1
+
+        if len(diagnostics) == 0:
+            return
+
+        counts: list[str] = []
+        for type in DiagnosticType:
+            if type not in by_type:
+                continue
+            count: int = by_type[type]
+            color: int = self.COLORS.get(type, Ansi.WHITE)
+            counts.append(f"{Ansi.FG(color)}{type.value}s{Ansi.RESET}: {count}")
+
+        print("    ".join(counts))
 
     def print(self, lines: list[str], diagnostic: Diagnostic, indent: int = 4):
         """Pretty-print a diagnostic, showing some context if possible
@@ -55,11 +78,7 @@ class DiagnosticPrinter:
         before: str = line[:start_offset]
         after: str = line[end_offset:]
 
-        color: int = {
-            DiagnosticType.ERROR: Ansi.RED,
-            DiagnosticType.WARNING: Ansi.YELLOW,
-            DiagnosticType.INFO: Ansi.CYAN,
-        }.get(diagnostic.type, Ansi.WHITE)
+        color: int = self.COLORS.get(diagnostic.type, Ansi.WHITE)
 
         subject: str = Ansi.FG(color) + line[start_offset:end_offset] + Ansi.RESET
         cursor: str = (

midas/generator/constraints.py

@@ -0,0 +1,224 @@
+import ast
+from typing import Optional
+
+import midas.ast.midas as m
+from midas.checker.registry import TypesRegistry
+from midas.checker.types import (
+    Function,
+    Predicate,
+    Type,
+    to_annotation,
+)
+from midas.lexer.token import TokenType
+
+LOGICAL_OPERATORS: dict[TokenType, type[ast.boolop]] = {
+    TokenType.AND: ast.And,
+    # TokenType.OR: ast.Or,
+}
+
+BINARY_OPERATORS: dict[TokenType, type[ast.operator]] = {
+    # TokenType.PLUS: ast.Add,
+    TokenType.MINUS: ast.Sub,
+    TokenType.STAR: ast.Mult,
+    TokenType.SLASH: ast.Div,
+}
+
+UNARY_OPERATORS: dict[TokenType, type[ast.unaryop]] = {
+    # TokenType.PLUS: ast.UAdd,
+    TokenType.MINUS: ast.USub,
+}
+
+COMPARISON_OPERATORS: dict[TokenType, type[ast.cmpop]] = {
+    TokenType.GREATER: ast.Gt,
+    TokenType.GREATER_EQUAL: ast.GtE,
+    TokenType.LESS: ast.Lt,
+    TokenType.LESS_EQUAL: ast.LtE,
+    TokenType.EQUAL_EQUAL: ast.Eq,
+    TokenType.BANG_EQUAL: ast.NotEq,
+}
+
+
+class ConstraintGenerator(m.Expr.Visitor[ast.expr]):
+    def __init__(self, types: TypesRegistry):
+        self.types: TypesRegistry = types
+        self._id: int = 0
+        self._definitions: list[ast.stmt] = []
+        self._aliases: dict[str, str] = {}
+
+    def get_definitions(self) -> list[ast.stmt]:
+        return self._definitions
+
+    def generate(self, expr: m.Expr) -> ast.expr:
+        match expr:
+            case m.VariableExpr():
+                return expr.accept(self)
+            case _:
+                func = Function(
+                    pos_args=[],
+                    args=[
+                        Function.Argument(
+                            pos=0,
+                            name="_",
+                            type=self.types.get_type("Any"),
+                            required=True,
+                        )
+                    ],
+                    kw_args=[],
+                    returns=self.types.get_type("bool"),
+                )
+                alias: str = self.make_alias(None)
+                definition: ast.stmt = self.make_definition(
+                    alias, Predicate(type=func, body=expr, alias=False)
+                )
+                self._definitions.append(definition)
+                return ast.Name(id=alias)
+
+    def make_alias(self, name: Optional[str]) -> str:
+        suffix: str
+        if name is None:
+            suffix = f"p{self._id}"
+            self._id += 1
+        else:
+            suffix = name
+        alias: str = f"__midas_{suffix}__"
+        return alias
+
+    def make_definition(self, name: str, predicate: Predicate) -> ast.stmt:
+        body: ast.expr = predicate.body.accept(self)
+        if predicate.alias:
+            return ast.Assign(
+                targets=[
+                    ast.Name(id=name),
+                ],
+                value=body,
+            )
+        return self.make_func(name, [ast.Return(value=body)], predicate.type)
+
+    def make_args(self, func: Function) -> ast.arguments:
+        return ast.arguments(
+            posonlyargs=[
+                ast.arg(
+                    arg=arg.name,
+                    annotation=ast.Constant(value=to_annotation(arg.type)),
+                )
+                for arg in func.pos_args
+            ],
+            args=[
+                ast.arg(
+                    arg=arg.name,
+                    annotation=ast.Constant(value=to_annotation(arg.type)),
+                )
+                for arg in func.args
+            ],
+            kwonlyargs=[
+                ast.arg(
+                    arg=arg.name,
+                    annotation=ast.Constant(value=to_annotation(arg.type)),
+                )
+                for arg in func.kw_args
+            ],
+            defaults=[],
+            kw_defaults=[],
+        )
+
+    def make_func(
+        self, name: str, inner_body: list[ast.stmt], type: Type, level: int = 0
+    ) -> ast.stmt:
+        match type:
+            case Function(returns=Function()):
+                inner_name: str = f"inner{level}"
+                return ast.FunctionDef(
+                    name=name,
+                    args=self.make_args(type),
+                    body=[
+                        self.make_func(inner_name, inner_body, type.returns, level + 1),
+                        ast.Return(value=ast.Name(id=inner_name)),
+                    ],
+                    returns=ast.Constant(value=to_annotation(type.returns)),
+                    decorator_list=[],
+                )
+
+            case Function():
+                return ast.FunctionDef(
+                    name=name,
+                    args=self.make_args(type),
+                    body=inner_body,
+                    returns=ast.Constant(value=to_annotation(type.returns)),
+                    decorator_list=[],
+                )
+
+            case _:
+                raise ValueError(f"Expected function, got {type!r}")
+
+    def get_predicate(self, name: str) -> Optional[ast.expr]:
+        if name not in self._aliases:
+            predicate: Optional[Predicate] = self.types.lookup_predicate(name)
+            if predicate is None:
+                return None
+            alias: str = self.make_alias(name)
+            self._aliases[name] = alias
+            self._definitions.append(self.make_definition(alias, predicate))
+
+        return ast.Name(id=self._aliases[name])
+
+    def visit_logical_expr(self, expr: m.LogicalExpr) -> ast.expr:
+        return ast.BoolOp(
+            op=LOGICAL_OPERATORS[expr.operator.type](),
+            values=[
+                expr.left.accept(self),
+                expr.right.accept(self),
+            ],
+        )
+
+    def visit_binary_expr(self, expr: m.BinaryExpr) -> ast.expr:
+        op: TokenType = expr.operator.type
+        if op in BINARY_OPERATORS:
+            return ast.BinOp(
+                left=expr.left.accept(self),
+                op=BINARY_OPERATORS[op](),
+                right=expr.right.accept(self),
+            )
+        if op in COMPARISON_OPERATORS:
+            return ast.Compare(
+                left=expr.left.accept(self),
+                ops=[COMPARISON_OPERATORS[op]()],
+                comparators=[expr.right.accept(self)],
+            )
+        raise ValueError(f"Unexpected binary operator {op}")
+
+    def visit_unary_expr(self, expr: m.UnaryExpr) -> ast.expr:
+        return ast.UnaryOp(
+            op=UNARY_OPERATORS[expr.operator.type](),
+            operand=expr.right.accept(self),
+        )
+
+    def visit_call_expr(self, expr: m.CallExpr) -> ast.expr:
+        return ast.Call(
+            func=expr.callee.accept(self),
+            args=[arg.accept(self) for arg in expr.arguments],
+            keywords=[
+                ast.keyword(arg=name, value=arg.accept(self))
+                for name, arg in expr.keywords.items()
+            ],
+        )
+
+    def visit_get_expr(self, expr: m.GetExpr) -> ast.expr:
+        return ast.Attribute(
+            value=expr.expr.accept(self),
+            attr=expr.name.lexeme,
+        )
+
+    def visit_variable_expr(self, expr: m.VariableExpr) -> ast.expr:
+        name: str = expr.name.lexeme
+        if (p := self.get_predicate(name)) is not None:
+            return p
+        return ast.Name(id=name)
+
+    def visit_grouping_expr(self, expr: m.GroupingExpr) -> ast.expr:
+        return expr.accept(self)
+
+    def visit_literal_expr(self, expr: m.LiteralExpr) -> ast.expr:
+        return ast.Constant(value=expr.value)
+
+    def visit_wildcard_expr(self, expr: m.WildcardExpr) -> ast.expr:
+        return ast.Name(id="_")

midas/generator/generator.py

@@ -2,15 +2,19 @@ import ast
 import shutil
 from dataclasses import dataclass, field
 from pathlib import Path
-from typing import Optional
+from typing import Optional, assert_never
 
+import midas.ast.midas as m
 import midas.ast.python as p
 from midas.ast.location import Location
+from midas.ast.printer import MidasPrinter
+from midas.checker.registry import TypesRegistry
 from midas.checker.types import (
     AliasType,
     AppliedType,
     BaseType,
     ComplexType,
+    ConstraintType,
     ExtensionType,
     Function,
     GenericType,
@@ -19,7 +23,9 @@ from midas.checker.types import (
     Type,
     TypeVar,
     UnitType,
+    UnknownType,
 )
+from midas.generator.constraints import ConstraintGenerator
 from midas.utils import TypedAST
 
 
@@ -30,26 +36,29 @@ class Scope:
 
 
 class Generator(p.Stmt.Visitor[ast.stmt], p.Expr.Visitor[ast.expr]):
-    def __init__(self, workdir: Path) -> None:
+    def __init__(self, workdir: Path, types: TypesRegistry) -> None:
         self.workdir: Path = workdir.resolve()
         self.build_dir: Path = self.workdir / "build" / "midas"
-        if self.build_dir.exists():
-            shutil.rmtree(self.build_dir)
-        self.build_dir.mkdir(parents=True, exist_ok=True)
         self.rel_src_path: Path = Path()
 
         self._typed_ast: TypedAST = TypedAST(
             stmts=[],
             judgements=[],
+            evaluated_casts=[],
         )
         self._alias_count: int = 0
+        self._predicate_count: int = 0
         self._scopes: list[Scope] = []
 
+        self._constraint_generator: ConstraintGenerator = ConstraintGenerator(types)
+        self._constraints: list[tuple[m.Expr, ast.expr]] = []
+
     def generate_ast(self, typed_ast: TypedAST, src_path: Path) -> ast.AST:
-        self.rel_src_path = src_path.relative_to(self.workdir)
+        self.rel_src_path = src_path.resolve().relative_to(self.workdir)
         self._typed_ast = typed_ast
         body: list[ast.stmt] = self._visit_body(typed_ast.stmts)
-        module = ast.Module(body=body, type_ignores=[])
+        predicates: list[ast.stmt] = self._constraint_generator.get_definitions()
+        module = ast.Module(body=predicates + body, type_ignores=[])
         module = ast.fix_missing_locations(module)
         return module
 
@@ -59,6 +68,9 @@ class Generator(p.Stmt.Visitor[ast.stmt], p.Expr.Visitor[ast.expr]):
         module: ast.AST = self.generate_ast(typed_ast, src_path)
         compiled: str = ast.unparse(module)
         if out_path is None:
+            if self.build_dir.exists():
+                shutil.rmtree(self.build_dir)
+            self.build_dir.mkdir(parents=True, exist_ok=True)
             out_path = (self.build_dir / self.rel_src_path).resolve()
             try:
                 _ = out_path.relative_to(self.build_dir)
@@ -120,6 +132,10 @@ class Generator(p.Stmt.Visitor[ast.stmt], p.Expr.Visitor[ast.expr]):
 
     def visit_cast_expr(self, expr: p.CastExpr) -> ast.expr:
         expr2: ast.expr = expr.expr.accept(self)
+
+        if expr in self._typed_ast.evaluated_casts or expr.unsafe:
+            return expr2
+
         alias: ast.expr = self._make_alias(expr2)
 
         type: Type = self._get_expr_type(expr)
@@ -246,7 +262,7 @@ class Generator(p.Stmt.Visitor[ast.stmt], p.Expr.Visitor[ast.expr]):
         return generated
 
     def _make_alias(self, expr: ast.expr) -> ast.expr:
-        name: str = f"__midas_alias_{self._alias_count}__"
+        name: str = f"__midas_a{self._alias_count}__"
         alias = ast.Name(id=name)
         self._alias_count += 1
         self._scopes[-1].aliases.append(name)
@@ -276,6 +292,9 @@ class Generator(p.Stmt.Visitor[ast.stmt], p.Expr.Visitor[ast.expr]):
 
     def _make_cast_asserts(self, src_location: Location, expr: ast.expr, type: Type):
         match type:
+            case UnknownType():
+                pass
+
             case BaseType(name=name):
                 self._add_assert(
                     ast.Call(
@@ -301,8 +320,17 @@ class Generator(p.Stmt.Visitor[ast.stmt], p.Expr.Visitor[ast.expr]):
                     self._make_cast_assert_message(src_location, expr, type),
                 )
 
-            case AppliedType():
-                self._make_cast_asserts(src_location, expr, type.body)
+            case AppliedType(body=body):
+                self._make_cast_asserts(src_location, expr, body)
+
+            case ConstraintType(type=base, constraint=constraint):
+                self._make_cast_asserts(src_location, expr, base)
+                self._make_constraint_assert(src_location, expr, constraint)
+
+            case TypeVar(bound=bound):
+                # TODO: check with type from arguments / use call-site context
+                if bound is not None:
+                    self._make_cast_asserts(src_location, expr, bound)
 
             case (
                 TopType()
@@ -314,8 +342,9 @@ class Generator(p.Stmt.Visitor[ast.stmt], p.Expr.Visitor[ast.expr]):
             ):
                 raise NotImplementedError(f"Can't make assertion for type {type}")
 
-            case TypeVar():
-                raise RuntimeError("Unexpected TypeVar")
+            # Ensure exhaustiveness
+            case _:
+                assert_never(type)
 
     def _make_cast_assert_message(
         self, location: Location, expr: ast.expr, type: Type
@@ -339,3 +368,36 @@ class Generator(p.Stmt.Visitor[ast.stmt], p.Expr.Visitor[ast.expr]):
                 ast.Constant(f" to {type}"),
             ]
         )
+
+    def _make_constraint_assert(
+        self, src_location: Location, expr: ast.expr, constraint: m.Expr
+    ):
+        test_func: ast.expr = self._get_constraint(constraint)
+        self._add_assert(
+            ast.Call(
+                func=test_func,
+                args=[expr],
+                keywords=[],
+            ),
+            self._make_constraint_assert_message(src_location, expr, constraint),
+        )
+
+    def _make_constraint_assert_message(
+        self, location: Location, expr: ast.expr, constraint: m.Expr
+    ) -> ast.expr:
+        printer = MidasPrinter()
+        constraint_str: str = printer.print(constraint)
+        loc_str: str = f"{self.rel_src_path}:L{location.lineno}:{location.col_offset+1}"
+        # f"file.py:L1:1: ConstraintError: Value does not fit constraint 'v > 0'"
+        return ast.Constant(
+            f"{loc_str}: ConstraintError: Value does not fit constraint '{constraint_str}'"
+        )
+
+    def _get_constraint(self, expr: m.Expr) -> ast.expr:
+        for expr2, constraint in self._constraints:
+            if expr2 == expr:
+                return constraint
+
+        constraint: ast.expr = self._constraint_generator.generate(expr)
+        self._constraints.append((expr, constraint))
+        return constraint

midas/generator/stubs.py

@@ -1,5 +1,5 @@
 import ast
-from typing import Optional
+from typing import Optional, assert_never
 
 import midas.ast.midas as m
 from midas.checker.registry import Member, TypesRegistry
@@ -8,6 +8,7 @@ from midas.checker.types import (
     AppliedType,
     BaseType,
     ComplexType,
+    ConstraintType,
     ExtensionType,
     Function,
     GenericType,
@@ -17,6 +18,7 @@ from midas.checker.types import (
     TypeVar,
     UnitType,
     UnknownType,
+    Variance,
     substitute_typevars,
 )
 
@@ -37,6 +39,18 @@ class StubsGenerator:
         self.stubs = []
         self.typing_imports = set()
         for name, type in self.types._types.items():
+            # Skip builtin types, not just based on name so the user can override
+            # TODO: check if added members on builtin type
+            match type:
+                case BaseType(name=name_) if name == name_:
+                    continue
+                case GenericType(
+                    name=name1,
+                    body=BaseType(name=name2),
+                ) if (
+                    name == name1 == name2
+                ):
+                    continue
             self.generate_stub(name, type)
 
         imports = [
@@ -84,6 +98,7 @@ class StubsGenerator:
         match type:
             case AliasType(type=base):
                 return [self.dump_type(base)], {}
+
             case GenericType(params=params, body=body):
                 self.add_typing_import("Generic")
                 type_vars: ast.expr
@@ -111,6 +126,13 @@ class StubsGenerator:
                     ],
                     body_subsitutions | substitutions,
                 )
+
+            case ConstraintType(type=base):
+                return self.get_bases(base)
+
+            case TypeVar(bound=bound) if bound is not None:
+                return [self.dump_type(bound)], {}
+
             case _:
                 return [], {}
 
@@ -148,15 +170,20 @@ class StubsGenerator:
             case TopType() | UnknownType():
                 self.add_typing_import("Any")
                 return ast.Name(id="Any")
+
             case BaseType(name=name):
                 return ast.Name(id=name)
+
             case AliasType(name=name):
                 return ast.Name(id=name)
+
             case UnitType():
                 return ast.Constant(value=None)
+
             case Function():
                 name: str = self.define_protocol(type)
                 return ast.Name(id=name)
+
             case OverloadedFunction(overloads=overloads):
                 if len(overloads) == 1:
                     return self.dump_type(overloads[0])
@@ -176,6 +203,7 @@ class StubsGenerator:
 
             case TypeVar():
                 return ast.Name(id=type.name)
+
             case GenericType(name=name):
                 params: ast.expr
                 if len(type.params) == 1:
@@ -188,6 +216,7 @@ class StubsGenerator:
                     value=ast.Name(id=type.name),
                     slice=params,
                 )
+
             case AppliedType():
                 args: ast.expr
                 if len(type.args) == 1:
@@ -199,6 +228,12 @@ class StubsGenerator:
                     slice=args,
                 )
 
+            case ConstraintType():
+                return self.dump_type(type.type)
+
+            case _:
+                assert_never(type)
+
     def dump_method(
         self, name: str, method: Type, overloaded: bool = False
     ) -> list[ast.stmt]:
@@ -313,6 +348,29 @@ class StubsGenerator:
     def define_type_var(self, var: TypeVar) -> TypeVar:
         name: str = self.new_type_var_name()
         self.add_typing_import("TypeVar")
+
+        kwargs: list[ast.keyword] = []
+        if var.bound is not None:
+            kwargs.append(
+                ast.keyword(
+                    arg="bound",
+                    value=self.dump_type(var.bound),
+                )
+            )
+        if var.variance == Variance.COVARIANT:
+            kwargs.append(
+                ast.keyword(
+                    arg="covariant",
+                    value=ast.Constant(value=True),
+                )
+            )
+        elif var.variance == Variance.CONTRAVARIANT:
+            kwargs.append(
+                ast.keyword(
+                    arg="contravariant",
+                    value=ast.Constant(value=True),
+                )
+            )
         self.add_stub(
             ast.Assign(
                 targets=[ast.Name(id=name)],
@@ -321,16 +379,7 @@ class StubsGenerator:
                     args=[
                         ast.Constant(value=name),
                     ],
-                    keywords=(
-                        []
-                        if var.bound is None
-                        else [
-                            ast.keyword(
-                                arg="bound",
-                                value=self.dump_type(var.bound),
-                            )
-                        ]
-                    ),
+                    keywords=kwargs,
                 ),
             )
         )

midas/lexer/midas.py

@@ -69,6 +69,8 @@ class MidasLexer(Lexer):
                 ):
                     self.advance()
                 self.add_token(TokenType.WHITESPACE)
+            case '"' | "'":
+                self.scan_string(char)
             case _:
                 if char.isdigit():
                     self.scan_number()
@@ -78,6 +80,17 @@ class MidasLexer(Lexer):
                     self.error("Unexpected character")
         return None
 
+    def scan_string(self, opening: str):
+        while self.peek() != opening and not self.is_at_end():
+            self.advance()
+
+        if self.is_at_end():
+            self.error("Unterminated string")
+
+        self.advance()
+        value: str = self.source[self.start + 1 : self.idx - 1]
+        self.add_token(TokenType.STRING, value)
+
     def scan_number(self):
         """Scan the rest of number and add it as a token
 

midas/lexer/token.py

@@ -43,6 +43,7 @@ class TokenType(Enum):
     TRUE = auto()
     FALSE = auto()
     NONE = auto()
+    STRING = auto()
 
     # Keywords
     TYPE = auto()

midas/parser/midas.py

@@ -3,6 +3,7 @@ from typing import Optional
 from midas.ast.location import Location
 from midas.ast.midas import (
     BinaryExpr,
+    CallExpr,
     ComplexType,
     ConstraintType,
     Expr,
@@ -17,6 +18,7 @@ from midas.ast.midas import (
     MemberKind,
     MemberStmt,
     NamedType,
+    ParamSpec,
     PredicateStmt,
     Stmt,
     Type,
@@ -265,6 +267,9 @@ class MidasParser(Parser):
         Returns:
             Expr: the parsed constraint expression
         """
+        return self.expression()
+
+    def expression(self) -> Expr:
         return self.and_()
 
     def and_(self) -> Expr:
@@ -331,7 +336,55 @@ class MidasParser(Parser):
             right: Expr = self.unary()
             location: Location = Location.span(operator.get_location(), right.location)
             return UnaryExpr(location=location, operator=operator, right=right)
-        return self.reference()
+        return self.call()
+
+    def call(self) -> Expr:
+        expr: Expr = self.reference()
+        while self.match(TokenType.LEFT_PAREN):
+            expr = self.finish_call(expr)
+        return expr
+
+    def finish_call(self, callee: Expr) -> Expr:
+        pos_args: list[Expr] = []
+        kw_args: dict[str, Expr] = {}
+        keywords: bool = False
+        while not self.match(TokenType.RIGHT_PAREN):
+            if self.check_identifier() and self.check_next(TokenType.EQUAL):
+                keywords = True
+                keyword: Token = self.advance()
+                self.advance()
+                value: Expr = self.expression()
+                name: str = keyword.lexeme
+                if name in kw_args:
+                    self.error(
+                        self.peek(),
+                        f"Multiple values passed for '{name}', only the last occurrence will be used",
+                    )
+                kw_args[name] = value
+            else:
+                value = self.expression()
+                if self.check(TokenType.EQUAL):
+                    if keywords:
+                        raise self.error(self.peek(), "Invalid keyword argument name")
+                    else:
+                        raise self.error(
+                            self.peek(),
+                            "Cannot pass positional arguments after a keyword argument",
+                        )
+                pos_args.append(value)
+
+            if not self.match(TokenType.COMMA):
+                break
+
+        r_paren: Token = self.consume(
+            TokenType.RIGHT_PAREN, "Expected ')' after arguments."
+        )
+        return CallExpr(
+            location=Location.span(callee.location, r_paren.get_location()),
+            callee=callee,
+            arguments=pos_args,
+            keywords=kw_args,
+        )
 
     def reference(self) -> Expr:
         """Parse an attribute access expression or a simpler expression
@@ -365,6 +418,9 @@ class MidasParser(Parser):
         if self.match(TokenType.NUMBER):
             return LiteralExpr(location=token.get_location(), value=token.value)
 
+        if self.match(TokenType.STRING):
+            return LiteralExpr(location=token.get_location(), value=token.value)
+
         if self.match_identifier():
             return VariableExpr(location=token.get_location(), name=token)
 
@@ -453,23 +509,35 @@ class MidasParser(Parser):
             PredicateStmt: the parsed predicate declaration statement
         """
         keyword: Token = self.previous()
+
         name: Token = self.consume_identifier("Expected predicate name")
-        self.consume(TokenType.LEFT_PAREN, "Expected '(' before predicate subject")
-        subject: Token = self.consume_identifier("Expected subject name")
-        self.consume(TokenType.COLON, "Expected ':' after subject name")
-        type: Type = self.type_expr()
-        self.consume(TokenType.RIGHT_PAREN, "Expected ')' after predicate subject")
+
+        params: list[ParamSpec] = []
+        while self.check(TokenType.LEFT_PAREN):
+            params.append(self.function_args())
+
         self.consume(TokenType.EQUAL, "Expected '=' after predicate subject")
-        condition: Expr = self.constraint()
+        body: Expr = self.constraint()
         return PredicateStmt(
             location=keyword.location_to(self.previous()),
             name=name,
-            subject=subject,
-            type=type,
-            condition=condition,
+            params=params,
+            body=body,
         )
 
     def function(self) -> FunctionType:
+        params: ParamSpec = self.function_args()
+
+        self.consume(TokenType.ARROW, "Expected '->' before result type")
+        result: Type = self.type_expr()
+
+        return FunctionType(
+            location=params.l_paren.location_to(self.previous()),
+            params=params,
+            returns=result,
+        )
+
+    def function_args(self) -> ParamSpec:
         l_paren: Token = self.consume(
             TokenType.LEFT_PAREN, "Expected '(' before function parameters"
         )
@@ -526,14 +594,4 @@ class MidasParser(Parser):
                 self.error(token, "Unnamed mixed argument")
 
         self.consume(TokenType.RIGHT_PAREN, "Expected ')' after function parameters")
-
-        self.consume(TokenType.ARROW, "Expected '->' before result type")
-        result: Type = self.type_expr()
-
-        return FunctionType(
-            location=l_paren.location_to(self.previous()),
-            pos_args=pos_args,
-            args=args,
-            kw_args=kw_args,
-            returns=result,
-        )
+        return ParamSpec(l_paren=l_paren, pos=pos_args, mixed=args, kw=kw_args)

midas/parser/python.py

@@ -49,6 +49,7 @@ class UnsupportedSyntaxError(Exception):
 
 class PythonParser:
     CAST_FUNCTION = "cast"
+    UNSAFE_CAST_FUNCTION = "unsafe_cast"
 
     def parse_module(self, node: ast.Module) -> list[Stmt]:
         statements: list[Stmt] = []
@@ -423,6 +424,9 @@ class PythonParser:
             case ast.Call(func=ast.Name(id=self.CAST_FUNCTION)):
                 return self.parse_cast(node)
 
+            case ast.Call(func=ast.Name(id=self.UNSAFE_CAST_FUNCTION)):
+                return self.parse_cast(node)
+
             case ast.Call():
                 return self.parse_call(node)
 
@@ -527,16 +531,19 @@ class PythonParser:
         return expr
 
     def parse_cast(self, node: ast.Call) -> CastExpr:
+        assert isinstance(node.func, ast.Name)
+        func: str = node.func.id
         match node:
             case ast.Call(args=[type, expr], keywords=[]):
                 return CastExpr(
                     location=Location.from_ast(node),
                     type=self._parse_type(type),
                     expr=self.parse_expr(expr),
+                    unsafe=func == self.UNSAFE_CAST_FUNCTION,
                 )
             case _:
                 raise InvalidSyntaxError(
-                    f"Invalid call to {self.CAST_FUNCTION}, expected type and expression"
+                    f"Invalid call to {func}, expected type and expression"
                 )
 
     def parse_call(self, node: ast.Call) -> CallExpr:

midas/typing.py

@@ -0,0 +1,34 @@
+from typing import cast as typing_cast
+
+cast = typing_cast
+"""### Midas documentation
+Cast a value to a type.
+
+- **Compile-time**: tells the type checker that the return value has the designated type.
+- **Run-time**: generates assertions to ensure the value can be interpreted as the given type.
+
+---
+<br>
+<br>
+<br>
+
+_**Internal Python documentation**_
+"""
+
+
+unsafe_cast = typing_cast
+"""### Midas documentation
+Cast a value to a type.
+
+- **Compile-time**: tells the type checker that the return value has the designated type.
+- **Run-time**: -
+
+This operation is unsound, use at your own risk!
+
+---
+<br>
+<br>
+<br>
+
+_**Internal Python documentation**_
+"""

midas/utils.py

@@ -62,3 +62,4 @@ class UniversalJSONDumper:
 class TypedAST:
     stmts: list[p.Stmt]
     judgements: list[tuple[p.Expr, Type]]
+    evaluated_casts: list[p.CastExpr]

pyproject.toml

@@ -8,7 +8,11 @@ authors = [
     { name = "Louis Heredero", email = "louis.heredero@students.hevs.ch" },
 ]
 classifiers = ["Programming Language :: Python :: 3"]
-dependencies = ["click>=8.4.1"]
+dependencies = [
+    "black>=26.5.1",
+    "click>=8.4.1",
+    "watchdog>=6.0.0",
+]
 
 [project.urls]
 Homepage = "https://git.kbk28.ch/HEL/midas"

tests/cases/checker/04_custom_types.py.ref.json

@@ -1,6 +1,19 @@
 {
   "diagnostics": [],
   "judgments": [
+    {
+      "location": {
+        "from": "L4:30",
+        "to": "L4:36"
+      },
+      "expr": {
+        "_type": "LiteralExpr",
+        "value": 123.45
+      },
+      "type": {
+        "name": "float"
+      }
+    },
     {
       "location": {
         "from": "L4:18",
@@ -16,7 +29,8 @@
         "expr": {
           "_type": "LiteralExpr",
           "value": 123.45
-        }
+        },
+        "unsafe": false
       },
       "type": {
         "name": "Meter",
@@ -25,6 +39,19 @@
         }
       }
     },
+    {
+      "location": {
+        "from": "L5:28",
+        "to": "L5:31"
+      },
+      "expr": {
+        "_type": "LiteralExpr",
+        "value": 6.7
+      },
+      "type": {
+        "name": "float"
+      }
+    },
     {
       "location": {
         "from": "L5:15",
@@ -40,7 +67,8 @@
         "expr": {
           "_type": "LiteralExpr",
           "value": 6.7
-        }
+        },
+        "unsafe": false
       },
       "type": {
         "name": "Second",

tests/cases/checker/07_variance.midas

@@ -0,0 +1,59 @@
+// T is invariant (unused)
+type Unused[T] = object
+
+// T is covariant
+type Covariant[T] = object
+
+// T is contravariant
+type Contravariant[T] = object
+
+// T is invariant
+type Invariant[T] = object
+
+extend Covariant[T] {
+    def foo: fn() -> T
+}
+
+extend Contravariant[T] {
+    def foo: fn(T, /) -> None
+}
+
+extend Invariant[T] {
+    def foo: fn(T, /) -> T
+}
+
+// T is covariant
+type Coco[T] = object
+extend Coco[T] {
+    def foo: fn() -> Covariant[T]
+}
+
+// T is contravariant
+type Cocontra[T] = object
+extend Cocontra[T] {
+    def foo: fn() -> Contravariant[T]
+}
+
+// T is contravariant
+type Contraco[T] = object
+extend Contraco[T] {
+    def foo: fn(Covariant[T], /) -> None
+}
+
+// T is covariant
+type Contracontra[T] = object
+extend Contracontra[T] {
+    def foo: fn(Contravariant[T], /) -> None
+}
+
+
+type T1[T] = object
+type T2[T] = object
+
+extend T1[T] {
+    def foo: fn() -> T2[T]
+}
+
+extend T2[T] {
+    def foo: fn() -> T1[T]
+}

tests/cases/checker/07_variance.py

@@ -0,0 +1,52 @@
+from _ import (
+    T1,
+    T2,
+    Coco,
+    Cocontra,
+    Contraco,
+    Contracontra,
+    Contravariant,
+    Covariant,
+    Invariant,
+    Unused,
+)
+
+unused: Unused
+covariant: Covariant
+contravariant: Contravariant
+invariant: Invariant
+coco: Coco
+cocontra: Cocontra
+contraco: Contraco
+contracontra: Contracontra
+t1: T1
+t2: T2
+
+# Dummy print to prudce judgements for the expressions
+print(
+    unused,
+    covariant,
+    contravariant,
+    invariant,
+    coco,
+    cocontra,
+    contraco,
+    contracontra,
+    t1,
+    t2,
+)
+
+cov1: Covariant[float]
+cov2: Covariant[int]
+cov1 = cov2  # Ok because int <: float => Covariant[int] <: Covariant[float]
+cov2 = cov1  # Invalid
+
+contra1: Contravariant[float]
+contra2: Contravariant[int]
+contra1 = contra2  # Invalid
+contra2 = contra1  # Ok because int <: float => Covariant[float] <: Covariant[int]
+
+inv1: Invariant[float]
+inv2: Invariant[int]
+inv1 = inv2  # Invalid
+inv2 = inv1  # Invalid

tests/cases/checker/07_variance.py.ref.json

@@ -0,0 +1,512 @@
+{
+  "diagnostics": [
+    {
+      "type": "Error",
+      "location": {
+        "start": [
+          28,
+          4
+        ],
+        "end": [
+          28,
+          13
+        ]
+      },
+      "message": "Too many positional arguments"
+    },
+    {
+      "type": "Error",
+      "location": {
+        "start": [
+          42,
+          0
+        ],
+        "end": [
+          42,
+          11
+        ]
+      },
+      "message": "Cannot assign Covariant[float] to variable 'cov2' of type Covariant[int]"
+    },
+    {
+      "type": "Error",
+      "location": {
+        "start": [
+          46,
+          0
+        ],
+        "end": [
+          46,
+          17
+        ]
+      },
+      "message": "Cannot assign Contravariant[int] to variable 'contra1' of type Contravariant[float]"
+    },
+    {
+      "type": "Error",
+      "location": {
+        "start": [
+          51,
+          0
+        ],
+        "end": [
+          51,
+          11
+        ]
+      },
+      "message": "Cannot assign Invariant[int] to variable 'inv1' of type Invariant[float]"
+    },
+    {
+      "type": "Error",
+      "location": {
+        "start": [
+          52,
+          0
+        ],
+        "end": [
+          52,
+          11
+        ]
+      },
+      "message": "Cannot assign Invariant[float] to variable 'inv2' of type Invariant[int]"
+    }
+  ],
+  "judgments": [
+    {
+      "location": {
+        "from": "L26:0",
+        "to": "L26:5"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "print"
+      },
+      "type": {
+        "pos_args": [
+          {
+            "pos": 0,
+            "name": "object",
+            "type": {},
+            "required": true
+          }
+        ],
+        "args": [],
+        "kw_args": [],
+        "returns": {}
+      }
+    },
+    {
+      "location": {
+        "from": "L27:4",
+        "to": "L27:10"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "unused"
+      },
+      "type": {
+        "name": "Unused",
+        "params": [
+          {
+            "name": "T",
+            "bound": null,
+            "variance": "INVARIANT"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L28:4",
+        "to": "L28:13"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "covariant"
+      },
+      "type": {
+        "name": "Covariant",
+        "params": [
+          {
+            "name": "T",
+            "bound": null,
+            "variance": "COVARIANT"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L29:4",
+        "to": "L29:17"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "contravariant"
+      },
+      "type": {
+        "name": "Contravariant",
+        "params": [
+          {
+            "name": "T",
+            "bound": null,
+            "variance": "CONTRAVARIANT"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L30:4",
+        "to": "L30:13"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "invariant"
+      },
+      "type": {
+        "name": "Invariant",
+        "params": [
+          {
+            "name": "T",
+            "bound": null,
+            "variance": "INVARIANT"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L31:4",
+        "to": "L31:8"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "coco"
+      },
+      "type": {
+        "name": "Coco",
+        "params": [
+          {
+            "name": "T",
+            "bound": null,
+            "variance": "COVARIANT"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L32:4",
+        "to": "L32:12"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "cocontra"
+      },
+      "type": {
+        "name": "Cocontra",
+        "params": [
+          {
+            "name": "T",
+            "bound": null,
+            "variance": "CONTRAVARIANT"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L33:4",
+        "to": "L33:12"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "contraco"
+      },
+      "type": {
+        "name": "Contraco",
+        "params": [
+          {
+            "name": "T",
+            "bound": null,
+            "variance": "CONTRAVARIANT"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L34:4",
+        "to": "L34:16"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "contracontra"
+      },
+      "type": {
+        "name": "Contracontra",
+        "params": [
+          {
+            "name": "T",
+            "bound": null,
+            "variance": "COVARIANT"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L35:4",
+        "to": "L35:6"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "t1"
+      },
+      "type": {
+        "name": "T1",
+        "params": [
+          {
+            "name": "T",
+            "bound": null,
+            "variance": "INVARIANT"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L36:4",
+        "to": "L36:6"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "t2"
+      },
+      "type": {
+        "name": "T2",
+        "params": [
+          {
+            "name": "T",
+            "bound": null,
+            "variance": "INVARIANT"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L26:0",
+        "to": "L37:1"
+      },
+      "expr": {
+        "_type": "CallExpr",
+        "callee": {
+          "_type": "VariableExpr",
+          "name": "print"
+        },
+        "arguments": [
+          {
+            "_type": "VariableExpr",
+            "name": "unused"
+          },
+          {
+            "_type": "VariableExpr",
+            "name": "covariant"
+          },
+          {
+            "_type": "VariableExpr",
+            "name": "contravariant"
+          },
+          {
+            "_type": "VariableExpr",
+            "name": "invariant"
+          },
+          {
+            "_type": "VariableExpr",
+            "name": "coco"
+          },
+          {
+            "_type": "VariableExpr",
+            "name": "cocontra"
+          },
+          {
+            "_type": "VariableExpr",
+            "name": "contraco"
+          },
+          {
+            "_type": "VariableExpr",
+            "name": "contracontra"
+          },
+          {
+            "_type": "VariableExpr",
+            "name": "t1"
+          },
+          {
+            "_type": "VariableExpr",
+            "name": "t2"
+          }
+        ],
+        "keywords": {}
+      },
+      "type": {}
+    },
+    {
+      "location": {
+        "from": "L41:7",
+        "to": "L41:11"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "cov2"
+      },
+      "type": {
+        "name": "Covariant",
+        "args": [
+          {
+            "name": "int"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L42:7",
+        "to": "L42:11"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "cov1"
+      },
+      "type": {
+        "name": "Covariant",
+        "args": [
+          {
+            "name": "float"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L46:10",
+        "to": "L46:17"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "contra2"
+      },
+      "type": {
+        "name": "Contravariant",
+        "args": [
+          {
+            "name": "int"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L47:10",
+        "to": "L47:17"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "contra1"
+      },
+      "type": {
+        "name": "Contravariant",
+        "args": [
+          {
+            "name": "float"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L51:7",
+        "to": "L51:11"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "inv2"
+      },
+      "type": {
+        "name": "Invariant",
+        "args": [
+          {
+            "name": "int"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L52:7",
+        "to": "L52:11"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "inv1"
+      },
+      "type": {
+        "name": "Invariant",
+        "args": [
+          {
+            "name": "float"
+          }
+        ],
+        "body": {
+          "name": "object"
+        }
+      }
+    }
+  ]
+}

tests/cases/checker/08_unification.py

@@ -0,0 +1,14 @@
+def double(value: float) -> float:
+    return value * 2
+
+
+def is_odd(value: int) -> bool:
+    return bool(value % 2)
+
+
+floats: list[float] = [0.2, 0.5, 0.1, 1.2]
+ints: list[int] = [1, 2, 6, -3]
+
+doubled_floats = map(double, floats)
+doubled_ints = map(double, ints)
+odd_ints = map(is_odd, ints)

tests/cases/checker/08_unification.py.ref.json

@@ -0,0 +1,874 @@
+{
+  "diagnostics": [
+    {
+      "type": "Error",
+      "location": {
+        "start": [
+          13,
+          15
+        ],
+        "end": [
+          13,
+          32
+        ]
+      },
+      "message": "Could not unify map[T, U]=(transform: (v: T, /) -> U, iterable: list[T], /) -> list[U] with pos=[(value: float) -> float, list[int]] and kw={}"
+    }
+  ],
+  "judgments": [
+    {
+      "location": {
+        "from": "L2:11",
+        "to": "L2:16"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "value"
+      },
+      "type": {
+        "name": "float"
+      }
+    },
+    {
+      "location": {
+        "from": "L2:19",
+        "to": "L2:20"
+      },
+      "expr": {
+        "_type": "LiteralExpr",
+        "value": 2
+      },
+      "type": {
+        "name": "int"
+      }
+    },
+    {
+      "location": {
+        "from": "L2:11",
+        "to": "L2:20"
+      },
+      "expr": {
+        "_type": "BinaryExpr",
+        "left": {
+          "_type": "VariableExpr",
+          "name": "value"
+        },
+        "operator": "*",
+        "right": {
+          "_type": "LiteralExpr",
+          "value": 2
+        }
+      },
+      "type": {
+        "name": "float"
+      }
+    },
+    {
+      "location": {
+        "from": "L6:11",
+        "to": "L6:15"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "bool"
+      },
+      "type": {
+        "pos_args": [
+          {
+            "pos": 0,
+            "name": "object",
+            "type": {},
+            "required": false
+          }
+        ],
+        "args": [],
+        "kw_args": [],
+        "returns": {
+          "name": "bool"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L6:16",
+        "to": "L6:21"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "value"
+      },
+      "type": {
+        "name": "int"
+      }
+    },
+    {
+      "location": {
+        "from": "L6:24",
+        "to": "L6:25"
+      },
+      "expr": {
+        "_type": "LiteralExpr",
+        "value": 2
+      },
+      "type": {
+        "name": "int"
+      }
+    },
+    {
+      "location": {
+        "from": "L6:16",
+        "to": "L6:25"
+      },
+      "expr": {
+        "_type": "BinaryExpr",
+        "left": {
+          "_type": "VariableExpr",
+          "name": "value"
+        },
+        "operator": "%",
+        "right": {
+          "_type": "LiteralExpr",
+          "value": 2
+        }
+      },
+      "type": {
+        "name": "int"
+      }
+    },
+    {
+      "location": {
+        "from": "L6:11",
+        "to": "L6:26"
+      },
+      "expr": {
+        "_type": "CallExpr",
+        "callee": {
+          "_type": "VariableExpr",
+          "name": "bool"
+        },
+        "arguments": [
+          {
+            "_type": "BinaryExpr",
+            "left": {
+              "_type": "VariableExpr",
+              "name": "value"
+            },
+            "operator": "%",
+            "right": {
+              "_type": "LiteralExpr",
+              "value": 2
+            }
+          }
+        ],
+        "keywords": {}
+      },
+      "type": {
+        "name": "bool"
+      }
+    },
+    {
+      "location": {
+        "from": "L9:23",
+        "to": "L9:26"
+      },
+      "expr": {
+        "_type": "LiteralExpr",
+        "value": 0.2
+      },
+      "type": {
+        "name": "float"
+      }
+    },
+    {
+      "location": {
+        "from": "L9:28",
+        "to": "L9:31"
+      },
+      "expr": {
+        "_type": "LiteralExpr",
+        "value": 0.5
+      },
+      "type": {
+        "name": "float"
+      }
+    },
+    {
+      "location": {
+        "from": "L9:33",
+        "to": "L9:36"
+      },
+      "expr": {
+        "_type": "LiteralExpr",
+        "value": 0.1
+      },
+      "type": {
+        "name": "float"
+      }
+    },
+    {
+      "location": {
+        "from": "L9:38",
+        "to": "L9:41"
+      },
+      "expr": {
+        "_type": "LiteralExpr",
+        "value": 1.2
+      },
+      "type": {
+        "name": "float"
+      }
+    },
+    {
+      "location": {
+        "from": "L9:22",
+        "to": "L9:42"
+      },
+      "expr": {
+        "_type": "ListExpr",
+        "items": [
+          {
+            "_type": "LiteralExpr",
+            "value": 0.2
+          },
+          {
+            "_type": "LiteralExpr",
+            "value": 0.5
+          },
+          {
+            "_type": "LiteralExpr",
+            "value": 0.1
+          },
+          {
+            "_type": "LiteralExpr",
+            "value": 1.2
+          }
+        ]
+      },
+      "type": {
+        "name": "list",
+        "args": [
+          {
+            "name": "float"
+          }
+        ],
+        "body": {
+          "name": "list"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L10:19",
+        "to": "L10:20"
+      },
+      "expr": {
+        "_type": "LiteralExpr",
+        "value": 1
+      },
+      "type": {
+        "name": "int"
+      }
+    },
+    {
+      "location": {
+        "from": "L10:22",
+        "to": "L10:23"
+      },
+      "expr": {
+        "_type": "LiteralExpr",
+        "value": 2
+      },
+      "type": {
+        "name": "int"
+      }
+    },
+    {
+      "location": {
+        "from": "L10:25",
+        "to": "L10:26"
+      },
+      "expr": {
+        "_type": "LiteralExpr",
+        "value": 6
+      },
+      "type": {
+        "name": "int"
+      }
+    },
+    {
+      "location": {
+        "from": "L10:29",
+        "to": "L10:30"
+      },
+      "expr": {
+        "_type": "LiteralExpr",
+        "value": 3
+      },
+      "type": {
+        "name": "int"
+      }
+    },
+    {
+      "location": {
+        "from": "L10:28",
+        "to": "L10:30"
+      },
+      "expr": {
+        "_type": "UnaryExpr",
+        "operator": "-",
+        "right": {
+          "_type": "LiteralExpr",
+          "value": 3
+        }
+      },
+      "type": {
+        "name": "int"
+      }
+    },
+    {
+      "location": {
+        "from": "L10:18",
+        "to": "L10:31"
+      },
+      "expr": {
+        "_type": "ListExpr",
+        "items": [
+          {
+            "_type": "LiteralExpr",
+            "value": 1
+          },
+          {
+            "_type": "LiteralExpr",
+            "value": 2
+          },
+          {
+            "_type": "LiteralExpr",
+            "value": 6
+          },
+          {
+            "_type": "UnaryExpr",
+            "operator": "-",
+            "right": {
+              "_type": "LiteralExpr",
+              "value": 3
+            }
+          }
+        ]
+      },
+      "type": {
+        "name": "list",
+        "args": [
+          {
+            "name": "int"
+          }
+        ],
+        "body": {
+          "name": "list"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L12:17",
+        "to": "L12:20"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "map"
+      },
+      "type": {
+        "name": "map",
+        "params": [
+          {
+            "name": "T",
+            "bound": null,
+            "variance": "INVARIANT"
+          },
+          {
+            "name": "U",
+            "bound": null,
+            "variance": "INVARIANT"
+          }
+        ],
+        "body": {
+          "pos_args": [
+            {
+              "pos": 0,
+              "name": "transform",
+              "type": {
+                "pos_args": [
+                  {
+                    "pos": 0,
+                    "name": "v",
+                    "type": {
+                      "name": "T",
+                      "bound": null,
+                      "variance": "INVARIANT"
+                    },
+                    "required": true
+                  }
+                ],
+                "args": [],
+                "kw_args": [],
+                "returns": {
+                  "name": "U",
+                  "bound": null,
+                  "variance": "INVARIANT"
+                }
+              },
+              "required": true
+            },
+            {
+              "pos": 1,
+              "name": "iterable",
+              "type": {
+                "name": "list",
+                "args": [
+                  {
+                    "name": "T",
+                    "bound": null,
+                    "variance": "INVARIANT"
+                  }
+                ],
+                "body": {
+                  "name": "list"
+                }
+              },
+              "required": true
+            }
+          ],
+          "args": [],
+          "kw_args": [],
+          "returns": {
+            "name": "list",
+            "args": [
+              {
+                "name": "U",
+                "bound": null,
+                "variance": "INVARIANT"
+              }
+            ],
+            "body": {
+              "name": "list"
+            }
+          }
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L12:21",
+        "to": "L12:27"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "double"
+      },
+      "type": {
+        "pos_args": [],
+        "args": [
+          {
+            "pos": 0,
+            "name": "value",
+            "type": {
+              "name": "float"
+            },
+            "required": true
+          }
+        ],
+        "kw_args": [],
+        "returns": {
+          "name": "float"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L12:29",
+        "to": "L12:35"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "floats"
+      },
+      "type": {
+        "name": "list",
+        "args": [
+          {
+            "name": "float"
+          }
+        ],
+        "body": {
+          "name": "list"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L12:17",
+        "to": "L12:36"
+      },
+      "expr": {
+        "_type": "CallExpr",
+        "callee": {
+          "_type": "VariableExpr",
+          "name": "map"
+        },
+        "arguments": [
+          {
+            "_type": "VariableExpr",
+            "name": "double"
+          },
+          {
+            "_type": "VariableExpr",
+            "name": "floats"
+          }
+        ],
+        "keywords": {}
+      },
+      "type": {
+        "name": "list",
+        "args": [
+          {
+            "name": "float"
+          }
+        ],
+        "body": {
+          "name": "list"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L13:15",
+        "to": "L13:18"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "map"
+      },
+      "type": {
+        "name": "map",
+        "params": [
+          {
+            "name": "T",
+            "bound": null,
+            "variance": "INVARIANT"
+          },
+          {
+            "name": "U",
+            "bound": null,
+            "variance": "INVARIANT"
+          }
+        ],
+        "body": {
+          "pos_args": [
+            {
+              "pos": 0,
+              "name": "transform",
+              "type": {
+                "pos_args": [
+                  {
+                    "pos": 0,
+                    "name": "v",
+                    "type": {
+                      "name": "T",
+                      "bound": null,
+                      "variance": "INVARIANT"
+                    },
+                    "required": true
+                  }
+                ],
+                "args": [],
+                "kw_args": [],
+                "returns": {
+                  "name": "U",
+                  "bound": null,
+                  "variance": "INVARIANT"
+                }
+              },
+              "required": true
+            },
+            {
+              "pos": 1,
+              "name": "iterable",
+              "type": {
+                "name": "list",
+                "args": [
+                  {
+                    "name": "T",
+                    "bound": null,
+                    "variance": "INVARIANT"
+                  }
+                ],
+                "body": {
+                  "name": "list"
+                }
+              },
+              "required": true
+            }
+          ],
+          "args": [],
+          "kw_args": [],
+          "returns": {
+            "name": "list",
+            "args": [
+              {
+                "name": "U",
+                "bound": null,
+                "variance": "INVARIANT"
+              }
+            ],
+            "body": {
+              "name": "list"
+            }
+          }
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L13:19",
+        "to": "L13:25"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "double"
+      },
+      "type": {
+        "pos_args": [],
+        "args": [
+          {
+            "pos": 0,
+            "name": "value",
+            "type": {
+              "name": "float"
+            },
+            "required": true
+          }
+        ],
+        "kw_args": [],
+        "returns": {
+          "name": "float"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L13:27",
+        "to": "L13:31"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "ints"
+      },
+      "type": {
+        "name": "list",
+        "args": [
+          {
+            "name": "int"
+          }
+        ],
+        "body": {
+          "name": "list"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L13:15",
+        "to": "L13:32"
+      },
+      "expr": {
+        "_type": "CallExpr",
+        "callee": {
+          "_type": "VariableExpr",
+          "name": "map"
+        },
+        "arguments": [
+          {
+            "_type": "VariableExpr",
+            "name": "double"
+          },
+          {
+            "_type": "VariableExpr",
+            "name": "ints"
+          }
+        ],
+        "keywords": {}
+      },
+      "type": {}
+    },
+    {
+      "location": {
+        "from": "L14:11",
+        "to": "L14:14"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "map"
+      },
+      "type": {
+        "name": "map",
+        "params": [
+          {
+            "name": "T",
+            "bound": null,
+            "variance": "INVARIANT"
+          },
+          {
+            "name": "U",
+            "bound": null,
+            "variance": "INVARIANT"
+          }
+        ],
+        "body": {
+          "pos_args": [
+            {
+              "pos": 0,
+              "name": "transform",
+              "type": {
+                "pos_args": [
+                  {
+                    "pos": 0,
+                    "name": "v",
+                    "type": {
+                      "name": "T",
+                      "bound": null,
+                      "variance": "INVARIANT"
+                    },
+                    "required": true
+                  }
+                ],
+                "args": [],
+                "kw_args": [],
+                "returns": {
+                  "name": "U",
+                  "bound": null,
+                  "variance": "INVARIANT"
+                }
+              },
+              "required": true
+            },
+            {
+              "pos": 1,
+              "name": "iterable",
+              "type": {
+                "name": "list",
+                "args": [
+                  {
+                    "name": "T",
+                    "bound": null,
+                    "variance": "INVARIANT"
+                  }
+                ],
+                "body": {
+                  "name": "list"
+                }
+              },
+              "required": true
+            }
+          ],
+          "args": [],
+          "kw_args": [],
+          "returns": {
+            "name": "list",
+            "args": [
+              {
+                "name": "U",
+                "bound": null,
+                "variance": "INVARIANT"
+              }
+            ],
+            "body": {
+              "name": "list"
+            }
+          }
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L14:15",
+        "to": "L14:21"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "is_odd"
+      },
+      "type": {
+        "pos_args": [],
+        "args": [
+          {
+            "pos": 0,
+            "name": "value",
+            "type": {
+              "name": "int"
+            },
+            "required": true
+          }
+        ],
+        "kw_args": [],
+        "returns": {
+          "name": "bool"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L14:23",
+        "to": "L14:27"
+      },
+      "expr": {
+        "_type": "VariableExpr",
+        "name": "ints"
+      },
+      "type": {
+        "name": "list",
+        "args": [
+          {
+            "name": "int"
+          }
+        ],
+        "body": {
+          "name": "list"
+        }
+      }
+    },
+    {
+      "location": {
+        "from": "L14:11",
+        "to": "L14:28"
+      },
+      "expr": {
+        "_type": "CallExpr",
+        "callee": {
+          "_type": "VariableExpr",
+          "name": "map"
+        },
+        "arguments": [
+          {
+            "_type": "VariableExpr",
+            "name": "is_odd"
+          },
+          {
+            "_type": "VariableExpr",
+            "name": "ints"
+          }
+        ],
+        "keywords": {}
+      },
+      "type": {
+        "name": "list",
+        "args": [
+          {
+            "name": "bool"
+          }
+        ],
+        "body": {
+          "name": "list"
+        }
+      }
+    }
+  ]
+}

tests/cases/generator/01_simple_types.py.ref.txt

@@ -7,68 +7,14 @@ Module(
         alias(name='Meter'),
         alias(name='Second')],
       level=0),
-    Assign(
-      targets=[
-        Name(id='__midas_alias_0__')],
-      value=Constant(value=123.45)),
-    Assert(
-      test=Call(
-        func=Name(id='isinstance'),
-        args=[
-          Name(id='__midas_alias_0__'),
-          Name(id='float')],
-        keywords=[]),
-      msg=JoinedStr(
-        values=[
-          Constant(value='01_simple_types.py:L3:19: CastError: Cannot cast '),
-          FormattedValue(
-            value=Attribute(
-              value=Call(
-                func=Name(id='type'),
-                args=[
-                  Name(id='__midas_alias_0__')],
-                keywords=[]),
-              attr='__name__'),
-            conversion=-1),
-          Constant(value=' to float')])),
     Assign(
       targets=[
         Name(id='distance')],
-      value=Name(id='__midas_alias_0__')),
-    Delete(
-      targets=[
-        Name(id='__midas_alias_0__')]),
-    Assign(
-      targets=[
-        Name(id='__midas_alias_1__')],
-      value=Constant(value=6.7)),
-    Assert(
-      test=Call(
-        func=Name(id='isinstance'),
-        args=[
-          Name(id='__midas_alias_1__'),
-          Name(id='float')],
-        keywords=[]),
-      msg=JoinedStr(
-        values=[
-          Constant(value='01_simple_types.py:L4:16: CastError: Cannot cast '),
-          FormattedValue(
-            value=Attribute(
-              value=Call(
-                func=Name(id='type'),
-                args=[
-                  Name(id='__midas_alias_1__')],
-                keywords=[]),
-              attr='__name__'),
-            conversion=-1),
-          Constant(value=' to float')])),
+      value=Constant(value=123.45)),
     Assign(
       targets=[
         Name(id='time')],
-      value=Name(id='__midas_alias_1__')),
-    Delete(
-      targets=[
-        Name(id='__midas_alias_1__')]),
+      value=Constant(value=6.7)),
     Assign(
       targets=[
         Name(id='speed')],

tests/cases/generator/02_constraints.midas

@@ -0,0 +1,14 @@
+// Inline
+type T1 = float where _ > 0
+
+// Named
+predicate is_positive(v: float) = v > 0
+type T2 = float where is_positive(_)
+
+// Curried
+predicate in_range(mn: float, mx: float)(v: float) = v >= mn & v < mx
+type T3 = float where in_range(100, 200)(_)
+
+// Alias
+predicate minor = in_range(0, 18)
+type T4 = float where minor(_)

tests/cases/generator/02_constraints.py

@@ -0,0 +1,8 @@
+from midas import T1, T2, T3, T4, cast
+
+t: float = 12.5
+
+t1: T1 = cast(T1, t)
+t2: T2 = cast(T2, t)
+t3: T3 = cast(T3, t)
+t4: T4 = cast(T4, t)

tests/cases/generator/02_constraints.py.ref.txt

@@ -0,0 +1,333 @@
+Module(
+  body=[
+    FunctionDef(
+      name='__midas_p0__',
+      args=arguments(
+        posonlyargs=[],
+        args=[
+          arg(
+            arg='_',
+            annotation=Constant(value='Any'))],
+        kwonlyargs=[],
+        kw_defaults=[],
+        defaults=[]),
+      body=[
+        Return(
+          value=Compare(
+            left=Name(id='_'),
+            ops=[
+              Gt()],
+            comparators=[
+              Constant(value=0.0)]))],
+      decorator_list=[],
+      returns=Constant(value='bool')),
+    FunctionDef(
+      name='__midas_is_positive__',
+      args=arguments(
+        posonlyargs=[],
+        args=[
+          arg(
+            arg='v',
+            annotation=Constant(value='float'))],
+        kwonlyargs=[],
+        kw_defaults=[],
+        defaults=[]),
+      body=[
+        Return(
+          value=Compare(
+            left=Name(id='v'),
+            ops=[
+              Gt()],
+            comparators=[
+              Constant(value=0.0)]))],
+      decorator_list=[],
+      returns=Constant(value='bool')),
+    FunctionDef(
+      name='__midas_p1__',
+      args=arguments(
+        posonlyargs=[],
+        args=[
+          arg(
+            arg='_',
+            annotation=Constant(value='Any'))],
+        kwonlyargs=[],
+        kw_defaults=[],
+        defaults=[]),
+      body=[
+        Return(
+          value=Call(
+            func=Name(id='__midas_is_positive__'),
+            args=[
+              Name(id='_')],
+            keywords=[]))],
+      decorator_list=[],
+      returns=Constant(value='bool')),
+    FunctionDef(
+      name='__midas_in_range__',
+      args=arguments(
+        posonlyargs=[],
+        args=[
+          arg(
+            arg='mn',
+            annotation=Constant(value='float')),
+          arg(
+            arg='mx',
+            annotation=Constant(value='float'))],
+        kwonlyargs=[],
+        kw_defaults=[],
+        defaults=[]),
+      body=[
+        FunctionDef(
+          name='inner0',
+          args=arguments(
+            posonlyargs=[],
+            args=[
+              arg(
+                arg='v',
+                annotation=Constant(value='float'))],
+            kwonlyargs=[],
+            kw_defaults=[],
+            defaults=[]),
+          body=[
+            Return(
+              value=BoolOp(
+                op=And(),
+                values=[
+                  Compare(
+                    left=Name(id='v'),
+                    ops=[
+                      GtE()],
+                    comparators=[
+                      Name(id='mn')]),
+                  Compare(
+                    left=Name(id='v'),
+                    ops=[
+                      Lt()],
+                    comparators=[
+                      Name(id='mx')])]))],
+          decorator_list=[],
+          returns=Constant(value='bool')),
+        Return(
+          value=Name(id='inner0'))],
+      decorator_list=[],
+      returns=Constant(value='Callable[[float], bool]')),
+    FunctionDef(
+      name='__midas_p2__',
+      args=arguments(
+        posonlyargs=[],
+        args=[
+          arg(
+            arg='_',
+            annotation=Constant(value='Any'))],
+        kwonlyargs=[],
+        kw_defaults=[],
+        defaults=[]),
+      body=[
+        Return(
+          value=Call(
+            func=Call(
+              func=Name(id='__midas_in_range__'),
+              args=[
+                Constant(value=100.0),
+                Constant(value=200.0)],
+              keywords=[]),
+            args=[
+              Name(id='_')],
+            keywords=[]))],
+      decorator_list=[],
+      returns=Constant(value='bool')),
+    Assign(
+      targets=[
+        Name(id='__midas_minor__')],
+      value=Call(
+        func=Name(id='__midas_in_range__'),
+        args=[
+          Constant(value=0.0),
+          Constant(value=18.0)],
+        keywords=[])),
+    FunctionDef(
+      name='__midas_p3__',
+      args=arguments(
+        posonlyargs=[],
+        args=[
+          arg(
+            arg='_',
+            annotation=Constant(value='Any'))],
+        kwonlyargs=[],
+        kw_defaults=[],
+        defaults=[]),
+      body=[
+        Return(
+          value=Call(
+            func=Name(id='__midas_minor__'),
+            args=[
+              Name(id='_')],
+            keywords=[]))],
+      decorator_list=[],
+      returns=Constant(value='bool')),
+    ImportFrom(
+      module='midas',
+      names=[
+        alias(name='T1'),
+        alias(name='T2'),
+        alias(name='T3'),
+        alias(name='T4'),
+        alias(name='cast')],
+      level=0),
+    Assign(
+      targets=[
+        Name(id='t')],
+      value=Constant(value=12.5)),
+    Assign(
+      targets=[
+        Name(id='__midas_a0__')],
+      value=Name(id='t')),
+    Assert(
+      test=Call(
+        func=Name(id='isinstance'),
+        args=[
+          Name(id='__midas_a0__'),
+          Name(id='float')],
+        keywords=[]),
+      msg=JoinedStr(
+        values=[
+          Constant(value='02_constraints.py:L5:10: CastError: Cannot cast '),
+          FormattedValue(
+            value=Attribute(
+              value=Call(
+                func=Name(id='type'),
+                args=[
+                  Name(id='__midas_a0__')],
+                keywords=[]),
+              attr='__name__'),
+            conversion=-1),
+          Constant(value=' to float')])),
+    Assert(
+      test=Call(
+        func=Name(id='__midas_p0__'),
+        args=[
+          Name(id='__midas_a0__')],
+        keywords=[]),
+      msg=Constant(value="02_constraints.py:L5:10: ConstraintError: Value does not fit constraint '_ > 0.0'")),
+    Assign(
+      targets=[
+        Name(id='t1')],
+      value=Name(id='__midas_a0__')),
+    Delete(
+      targets=[
+        Name(id='__midas_a0__')]),
+    Assign(
+      targets=[
+        Name(id='__midas_a1__')],
+      value=Name(id='t')),
+    Assert(
+      test=Call(
+        func=Name(id='isinstance'),
+        args=[
+          Name(id='__midas_a1__'),
+          Name(id='float')],
+        keywords=[]),
+      msg=JoinedStr(
+        values=[
+          Constant(value='02_constraints.py:L6:10: CastError: Cannot cast '),
+          FormattedValue(
+            value=Attribute(
+              value=Call(
+                func=Name(id='type'),
+                args=[
+                  Name(id='__midas_a1__')],
+                keywords=[]),
+              attr='__name__'),
+            conversion=-1),
+          Constant(value=' to float')])),
+    Assert(
+      test=Call(
+        func=Name(id='__midas_p1__'),
+        args=[
+          Name(id='__midas_a1__')],
+        keywords=[]),
+      msg=Constant(value="02_constraints.py:L6:10: ConstraintError: Value does not fit constraint 'is_positive(_)'")),
+    Assign(
+      targets=[
+        Name(id='t2')],
+      value=Name(id='__midas_a1__')),
+    Delete(
+      targets=[
+        Name(id='__midas_a1__')]),
+    Assign(
+      targets=[
+        Name(id='__midas_a2__')],
+      value=Name(id='t')),
+    Assert(
+      test=Call(
+        func=Name(id='isinstance'),
+        args=[
+          Name(id='__midas_a2__'),
+          Name(id='float')],
+        keywords=[]),
+      msg=JoinedStr(
+        values=[
+          Constant(value='02_constraints.py:L7:10: CastError: Cannot cast '),
+          FormattedValue(
+            value=Attribute(
+              value=Call(
+                func=Name(id='type'),
+                args=[
+                  Name(id='__midas_a2__')],
+                keywords=[]),
+              attr='__name__'),
+            conversion=-1),
+          Constant(value=' to float')])),
+    Assert(
+      test=Call(
+        func=Name(id='__midas_p2__'),
+        args=[
+          Name(id='__midas_a2__')],
+        keywords=[]),
+      msg=Constant(value="02_constraints.py:L7:10: ConstraintError: Value does not fit constraint 'in_range(100.0, 200.0)(_)'")),
+    Assign(
+      targets=[
+        Name(id='t3')],
+      value=Name(id='__midas_a2__')),
+    Delete(
+      targets=[
+        Name(id='__midas_a2__')]),
+    Assign(
+      targets=[
+        Name(id='__midas_a3__')],
+      value=Name(id='t')),
+    Assert(
+      test=Call(
+        func=Name(id='isinstance'),
+        args=[
+          Name(id='__midas_a3__'),
+          Name(id='float')],
+        keywords=[]),
+      msg=JoinedStr(
+        values=[
+          Constant(value='02_constraints.py:L8:10: CastError: Cannot cast '),
+          FormattedValue(
+            value=Attribute(
+              value=Call(
+                func=Name(id='type'),
+                args=[
+                  Name(id='__midas_a3__')],
+                keywords=[]),
+              attr='__name__'),
+            conversion=-1),
+          Constant(value=' to float')])),
+    Assert(
+      test=Call(
+        func=Name(id='__midas_p3__'),
+        args=[
+          Name(id='__midas_a3__')],
+        keywords=[]),
+      msg=Constant(value="02_constraints.py:L8:10: ConstraintError: Value does not fit constraint 'minor(_)'")),
+    Assign(
+      targets=[
+        Name(id='t4')],
+      value=Name(id='__midas_a3__')),
+    Delete(
+      targets=[
+        Name(id='__midas_a3__')])],
+  type_ignores=[])

tests/cases/midas-parser/01_simple_types.midas.ref.json

@@ -2582,7 +2582,9 @@
           "name": "__sub__",
           "type": {
             "_type": "FunctionType",
-            "pos_args": [
+            "params": {
+              "_type": "ParamSpec",
+              "pos": [
                 {
                   "name": null,
                   "type": {
@@ -2592,8 +2594,9 @@
                   "required": true
                 }
               ],
-            "args": [],
-            "kw_args": [],
+              "mixed": [],
+              "kw": []
+            },
             "returns": {
               "_type": "GenericType",
               "type": {
@@ -2673,7 +2676,9 @@
           "name": "__sub__",
           "type": {
             "_type": "FunctionType",
-            "pos_args": [
+            "params": {
+              "_type": "ParamSpec",
+              "pos": [
                 {
                   "name": null,
                   "type": {
@@ -2683,8 +2688,9 @@
                   "required": true
                 }
               ],
-            "args": [],
-            "kw_args": [],
+              "mixed": [],
+              "kw": []
+            },
             "returns": {
               "_type": "GenericType",
               "type": {
@@ -2713,7 +2719,9 @@
           "name": "__sub__",
           "type": {
             "_type": "FunctionType",
-            "pos_args": [
+            "params": {
+              "_type": "ParamSpec",
+              "pos": [
                 {
                   "name": null,
                   "type": {
@@ -2723,8 +2731,9 @@
                   "required": true
                 }
               ],
-            "args": [],
-            "kw_args": [],
+              "mixed": [],
+              "kw": []
+            },
             "returns": {
               "_type": "GenericType",
               "type": {
@@ -2745,12 +2754,24 @@
     {
       "_type": "PredicateStmt",
       "name": "Positive",
-      "subject": "v",
+      "params": [
+        {
+          "_type": "ParamSpec",
+          "pos": [],
+          "mixed": [
+            {
+              "name": "v",
               "type": {
                 "_type": "NamedType",
                 "name": "float"
               },
-      "condition": {
+              "required": true
+            }
+          ],
+          "kw": []
+        }
+      ],
+      "body": {
         "_type": "BinaryExpr",
         "left": {
           "_type": "VariableExpr",
@@ -2766,12 +2787,24 @@
     {
       "_type": "PredicateStmt",
       "name": "StrictlyPositive",
-      "subject": "v",
+      "params": [
+        {
+          "_type": "ParamSpec",
+          "pos": [],
+          "mixed": [
+            {
+              "name": "v",
               "type": {
                 "_type": "NamedType",
                 "name": "float"
               },
-      "condition": {
+              "required": true
+            }
+          ],
+          "kw": []
+        }
+      ],
+      "body": {
         "_type": "BinaryExpr",
         "left": {
           "_type": "VariableExpr",
@@ -2787,12 +2820,24 @@
     {
       "_type": "PredicateStmt",
       "name": "Equatorial",
-      "subject": "loc",
+      "params": [
+        {
+          "_type": "ParamSpec",
+          "pos": [],
+          "mixed": [
+            {
+              "name": "loc",
               "type": {
                 "_type": "NamedType",
                 "name": "GeoLocation"
               },
-      "condition": {
+              "required": true
+            }
+          ],
+          "kw": []
+        }
+      ],
+      "body": {
         "_type": "GroupingExpr",
         "expr": {
           "_type": "BinaryExpr",
@@ -2827,12 +2872,24 @@
     {
       "_type": "PredicateStmt",
       "name": "Arctic",
-      "subject": "loc",
+      "params": [
+        {
+          "_type": "ParamSpec",
+          "pos": [],
+          "mixed": [
+            {
+              "name": "loc",
               "type": {
                 "_type": "NamedType",
                 "name": "GeoLocation"
               },
-      "condition": {
+              "required": true
+            }
+          ],
+          "kw": []
+        }
+      ],
+      "body": {
         "_type": "GroupingExpr",
         "expr": {
           "_type": "BinaryExpr",

tests/generator.py

@@ -45,7 +45,7 @@ class GeneratorTester(Tester):
         typed_ast: TypedAST = checker.type_check(path)
 
         if not any(d.type == DiagnosticType.ERROR for d in checker.diagnostics):
-            generator = Generator(workdir=path.parent)
+            generator = Generator(workdir=path.parent, types=checker.types)
             result.compiled_ast = generator.generate_ast(typed_ast, path)
 
         return result

tests/serializer/midas.py

@@ -2,6 +2,7 @@ from typing import Optional, Sequence
 
 from midas.ast.midas import (
     BinaryExpr,
+    CallExpr,
     ComplexType,
     ConstraintType,
     Expr,
@@ -15,6 +16,7 @@ from midas.ast.midas import (
     LogicalExpr,
     MemberStmt,
     NamedType,
+    ParamSpec,
     PredicateStmt,
     Stmt,
     Type,
@@ -78,9 +80,8 @@ class MidasAstJsonSerializer(
         return {
             "_type": "PredicateStmt",
             "name": stmt.name.lexeme,
-            "subject": stmt.subject.lexeme,
-            "type": stmt.type.accept(self),
-            "condition": stmt.condition.accept(self),
+            "params": [self._serialize_param_spec(spec) for spec in stmt.params],
+            "body": stmt.body.accept(self),
         }
 
     def visit_logical_expr(self, expr: LogicalExpr) -> dict:
@@ -106,6 +107,14 @@ class MidasAstJsonSerializer(
             "right": expr.right.accept(self),
         }
 
+    def visit_call_expr(self, expr: CallExpr) -> dict:
+        return {
+            "_type": "CallExpr",
+            "callee": expr.callee.accept(self),
+            "arguments": self._serialize_list(expr.arguments),
+            "keywords": {name: arg.accept(self) for name, arg in expr.keywords.items()},
+        }
+
     def visit_get_expr(self, expr: GetExpr) -> dict:
         return {
             "_type": "GetExpr",
@@ -163,15 +172,21 @@ class MidasAstJsonSerializer(
     def visit_function_type(self, type: FunctionType) -> dict:
         return {
             "_type": "FunctionType",
-            "pos_args": [self._serialize_func_arg(arg) for arg in type.pos_args],
-            "args": [self._serialize_func_arg(arg) for arg in type.args],
-            "kw_args": [self._serialize_func_arg(arg) for arg in type.kw_args],
+            "params": self._serialize_param_spec(type.params),
             "returns": type.returns.accept(self),
         }
 
+    def _serialize_param_spec(self, spec: ParamSpec) -> dict:
+        return {
+            "_type": "ParamSpec",
+            "pos": [self._serialize_func_arg(arg) for arg in spec.pos],
+            "mixed": [self._serialize_func_arg(arg) for arg in spec.mixed],
+            "kw": [self._serialize_func_arg(arg) for arg in spec.kw],
+        }
+
     def _serialize_func_arg(self, arg: FunctionType.Argument) -> dict:
         return {
-            "name": arg.name,
+            "name": arg.name.lexeme if arg.name is not None else None,
             "type": arg.type.accept(self),
             "required": arg.required,
         }

tests/serializer/python.py

@@ -263,6 +263,7 @@ class PythonAstJsonSerializer(
             "_type": "CastExpr",
             "type": expr.type.accept(self),
             "expr": expr.expr.accept(self),
+            "unsafe": expr.unsafe,
         }
 
     def visit_ternary_expr(self, expr: TernaryExpr) -> dict: