feat(tests): update serializer

gen/midas.py

@@ -4,6 +4,7 @@
 ###> Imports
 from abc import ABC, abstractmethod
 from dataclasses import dataclass
+from enum import Enum, auto
 from typing import Any, Generic, Optional, TypeVar
 
 from midas.ast.location import Location
@@ -20,6 +21,11 @@ class TypeParam:
     bound: Optional[Type]
 
 
+class MemberKind(Enum):
+    PROPERTY = auto()
+    METHOD = auto()
+
+
 ###<
 
 
@@ -30,15 +36,16 @@ class TypeStmt:
     type: Type
 
 
-class PropertyStmt:
+class MemberStmt:
     name: Token
     type: Type
+    kind: MemberKind
 
 
 class ExtendStmt:
+    name: Token
     params: list[TypeParam]
-    type: Type
-    operations: list[OpStmt]
+    members: list[MemberStmt]
 
 
 class OpStmt:
@@ -118,7 +125,12 @@ class ConstraintType:
 
 
 class ComplexType:
-    properties: list[PropertyStmt]
+    members: list[MemberStmt]
+
+
+class ExtensionType:
+    base: Type
+    extension: ComplexType
 
 
 class FunctionType:

midas/ast/midas.py

@@ -7,6 +7,7 @@ from __future__ import annotations
 
 from abc import ABC, abstractmethod
 from dataclasses import dataclass
+from enum import Enum, auto
 from typing import Any, Generic, Optional, TypeVar
 
 from midas.ast.location import Location
@@ -21,6 +22,11 @@ class TypeParam:
     bound: Optional[Type]
 
 
+class MemberKind(Enum):
+    PROPERTY = auto()
+    METHOD = auto()
+
+
 ##############
 # Statements #
 ##############
@@ -38,7 +44,7 @@ class Stmt(ABC):
         def visit_type_stmt(self, stmt: TypeStmt) -> T: ...
 
         @abstractmethod
-        def visit_property_stmt(self, stmt: PropertyStmt) -> T: ...
+        def visit_member_stmt(self, stmt: MemberStmt) -> T: ...
 
         @abstractmethod
         def visit_extend_stmt(self, stmt: ExtendStmt) -> T: ...
@@ -61,19 +67,20 @@ class TypeStmt(Stmt):
 
 
 @dataclass(frozen=True)
-class PropertyStmt(Stmt):
+class MemberStmt(Stmt):
     name: Token
     type: Type
+    kind: MemberKind
 
     def accept(self, visitor: Stmt.Visitor[T]) -> T:
-        return visitor.visit_property_stmt(self)
+        return visitor.visit_member_stmt(self)
 
 
 @dataclass(frozen=True)
 class ExtendStmt(Stmt):
+    name: Token
     params: list[TypeParam]
-    type: Type
-    operations: list[OpStmt]
+    members: list[MemberStmt]
 
     def accept(self, visitor: Stmt.Visitor[T]) -> T:
         return visitor.visit_extend_stmt(self)
@@ -233,6 +240,9 @@ class Type(ABC):
         @abstractmethod
         def visit_complex_type(self, type: ComplexType) -> T: ...
 
+        @abstractmethod
+        def visit_extension_type(self, type: ExtensionType) -> T: ...
+
         @abstractmethod
         def visit_function_type(self, type: FunctionType) -> T: ...
 
@@ -265,12 +275,21 @@ class ConstraintType(Type):
 
 @dataclass(frozen=True)
 class ComplexType(Type):
-    properties: list[PropertyStmt]
+    members: list[MemberStmt]
 
     def accept(self, visitor: Type.Visitor[T]) -> T:
         return visitor.visit_complex_type(self)
 
 
+@dataclass(frozen=True)
+class ExtensionType(Type):
+    base: Type
+    extension: ComplexType
+
+    def accept(self, visitor: Type.Visitor[T]) -> T:
+        return visitor.visit_extension_type(self)
+
+
 @dataclass(frozen=True)
 class FunctionType(Type):
     pos_args: list[Argument]

midas/ast/printer.py

@@ -111,9 +111,10 @@ class MidasAstPrinter(
             self._write_line(f'name: "{param.name.lexeme}"')
             self._write_optional_child("bound", param.bound, last=True)
 
-    def visit_property_stmt(self, stmt: m.PropertyStmt):
-        self._write_line("PropertyStmt")
+    def visit_member_stmt(self, stmt: m.MemberStmt):
+        self._write_line("MemberStmt")
         with self._child_level():
+            self._write_line(f"kind: {stmt.kind.name}")
             self._write_line(f'name: "{stmt.name.lexeme}"')
             self._write_line("type", last=True)
             with self._child_level(single=True):
@@ -129,16 +130,21 @@ class MidasAstPrinter(
                     if i == len(stmt.params) - 1:
                         self._mark_last()
                     self._print_type_param(param)
-            self._write_line("type")
-            with self._child_level(single=True):
-                stmt.type.accept(self)
-            self._write_line("operations", last=True)
+            self._write_line(f'name: "{stmt.name.lexeme}"')
+            self._write_line("params")
             with self._child_level():
-                for i, op in enumerate(stmt.operations):
+                for i, param in enumerate(stmt.params):
                     self._idx = i
-                    if i == len(stmt.operations) - 1:
+                    if i == len(stmt.params) - 1:
                         self._mark_last()
-                    op.accept(self)
+                    self._print_type_param(param)
+            self._write_line("members", last=True)
+            with self._child_level():
+                for i, member in enumerate(stmt.members):
+                    self._idx = i
+                    if i == len(stmt.members) - 1:
+                        self._mark_last()
+                    member.accept(self)
 
     def visit_op_stmt(self, stmt: m.OpStmt) -> None:
         self._write_line("OpStmt")
@@ -262,13 +268,23 @@ class MidasAstPrinter(
     def visit_complex_type(self, type: m.ComplexType) -> None:
         self._write_line("ComplexType")
         with self._child_level():
-            self._write_line("properties", last=True)
+            self._write_line("members", last=True)
             with self._child_level():
-                for i, prop in enumerate(type.properties):
+                for i, member in enumerate(type.members):
                     self._idx = i
-                    if i == len(type.properties) - 1:
+                    if i == len(type.members) - 1:
                         self._mark_last()
-                    prop.accept(self)
+                    member.accept(self)
+
+    def visit_extension_type(self, type: m.ExtensionType) -> None:
+        self._write_line("ExtensionType")
+        with self._child_level():
+            self._write_line("base")
+            with self._child_level(single=True):
+                type.base.accept(self)
+            self._write_line("extension", last=True)
+            with self._child_level(single=True):
+                type.extension.accept(self)
 
     def visit_function_type(self, type: m.FunctionType) -> None:
         self._write_line("FunctionType")
@@ -332,16 +348,24 @@ class MidasPrinter(m.Expr.Visitor[str], m.Stmt.Visitor[str], m.Type.Visitor[str]
             res += "<:" + param.bound.accept(self)
         return res
 
-    def visit_property_stmt(self, stmt: m.PropertyStmt):
-        res: str = f"{stmt.name.lexeme}: {stmt.type.accept(self)}"
+    def visit_member_stmt(self, stmt: m.MemberStmt):
+        keyword: str = {
+            m.MemberKind.PROPERTY: "prop",
+            m.MemberKind.METHOD: "def",
+        }.get(stmt.kind, "")
+        res: str = f"{keyword} {stmt.name.lexeme}: {stmt.type.accept(self)}"
         return self.indented(res)
 
     def visit_extend_stmt(self, stmt: m.ExtendStmt):
-        res: str = self.indented(f"extend {stmt.type.accept(self)}")
+        template: str = ""
+        if len(stmt.params) != 0:
+            params: list[str] = [self._print_type_param(param) for param in stmt.params]
+            template = f"[{', '.join(params)}]"
+        res: str = self.indented(f"extend {stmt.name.lexeme}{template}")
         res += " {\n"
         self.level += 1
-        for op in stmt.operations:
-            res += op.accept(self)
+        for member in stmt.members:
+            res += member.accept(self) + "\n"
         self.level -= 1
         res += self.indented("}")
         return res
@@ -411,16 +435,19 @@ class MidasPrinter(m.Expr.Visitor[str], m.Stmt.Visitor[str], m.Type.Visitor[str]
     def visit_complex_type(self, type: m.ComplexType) -> str:
         res: str = "{\n"
         self.level += 1
-        for prop in type.properties:
-            res += prop.accept(self)
+        for member in type.members:
+            res += member.accept(self)
             res += "\n"
         self.level -= 1
         res += self.indented("}")
         return res
 
+    def visit_extension_type(self, type: m.ExtensionType) -> 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]
-        kw_args: list[str] = [self._print_arg(arg) for arg in type.pos_args]
+        kw_args: list[str] = [self._print_arg(arg) for arg in type.kw_args]
         args: list[str] = pos_args
 
         if len(pos_args) != 0:
@@ -429,7 +456,7 @@ class MidasPrinter(m.Expr.Visitor[str], m.Stmt.Visitor[str], m.Type.Visitor[str]
             args.append("*")
         args += kw_args
 
-        return f"({', '.join(args)}) -> {type.returns.accept(self)}"
+        return f"fn ({', '.join(args)}) -> {type.returns.accept(self)}"
 
     def _print_arg(self, arg: m.FunctionType.Argument) -> str:
         res: str = ""

midas/checker/midas.py

@@ -8,6 +8,7 @@ from midas.checker.reporter import FileReporter, Reporter
 from midas.checker.types import (
     AliasType,
     ComplexType,
+    ExtensionType,
     Function,
     GenericType,
     Type,
@@ -29,6 +30,8 @@ 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._current_name: Optional[str] = None
+
         define_builtins(self.types)
 
     def process(self, source: str, path: Optional[str]):
@@ -65,9 +68,10 @@ class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type
             stmt.accept(self)
 
     def visit_type_stmt(self, stmt: m.TypeStmt) -> None:
+        name: str = stmt.name.lexeme
+        self._current_name = name
         params: list[TypeVar] = self._resolve_type_params(stmt.params)
 
-        name: str = stmt.name.lexeme
         type: Type = stmt.type.accept(self)
         if len(params) != 0:
             type = GenericType(name=name, params=params, body=type)
@@ -75,20 +79,25 @@ class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type
             type = AliasType(name=name, type=type)
         self.types.define_type(name, type)
         self._local_variables.clear()
+        self._current_name = None
 
-    def visit_property_stmt(self, stmt: m.PropertyStmt) -> None: ...
+    def visit_member_stmt(self, stmt: m.MemberStmt) -> None: ...
 
     def visit_extend_stmt(self, stmt: m.ExtendStmt) -> None:
         self._resolve_type_params(stmt.params)
-        base: Type = stmt.type.accept(self)
-        for op in stmt.operations:
-            right: Type = op.operand.accept(self)
-            result: Type = op.result.accept(self)
-            self.types.define_operation(
-                left=base,
-                operator=op.name.lexeme,
-                right=right,
-                result=result,
+        base_name: str = stmt.name.lexeme
+        try:
+            _ = self.get_type(base_name)
+        except NameError:
+            self.reporter.error(stmt.name.get_location(), f"Unknown type '{base_name}'")
+
+        for member in stmt.members:
+            member_type: Type = member.type.accept(self)
+            self.types.define_member(
+                base_name,
+                member.name.lexeme,
+                member_type,
+                member.kind == m.MemberKind.METHOD,
             )
 
     def visit_op_stmt(self, stmt: m.OpStmt) -> None: ...
@@ -113,12 +122,24 @@ class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type
     def visit_wildcard_expr(self, expr: m.WildcardExpr) -> None: ...
 
     def visit_named_type(self, type: m.NamedType) -> Type:
-        return self.get_type(type.name.lexeme)
+        name: str = type.name.lexeme
+        try:
+            return self.get_type(name)
+        except NameError:
+            msg: str = f"Undefined type {name}"
+            if self._current_name == name:
+                msg += ". Recursive types are not supported, use an extend block"
+            self.reporter.error(type.name.get_location(), msg)
+            return UnknownType()
 
     def visit_generic_type(self, type: m.GenericType) -> Type:
         type_: Type = type.type.accept(self)
         args: list[Type] = [arg.accept(self) for arg in type.args]
-        return self.types.apply_generic(type_, args)
+        try:
+            return self.types.apply_generic(type_, args)
+        except Exception as e:
+            self.reporter.error(type.location, f"Cannot apply generic type: {e}")
+            return UnknownType()
 
     def visit_constraint_type(self, type: m.ConstraintType) -> Type:
         type_: Type = type.type.accept(self)
@@ -126,16 +147,21 @@ class MidasTyper(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type
         # TODO
         return UnknownType()
 
-    def visit_complex_type(self, type: m.ComplexType) -> Type:
+    def visit_complex_type(self, type: m.ComplexType) -> ComplexType:
         return ComplexType(
-            properties={
-                prop.name.lexeme: prop.type.accept(self) for prop in type.properties
+            members={
+                member.name.lexeme: member.type.accept(self) for member in type.members
             }
         )
 
+    def visit_extension_type(self, type: m.ExtensionType) -> Type:
+        return ExtensionType(
+            base=type.base.accept(self),
+            extension=self.visit_complex_type(type.extension),
+        )
+
     def visit_function_type(self, type: m.FunctionType) -> Type:
         return Function(
-            name="<anonymous>",
             pos_args=[
                 Function.Argument(
                     pos=i,

midas/checker/python.py

@@ -11,13 +11,10 @@ from midas.checker.registry import TypesRegistry
 from midas.checker.reporter import FileReporter, Reporter
 from midas.checker.resolver import Resolver
 from midas.checker.types import (
-    ComplexType,
     Function,
-    Operation,
     Type,
     UnitType,
     UnknownType,
-    unfold_type,
 )
 from midas.parser.python import PythonParser
 
@@ -192,7 +189,6 @@ class PythonTyper(
             returns_hint = stmt.returns.accept(self)
             # Early define to handle simple fully-typed recursion
             inside_function: Function = Function(
-                name=stmt.name,
                 pos_args=pos_args,
                 args=args,
                 kw_args=kw_args,
@@ -227,7 +223,6 @@ class PythonTyper(
 
         # TODO: handle *args and **kwargs sinks
         function: Function = Function(
-            name=stmt.name,
             pos_args=pos_args,
             args=args,
             kw_args=kw_args,
@@ -250,8 +245,8 @@ class PythonTyper(
             case p.VariableExpr():
                 self._assign_var(location, target, value_type)
 
-            case p.GetExpr():
-                self._assign_attr(location, target, value_type)
+            case p.GetExpr(object=object, name=name):
+                self._assign_attr(location, object, name, value_type)
 
             case _:
                 if not isinstance(target, p.VariableExpr):
@@ -276,33 +271,20 @@ class PythonTyper(
                     f"Cannot assign {value_type} to variable '{name}' of type {var_type}",
                 )
 
-    def _assign_attr(self, location: Location, target: p.GetExpr, value_type: Type):
-        object: Type = self.type_of(target.object)
-        base_object: Type = unfold_type(object)
-        match base_object:
-            case ComplexType(properties=properties):
-                if target.name not in properties:
-                    self.reporter.error(
-                        target.location, f"Unknown property '{object}.{target.name}'"
-                    )
-                    return
-
-                prop_type: Type = properties[target.name]
-                if not self.is_subtype(value_type, prop_type):
-                    self.reporter.error(
-                        location,
-                        f"Cannot assign {value_type} to property '{object}.{target.name}' of type {prop_type}",
-                    )
-                    return
-
-            case UnknownType():
-                pass
-
-            case _:
-                self.reporter.error(
-                    target.location,
-                    f"Cannot assign {value_type} to unknown property '{object}.{target.name}'",
-                )
+    def _assign_attr(
+        self, location: Location, object: p.Expr, name: str, value_type: Type
+    ):
+        object_type: Type = self.type_of(object)
+        member: Optional[Type] = self.types.lookup_member(object_type, name)
+        if member is None:
+            self.reporter.error(location, f"Unknown member '{name}' of {object_type}")
+            return
+        self.logger.debug(f"Member '{name}' of {object_type} has type {member}")
+        if not self.is_subtype(value_type, member):
+            self.reporter.error(
+                location,
+                f"Cannot assign {value_type} to member '{object_type}.{name}' of type {member}",
+            )
 
     def visit_return_stmt(self, stmt: p.ReturnStmt) -> None:
         type: Type = stmt.value.accept(self) if stmt.value is not None else UnitType()
@@ -341,47 +323,36 @@ class PythonTyper(
         left: Type = self.type_of(expr.left)
         right: Type = self.type_of(expr.right)
 
-        operations: list[Operation] = self.types.get_operations_by_name(method)
-        valid_operations: list[Operation] = []
-        for op in operations:
-            sig: Operation.CallSignature = op.signature
-            if self.is_subtype(left, sig.left) and self.is_subtype(right, sig.right):
-                valid_operations.append(op)
-
-        if len(valid_operations) == 0:
+        operation: Optional[Type] = self.types.lookup_member(left, method)
+        if operation is None:
             self.reporter.error(
                 expr.location,
                 f"Undefined operation {method} between {left} and {right}",
             )
             return UnknownType()
-        elif len(valid_operations) == 1:
-            self.logger.debug(f"Unique operation {method} between {left} and {right}")
-            return valid_operations[0].result
 
-        for i, op1 in enumerate(valid_operations):
-            sig1: Operation.CallSignature = op1.signature
-            best_match: bool = True
-            for j, op2 in enumerate(valid_operations):
-                if i == j:
-                    continue
-                sig2: Operation.CallSignature = op2.signature
+        match operation:
+            case Function() as function:
+                if not self._is_binary_function(function):
+                    self.reporter.error(
+                        expr.location,
+                        f"Wrong definition of binary operation. Expected function with 2 positional-only parameters, got {function}",
+                    )
+                    return UnknownType()
 
-                # If op1 is not a full overload of op2 (i.e. operands of op1 are subtypes of op2's)
-                # ambiguity -> not best match
-                if not self.is_subtype(sig1.left, sig2.left) or not self.is_subtype(
-                    sig1.right, sig2.right
-                ):
-                    best_match = False
-                    break
-                self.logger.debug(f"{op1} is a full overload of {op2}")
-            if best_match:
-                return op1.result
-
-        self.reporter.error(
-            expr.location,
-            f"Ambiguous operation {method} between {left} and {right}, multiple matching overloads: {', '.join(map(str, valid_operations))}",
-        )
-        return UnknownType()
+                rhs: Function.Argument = function.pos_args[0]
+                if not self.is_subtype(right, rhs.type):
+                    self.reporter.error(
+                        expr.location,
+                        f"Wrong type for right-hand side, expected {rhs.type}, got {right}",
+                    )
+                    return UnknownType()
+                return function.returns
+            case _:
+                self.reporter.warning(
+                    expr.location, f"Unsupported operation {operation}"
+                )
+                return UnknownType()
 
     def visit_compare_expr(self, expr: p.CompareExpr) -> Type:
         method: Optional[str] = COMPARATOR_METHODS.get(expr.operator.__class__)
@@ -422,24 +393,14 @@ class PythonTyper(
 
     def visit_get_expr(self, expr: p.GetExpr) -> Type:
         object: Type = self.type_of(expr.object)
-        base_object: Type = unfold_type(object)
-        match base_object:
-            case ComplexType(properties=properties):
-                if expr.name not in properties:
-                    self.reporter.error(
-                        expr.location, f"Unknown property '{expr.name} on {object}"
-                    )
-                    return UnknownType()
-                return properties[expr.name]
-
-            case UnknownType():
-                return UnknownType()
-
-            case _:
-                self.reporter.error(
-                    expr.location, f"Cannot get property '{expr.name}' on {object}"
-                )
-                return UnknownType()
+        member: Optional[Type] = self.types.lookup_member(object, expr.name)
+        if member is None:
+            self.reporter.error(
+                expr.location, f"Unknown member '{expr.name}' of {object}"
+            )
+            return UnknownType()
+        self.logger.debug(f"Member '{expr.name}' of {object} has type {member}")
+        return member
 
     def visit_literal_expr(self, expr: p.LiteralExpr) -> Type:
         match expr.value:
@@ -456,7 +417,11 @@ class PythonTyper(
                 return UnknownType()
 
     def visit_variable_expr(self, expr: p.VariableExpr) -> Type:
-        return self.look_up_variable(expr.name, expr) or UnknownType()
+        type: Optional[Type] = self.look_up_variable(expr.name, expr)
+        if type is None:
+            self.logger.debug(f"Unknown variable {expr.name} in {self.env.flat_dict()}")
+            self.reporter.warning(expr.location, "Unknown variable")
+        return type or UnknownType()
 
     def visit_logical_expr(self, expr: p.LogicalExpr) -> Type:
         left: Type = expr.left.accept(self)
@@ -644,3 +609,12 @@ class PythonTyper(
             )
 
         return mapped
+
+    def _is_binary_function(self, function: Function) -> bool:
+        if len(function.pos_args) != 1:
+            return False
+        if len(function.args) != 0:
+            return False
+        if len(function.kw_args) != 0:
+            return False
+        return True

midas/checker/registry.py

@@ -1,3 +1,4 @@
+import logging
 from typing import Optional
 
 from midas.checker.builtins import BUILTIN_SUBTYPES
@@ -6,17 +7,23 @@ from midas.checker.types import (
     AppliedType,
     BaseType,
     ComplexType,
+    ExtensionType,
     Function,
     GenericType,
     Operation,
+    OverloadedFunction,
     Type,
+    TypeVar,
+    UnknownType,
     substitute_typevars,
 )
 
 
 class TypesRegistry:
     def __init__(self) -> None:
+        self.logger: logging.Logger = logging.getLogger("TypesRegistry")
         self._types: dict[str, Type] = {}
+        self._members: dict[str, dict[str, Type]] = {}
         self._operations: dict[Operation.CallSignature, Type] = {}
 
     def get_type(self, name: str) -> Type:
@@ -86,6 +93,28 @@ class TypesRegistry:
         self._types[name] = type
         return type
 
+    def define_member(
+        self, type_name: str, member_name: str, member_type: Type, is_method: bool
+    ):
+        members: dict[str, Type] = self._members.setdefault(type_name, {})
+        if member_name in members:
+            if not is_method:
+                self.logger.error(
+                    f"Member '{member_name}' already defined for type {type_name}"
+                )
+                return
+            current: Type = members[member_name]
+            combined: Type
+            match current:
+                case OverloadedFunction(overloads=overloads):
+                    combined = OverloadedFunction(overloads=overloads + [member_type])
+                case _:
+                    combined = OverloadedFunction(overloads=[current, member_type])
+            members[member_name] = combined
+
+        else:
+            members[member_name] = member_type
+
     def define_operation(self, left: Type, operator: str, right: Type, result: Type):
         """Define an operation in the registry
 
@@ -143,6 +172,11 @@ class TypesRegistry:
             case (Function(), Function()):
                 return self.is_func_subtype(type1, type2)
 
+            case (TypeVar(bound=bound), _):
+                if bound is None:
+                    return False
+                return self.is_subtype(bound, type2)
+
         return False
 
     # TODO: verify the logic in here
@@ -311,3 +345,51 @@ class TypesRegistry:
                     reduced = True
                     break
         return [types[i] for i in keep]
+
+    def lookup_member(self, type: Type, member_name: str) -> Optional[Type]:
+        match type:
+            case AliasType(name=name, type=base):
+                if name in self._members:
+                    if member_name in self._members[name]:
+                        return self._members[name][member_name]
+                return self.lookup_member(base, member_name)
+
+            case AppliedType(name=name, body=body, args=args):
+                generic: Type = self.get_type(name)
+
+                if not isinstance(generic, GenericType):
+                    raise ValueError("AppliedType not derived from a GenericType")
+
+                substitutions = {
+                    type_var.name: arg for arg, type_var in zip(args, generic.params)
+                }
+                if name in self._members:
+                    if member_name in self._members[name]:
+                        member_type: Type = self._members[name][member_name]
+                        return substitute_typevars(member_type, substitutions)
+
+                member_type2: Optional[Type] = self.lookup_member(body, member_name)
+                if member_type2 is not None:
+                    member_type2 = substitute_typevars(member_type2, substitutions)
+                return member_type2
+
+            case ComplexType(members=members):
+                if member_name in members:
+                    return members[member_name]
+                self.logger.debug(f"No member '{member_name}' in {type}")
+                return None
+
+            case ExtensionType(base=base, extension=ComplexType(members=members)):
+                if member_name in members:
+                    return members[member_name]
+                self.logger.debug(
+                    f"No member '{member_name}' on {type}, looking up in base"
+                )
+                return self.lookup_member(base, member_name)
+
+            case UnknownType():
+                return UnknownType()
+
+            case _:
+                self.logger.debug(f"Can't get member on {type}")
+                return None

midas/checker/types.py

@@ -35,7 +35,6 @@ class UnitType:
 
 @dataclass(frozen=True, kw_only=True)
 class Function:
-    name: str
     pos_args: list[Argument]
     args: list[Argument]
     kw_args: list[Argument]
@@ -56,7 +55,7 @@ class Function:
                 args.append("*")
             args += list(map(str, self.kw_args))
 
-        return f"{self.name}({', '.join(args)}) -> {self.returns}"
+        return f"({', '.join(args)}) -> {self.returns}"
 
     @dataclass(frozen=True, kw_only=True)
     class Argument:
@@ -71,14 +70,31 @@ class Function:
 
 
 @dataclass(frozen=True, kw_only=True)
-class ComplexType:
-    properties: dict[str, Type]
+class OverloadedFunction:
+    overloads: list[Type]
 
     def __str__(self) -> str:
-        props: list[str] = [f"{name}: {type}" for name, type in self.properties.items()]
+        return "<overloaded function>"
+
+
+@dataclass(frozen=True, kw_only=True)
+class ComplexType:
+    members: dict[str, Type]
+
+    def __str__(self) -> str:
+        props: list[str] = [f"{name}: {type}" for name, type in self.members.items()]
         return f"{{{', '.join(props)}}}"
 
 
+@dataclass(frozen=True, kw_only=True)
+class ExtensionType:
+    base: Type
+    extension: ComplexType
+
+    def __str__(self) -> str:
+        return f"{self.base} & {self.extension}"
+
+
 @dataclass(frozen=True, kw_only=True)
 class Operation:
     signature: CallSignature
@@ -141,30 +157,49 @@ def substitute_typevars(type: Type, substitutions: dict[str, Type]) -> Type:
         case BaseType(name=name) if name in substitutions:
             return substitutions[name]
 
+        case BaseType():
+            return type
+
         case AliasType(name=name, type=type2):
             return AliasType(name=name, type=substitute_typevars(type2, substitutions))
 
         case Function(
-            name=name,
             pos_args=pos_args,
             args=args,
             kw_args=kw_args,
             returns=returns,
         ):
             return Function(
-                name=name,
                 pos_args=list(map(sub_argument, pos_args)),
                 args=list(map(sub_argument, args)),
                 kw_args=list(map(sub_argument, kw_args)),
                 returns=substitute_typevars(returns, substitutions),
             )
 
-        case ComplexType(properties=properties):
-            properties2: dict[str, Type] = {
+        case ComplexType(members=members):
+            members2: dict[str, Type] = {
                 name: substitute_typevars(prop, substitutions)
-                for name, prop in properties.items()
+                for name, prop in members.items()
             }
-            return ComplexType(properties=properties2)
+            return ComplexType(members=members2)
+
+        case ExtensionType(base=base, extension=ComplexType(members=members)):
+            return ExtensionType(
+                base=substitute_typevars(base, substitutions),
+                extension=ComplexType(
+                    members={
+                        name: substitute_typevars(prop, substitutions)
+                        for name, prop in members.items()
+                    }
+                ),
+            )
+
+        case AppliedType(name=name, args=args, body=body):
+            return AppliedType(
+                name=name,
+                args=[substitute_typevars(arg, substitutions) for arg in args],
+                body=substitute_typevars(body, substitutions),
+            )
 
         case TypeVar(name=name):
             if name in substitutions:
@@ -192,7 +227,9 @@ Type = (
     | UnknownType
     | UnitType
     | Function
+    | OverloadedFunction
     | ComplexType
+    | ExtensionType
     | TypeVar
     | GenericType
     | AppliedType

midas/cli/highlighter.py

@@ -232,15 +232,14 @@ class MidasHighlighter(
         self.wrap(LocatableToken(stmt.name), "type-name")
         stmt.type.accept(self)
 
-    def visit_property_stmt(self, stmt: m.PropertyStmt) -> None:
-        self.wrap(stmt, "property")
+    def visit_member_stmt(self, stmt: m.MemberStmt) -> None:
+        self.wrap(stmt, "member")
         stmt.type.accept(self)
 
     def visit_extend_stmt(self, stmt: m.ExtendStmt) -> None:
         self.wrap(stmt, "extend")
-        stmt.type.accept(self)
-        for op in stmt.operations:
-            op.accept(self)
+        for member in stmt.members:
+            member.accept(self)
 
     def visit_op_stmt(self, stmt: m.OpStmt) -> None:
         self.wrap(stmt, "op")
@@ -298,8 +297,8 @@ class MidasHighlighter(
 
     def visit_complex_type(self, type: m.ComplexType) -> None:
         self.wrap(type, "complex-type")
-        for prop in type.properties:
-            prop.accept(self)
+        for member in type.members:
+            member.accept(self)
 
     def visit_function_type(self, type: m.FunctionType) -> None:
         self.wrap(type, "function")
@@ -307,6 +306,11 @@ class MidasHighlighter(
             arg.type.accept(self)
         type.returns.accept(self)
 
+    def visit_extension_type(self, type: m.ExtensionType) -> None:
+        self.wrap(type, "extension")
+        type.base.accept(self)
+        type.extension.accept(self)
+
 
 class DiagnosticsHighlighter(Highlighter):
     EXTRA_CSS_PATH: Optional[Path] = Path(__file__).parent / "hl_diagnostic.css"

midas/cli/main.py

@@ -88,24 +88,50 @@ def print_diagnostic(lines: list[str], diagnostic: Diagnostic, indent: int = 4):
 @click.option("-l", "--highlight", type=click.File("w"))
 @click.option("-t", "--types", type=click.File("r"), multiple=True)
 @click.option("-v", "--verbose", is_flag=True)
+@click.option("-j", "--show-judgements", is_flag=True)
 @click.argument("file", type=click.File("r"))
 def compile(
     highlight: Optional[TextIO],
     types: tuple[TextIO],
     verbose: bool,
+    show_judgements: bool,
     file: TextIO,
 ):
     logging.basicConfig(level=logging.DEBUG if verbose else logging.WARN)
     source: str = file.read()
+    source_path: Path = Path(file.name).resolve()
 
     checker = TypeChecker()
-    for path in types:
-        checker.import_midas(Path(path.name).resolve())
+    for types_file in types:
+        checker.import_midas(Path(types_file.name).resolve())
 
-    checker.type_check_source(source, str(Path(file.name).resolve()))
-    diagnostics: list[Diagnostic] = checker.diagnostics
+    checker.type_check_source(source, str(source_path))
+    diagnostics: list[Diagnostic] = checker.diagnostics.copy()
     lines: list[str] = source.split("\n")
+    files: dict[Optional[str], list[str]] = {None: []}
+
+    if show_judgements:
+        for expr, type in checker.python_typer.judgements:
+            print(f"Judged that {expr} at {expr.location} is of type {type}")
+            diagnostics.append(
+                Diagnostic(
+                    file_path=str(source_path),
+                    location=expr.location,
+                    type=DiagnosticType.INFO,
+                    message=f"Type: {type}",
+                )
+            )
+
     for diagnostic in diagnostics:
+        filename: Optional[str] = diagnostic.file_path
+        if filename is not None and filename not in files:
+            path: Path = Path(filename)
+            if path.exists() and path.is_file():
+                files[filename] = path.read_text().split("\n")
+            else:
+                files[filename] = []
+
+        lines: list[str] = files[filename]
         print_diagnostic(lines, diagnostic)
 
     if verbose:

midas/lexer/token.py

@@ -50,6 +50,9 @@ class TokenType(Enum):
     PREDICATE = auto()
     EXTEND = auto()
     WHERE = auto()
+    PROP = auto()
+    DEF = auto()
+    FUNC = auto()
 
     # Misc
     COMMENT = auto()
@@ -67,6 +70,9 @@ KEYWORDS: dict[str, TokenType] = {
     "true": TokenType.TRUE,
     "false": TokenType.FALSE,
     "none": TokenType.NONE,
+    "prop": TokenType.PROP,
+    "def": TokenType.DEF,
+    "fn": TokenType.FUNC,
 }
 
 

midas/parser/midas.py

@@ -7,16 +7,18 @@ from midas.ast.midas import (
     ConstraintType,
     Expr,
     ExtendStmt,
+    ExtensionType,
     FunctionType,
     GenericType,
     GetExpr,
     GroupingExpr,
     LiteralExpr,
     LogicalExpr,
+    MemberKind,
+    MemberStmt,
     NamedType,
     OpStmt,
     PredicateStmt,
-    PropertyStmt,
     Stmt,
     Type,
     TypeParam,
@@ -163,7 +165,19 @@ class MidasParser(Parser):
         Returns:
             TypeExpr: the parsed type expression
         """
-        return self.constraint_type()
+        base: Type
+        if self.match(TokenType.FUNC):
+            base = self.function()
+        else:
+            base = self.constraint_type()
+        if self.match(TokenType.AND):
+            extension: ComplexType = self.complex_type()
+            return ExtensionType(
+                location=Location.span(base.location, extension.location),
+                base=base,
+                extension=extension,
+            )
+        return base
 
     def constraint_type(self) -> Type:
         type: Type = self.base_type()
@@ -215,30 +229,32 @@ class MidasParser(Parser):
             name=name,
         )
 
-    def complex_type(self) -> Type:
+    def complex_type(self) -> ComplexType:
         """Parse a type definition body
 
         A type definition body is a set of whitespace-separated
         property statements enclosed in curly braces
 
         Returns:
-            list[PropertyStmt]: the parsed type properties
+            ComplexType: the parsed complex type
         """
         left: Token = self.consume(
             TokenType.LEFT_BRACE, "Expected '{' to start type body"
         )
-        properties: list[PropertyStmt] = []
+        members: list[MemberStmt] = []
+        # TODO: add keyword to differentiate properties and methods,
+        # and allow multiple methods with the same name but not properties
         names: set[str] = set()
         while not self.check(TokenType.RIGHT_BRACE) and not self.is_at_end():
-            prop: PropertyStmt = self.property_stmt()
-            if prop.name.lexeme in names:
-                raise self.error(prop.name, "Duplicate property")
-            names.add(prop.name.lexeme)
-            properties.append(prop)
+            member: MemberStmt = self.member_stmt()
+            # if member.name.lexeme in names:
+            #    raise self.error(member.name, "Duplicate property")
+            # names.add(member.name.lexeme)
+            members.append(member)
         right: Token = self.consume(TokenType.RIGHT_BRACE, "Unclosed type body")
         return ComplexType(
             location=left.location_to(right),
-            properties=properties,
+            members=members,
         )
 
     def constraint(self) -> Expr:
@@ -376,21 +392,31 @@ class MidasParser(Parser):
                 return True
         return False
 
-    def property_stmt(self) -> PropertyStmt:
-        """Parse a property statement
+    def member_stmt(self) -> MemberStmt:
+        """Parse a member statement
 
-        A type property statement is written `name: Type` or `name: Type where Condition`
+        A type member statement is written `prop name: Type` or `def name: Type`
 
         Returns:
-            PropertyStmt: the parsed property statement
+            MemberStmt: the parsed member statement
         """
-        name: Token = self.consume_identifier("Expected property name")
-        self.consume(TokenType.COLON, "Expected ':' after property name")
+        kind: MemberKind
+        if self.match(TokenType.PROP):
+            kind = MemberKind.PROPERTY
+        elif self.match(TokenType.DEF):
+            kind = MemberKind.METHOD
+        else:
+            raise self.error(self.peek(), "Expected 'prop' or 'def'")
+
+        name: Token = self.consume_identifier("Expected member name")
+        self.consume(TokenType.COLON, "Expected ':' after member name")
+
         type: Type = self.type_expr()
-        return PropertyStmt(
+        return MemberStmt(
             location=name.location_to(self.previous()),
             name=name,
             type=type,
+            kind=kind,
         )
 
     def extend_declaration(self) -> ExtendStmt:
@@ -402,20 +428,20 @@ class MidasParser(Parser):
             ExtendStmt: the parsed extension statement
         """
         keyword: Token = self.previous()
+        name: Token = self.consume_identifier("Expected type name")
         params: list[TypeParam] = self.type_params()
 
-        type: Type = self.type_expr()
         self.consume(TokenType.LEFT_BRACE, "Expected '{' to start extend body")
-        operations: list[OpStmt] = []
+        members: list[MemberStmt] = []
         while not self.is_at_end() and not self.check(TokenType.RIGHT_BRACE):
-            operations.append(self.op_declaration())
+            members.append(self.member_stmt())
         self.consume(TokenType.RIGHT_BRACE, "Unclosed extend body")
         location: Location = keyword.location_to(self.previous())
         return ExtendStmt(
             location=location,
+            name=name,
             params=params,
-            type=type,
-            operations=operations,
+            members=members,
         )
 
     def op_declaration(self) -> OpStmt:
@@ -487,12 +513,12 @@ class MidasParser(Parser):
                     name = self.advance()
                     self.advance()
                 type: Type = self.type_expr()
-                required: bool = self.match(TokenType.QMARK)
+                optional: bool = self.match(TokenType.QMARK)
                 arg = FunctionType.Argument(
                     location=None,
                     name=name,
                     type=type,
-                    required=required,
+                    required=not optional,
                 )
                 if positional:
                     pos_args.append(arg)

tests/serializer/midas.py

@@ -6,16 +6,17 @@ from midas.ast.midas import (
     ConstraintType,
     Expr,
     ExtendStmt,
+    ExtensionType,
     FunctionType,
     GenericType,
     GetExpr,
     GroupingExpr,
     LiteralExpr,
     LogicalExpr,
+    MemberStmt,
     NamedType,
     OpStmt,
     PredicateStmt,
-    PropertyStmt,
     Stmt,
     Type,
     TypeParam,
@@ -58,9 +59,10 @@ class MidasAstJsonSerializer(
             "bound": self._serialize_optional(param.bound),
         }
 
-    def visit_property_stmt(self, stmt: PropertyStmt) -> dict:
+    def visit_member_stmt(self, stmt: MemberStmt) -> dict:
         return {
-            "_type": "PropertyStmt",
+            "_type": "MemberStmt",
+            "kind": stmt.kind.name,
             "name": stmt.name.lexeme,
             "type": stmt.type.accept(self),
         }
@@ -68,8 +70,9 @@ class MidasAstJsonSerializer(
     def visit_extend_stmt(self, stmt: ExtendStmt) -> dict:
         return {
             "_type": "ExtendStmt",
-            "type": stmt.type.accept(self),
-            "operations": self._serialize_list(stmt.operations),
+            "name": stmt.name.lexeme,
+            "params": [self._serialize_type_param(param) for param in stmt.params],
+            "members": self._serialize_list(stmt.members),
         }
 
     def visit_op_stmt(self, stmt: OpStmt) -> dict:
@@ -163,7 +166,7 @@ class MidasAstJsonSerializer(
     def visit_complex_type(self, type: ComplexType) -> dict:
         return {
             "_type": "ComplexType",
-            "properties": self._serialize_list(type.properties),
+            "members": self._serialize_list(type.members),
         }
 
     def visit_function_type(self, type: FunctionType) -> dict:
@@ -180,3 +183,10 @@ class MidasAstJsonSerializer(
             "type": arg.type.accept(self),
             "required": arg.required,
         }
+
+    def visit_extension_type(self, type: ExtensionType) -> dict:
+        return {
+            "_type": "ExtensionType",
+            "base": type.base.accept(self),
+            "extension": type.extension.accept(self),
+        }