feat(checker)!: resolve new types

examples/00_syntax_prototype/05_custom_types_v3.midas

@@ -0,0 +1,33 @@
+type Foo1 = float
+type Foo2 = float where (_ > 3)
+type Foo3 = int | float
+type Foo4 = int where (_ > 3) | float where (_ > 3)
+type Foo5 = (int | float) where (_ > 3)
+type Foo6 = {
+    foo: float
+    bar: float where (_ > 3)
+}
+
+type Foo7[T] = T where (_ > 3)
+type Foo8[A, B<:int] = {
+    a: A
+    b: B
+}
+
+type Complex = {
+    a: int
+    b: int
+}
+type Complex2 = Complex where (_.a > 3 & _.b < 5)
+
+predicate Positive(n: int) = n >= 0
+
+extend Foo1 {
+    op __add__(Foo1) -> Foo1
+}
+
+extend Foo7[T] {
+    op __add__(Foo7[T]) -> Foo7[T]
+}
+
+type Optional[T] = None | T

gen/midas.py

@@ -13,40 +13,38 @@ from midas.lexer.token import Token
 
 
 ###> Stmt | Statements
-class SimpleTypeStmt:
+class TypeStmt:
     name: Token
-    template: Optional[TemplateExpr]
+    params: list[Param]
-    base: TypeExpr
+    type: Type
-    constraint: Optional[Expr]
 
-
+    @dataclass(frozen=True, kw_only=True)
-class ComplexTypeStmt:
+    class Param:
+        location: Location
         name: Token
-    template: Optional[TemplateExpr]
+        bound: Optional[Type]
-    properties: list[PropertyStmt]
 
 
 class PropertyStmt:
     name: Token
-    type: TypeExpr
+    type: Type
-    constraint: Optional[Expr]
 
 
 class ExtendStmt:
-    type: TypeExpr
+    type: Type
     operations: list[OpStmt]
 
 
 class OpStmt:
     name: Token
-    operand: TypeExpr
+    operand: Type
-    result: TypeExpr
+    result: Type
 
 
 class PredicateStmt:
     name: Token
     subject: Token
-    type: TypeExpr
+    type: Type
     condition: Expr
 
 
@@ -54,9 +52,6 @@ class PredicateStmt:
 
 
 ###> Expr | Expressions
-class SimpleTypeExpr:
-    name: Token
-    optional: bool
 
 
 class LogicalExpr:
@@ -97,14 +92,31 @@ class WildcardExpr:
     token: Token
 
 
-class TemplateExpr:
+###<
-    type: TypeExpr
+
+###> Type | Types
 
 
-class TypeExpr:
+class NamedType:
     name: Token
-    template: Optional[TemplateExpr]
+
-    optional: bool
+
+class GenericType:
+    type: Type
+    params: list[Type]
+
+
+class ConstraintType:
+    type: Type
+    constraint: Expr
+
+
+class UnionType:
+    types: list[Type]
+
+
+class ComplexType:
+    properties: list[PropertyStmt]
 
 
 ###<

midas/ast/midas.py

@@ -28,10 +28,7 @@ class Stmt(ABC):
 
     class Visitor(ABC, Generic[T]):
         @abstractmethod
-        def visit_simple_type_stmt(self, stmt: SimpleTypeStmt) -> T: ...
+        def visit_type_stmt(self, stmt: TypeStmt) -> T: ...
-
-        @abstractmethod
-        def visit_complex_type_stmt(self, stmt: ComplexTypeStmt) -> T: ...
 
         @abstractmethod
         def visit_property_stmt(self, stmt: PropertyStmt) -> T: ...
@@ -47,31 +44,25 @@ class Stmt(ABC):
 
 
 @dataclass(frozen=True)
-class SimpleTypeStmt(Stmt):
+class TypeStmt(Stmt):
     name: Token
-    template: Optional[TemplateExpr]
+    params: list[Param]
-    base: TypeExpr
+    type: Type
-    constraint: Optional[Expr]
+
+    @dataclass(frozen=True, kw_only=True)
+    class Param:
+        location: Location
+        name: Token
+        bound: Optional[Type]
 
     def accept(self, visitor: Stmt.Visitor[T]) -> T:
-        return visitor.visit_simple_type_stmt(self)
+        return visitor.visit_type_stmt(self)
-
-
-@dataclass(frozen=True)
-class ComplexTypeStmt(Stmt):
-    name: Token
-    template: Optional[TemplateExpr]
-    properties: list[PropertyStmt]
-
-    def accept(self, visitor: Stmt.Visitor[T]) -> T:
-        return visitor.visit_complex_type_stmt(self)
 
 
 @dataclass(frozen=True)
 class PropertyStmt(Stmt):
     name: Token
-    type: TypeExpr
+    type: Type
-    constraint: Optional[Expr]
 
     def accept(self, visitor: Stmt.Visitor[T]) -> T:
         return visitor.visit_property_stmt(self)
@@ -79,7 +70,7 @@ class PropertyStmt(Stmt):
 
 @dataclass(frozen=True)
 class ExtendStmt(Stmt):
-    type: TypeExpr
+    type: Type
     operations: list[OpStmt]
 
     def accept(self, visitor: Stmt.Visitor[T]) -> T:
@@ -89,8 +80,8 @@ class ExtendStmt(Stmt):
 @dataclass(frozen=True)
 class OpStmt(Stmt):
     name: Token
-    operand: TypeExpr
+    operand: Type
-    result: TypeExpr
+    result: Type
 
     def accept(self, visitor: Stmt.Visitor[T]) -> T:
         return visitor.visit_op_stmt(self)
@@ -100,7 +91,7 @@ class OpStmt(Stmt):
 class PredicateStmt(Stmt):
     name: Token
     subject: Token
-    type: TypeExpr
+    type: Type
     condition: Expr
 
     def accept(self, visitor: Stmt.Visitor[T]) -> T:
@@ -120,9 +111,6 @@ class Expr(ABC):
     def accept(self, visitor: Visitor[T]) -> T: ...
 
     class Visitor(ABC, Generic[T]):
-        @abstractmethod
-        def visit_simple_type_expr(self, expr: SimpleTypeExpr) -> T: ...
-
         @abstractmethod
         def visit_logical_expr(self, expr: LogicalExpr) -> T: ...
 
@@ -147,21 +135,6 @@ class Expr(ABC):
         @abstractmethod
         def visit_wildcard_expr(self, expr: WildcardExpr) -> T: ...
 
-        @abstractmethod
-        def visit_template_expr(self, expr: TemplateExpr) -> T: ...
-
-        @abstractmethod
-        def visit_type_expr(self, expr: TypeExpr) -> T: ...
-
-
-@dataclass(frozen=True)
-class SimpleTypeExpr(Expr):
-    name: Token
-    optional: bool
-
-    def accept(self, visitor: Expr.Visitor[T]) -> T:
-        return visitor.visit_simple_type_expr(self)
-
 
 @dataclass(frozen=True)
 class LogicalExpr(Expr):
@@ -233,19 +206,72 @@ class WildcardExpr(Expr):
         return visitor.visit_wildcard_expr(self)
 
 
-@dataclass(frozen=True)
+#########
-class TemplateExpr(Expr):
+# Types #
-    type: TypeExpr
+#########
 
-    def accept(self, visitor: Expr.Visitor[T]) -> T:
+
-        return visitor.visit_template_expr(self)
+@dataclass(frozen=True, kw_only=True)
+class Type(ABC):
+    location: Location
+
+    @abstractmethod
+    def accept(self, visitor: Visitor[T]) -> T: ...
+
+    class Visitor(ABC, Generic[T]):
+        @abstractmethod
+        def visit_named_type(self, type: NamedType) -> T: ...
+
+        @abstractmethod
+        def visit_generic_type(self, type: GenericType) -> T: ...
+
+        @abstractmethod
+        def visit_constraint_type(self, type: ConstraintType) -> T: ...
+
+        @abstractmethod
+        def visit_union_type(self, type: UnionType) -> T: ...
+
+        @abstractmethod
+        def visit_complex_type(self, type: ComplexType) -> T: ...
 
 
 @dataclass(frozen=True)
-class TypeExpr(Expr):
+class NamedType(Type):
     name: Token
-    template: Optional[TemplateExpr]
-    optional: bool
 
-    def accept(self, visitor: Expr.Visitor[T]) -> T:
+    def accept(self, visitor: Type.Visitor[T]) -> T:
-        return visitor.visit_type_expr(self)
+        return visitor.visit_named_type(self)
+
+
+@dataclass(frozen=True)
+class GenericType(Type):
+    type: Type
+    params: list[Type]
+
+    def accept(self, visitor: Type.Visitor[T]) -> T:
+        return visitor.visit_generic_type(self)
+
+
+@dataclass(frozen=True)
+class ConstraintType(Type):
+    type: Type
+    constraint: Expr
+
+    def accept(self, visitor: Type.Visitor[T]) -> T:
+        return visitor.visit_constraint_type(self)
+
+
+@dataclass(frozen=True)
+class UnionType(Type):
+    types: list[Type]
+
+    def accept(self, visitor: Type.Visitor[T]) -> T:
+        return visitor.visit_union_type(self)
+
+
+@dataclass(frozen=True)
+class ComplexType(Type):
+    properties: list[PropertyStmt]
+
+    def accept(self, visitor: Type.Visitor[T]) -> T:
+        return visitor.visit_complex_type(self)

midas/ast/printer.py

@@ -85,40 +85,39 @@ class AstPrinter(Generic[T]):
                 child.accept(self)
 
 
-class MidasAstPrinter(AstPrinter, m.Expr.Visitor[None], m.Stmt.Visitor[None]):
+class MidasAstPrinter(
+    AstPrinter, m.Expr.Visitor[None], m.Stmt.Visitor[None], m.Type.Visitor[None]
+):
     # Statements
 
-    def visit_simple_type_stmt(self, stmt: m.SimpleTypeStmt):
+    def visit_type_stmt(self, stmt: m.TypeStmt) -> None:
-        self._write_line("SimpleTypeStmt")
+        self._write_line("TypeStmt")
         with self._child_level():
             self._write_line(f'name: "{stmt.name.lexeme}"')
-            self._write_optional_child("template", stmt.template)
+            self._write_line("params")
-            self._write_line("base")
-            with self._child_level(single=True):
-                stmt.base.accept(self)
-            self._write_optional_child("constraint", stmt.constraint, last=True)
-
-    def visit_complex_type_stmt(self, stmt: m.ComplexTypeStmt):
-        self._write_line("ComplexTypeStmt")
             with self._child_level():
-            self._write_line(f'name: "{stmt.name.lexeme}"')
+                for i, param in enumerate(stmt.params):
-            self._write_optional_child("template", stmt.template)
-            self._write_line("properties", last=True)
-            with self._child_level():
-                for i, prop in enumerate(stmt.properties):
                     self._idx = i
-                    if i == len(stmt.properties) - 1:
+                    if i == len(stmt.params) - 1:
                         self._mark_last()
-                    prop.accept(self)
+                    self._print_type_stmt_param(param)
+            self._write_line("type", last=True)
+            with self._child_level(single=True):
+                stmt.type.accept(self)
+
+    def _print_type_stmt_param(self, param: m.TypeStmt.Param) -> None:
+        self._write_line("Param")
+        with self._child_level():
+            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")
         with self._child_level():
             self._write_line(f'name: "{stmt.name.lexeme}"')
-            self._write_line("type")
+            self._write_line("type", last=True)
             with self._child_level(single=True):
                 stmt.type.accept(self)
-            self._write_optional_child("constraint", stmt.constraint, last=True)
 
     def visit_extend_stmt(self, stmt: m.ExtendStmt) -> None:
         self._write_line("ExtendStmt")
@@ -161,12 +160,6 @@ class MidasAstPrinter(AstPrinter, m.Expr.Visitor[None], m.Stmt.Visitor[None]):
 
     # Expressions
 
-    def visit_simple_type_expr(self, expr: m.SimpleTypeExpr):
-        self._write_line("SimpleTypeExpr")
-        with self._child_level():
-            self._write_line(f'name: "{expr.name.lexeme}"')
-            self._write_line(f"optional: {expr.optional}", last=True)
-
     def visit_logical_expr(self, expr: m.LogicalExpr):
         self._write_line("LogicalExpr")
         with self._child_level():
@@ -230,22 +223,59 @@ class MidasAstPrinter(AstPrinter, m.Expr.Visitor[None], m.Stmt.Visitor[None]):
     def visit_wildcard_expr(self, expr: m.WildcardExpr) -> None:
         self._write_line("WildcardExpr")
 
-    def visit_template_expr(self, expr: m.TemplateExpr) -> None:
+    def visit_named_type(self, type: m.NamedType) -> None:
-        self._write_line("TemplateExpr")
+        self._write_line("NamedType")
-        with self._child_level(single=True):
+        with self._child_level():
+            self._write_line(f'name: "{type.name.lexeme}"', last=True)
+
+    def visit_generic_type(self, type: m.GenericType) -> None:
+        self._write_line("GenericType")
+        with self._child_level():
+            self._write_line("type")
+            with self._child_level():
+                type.type.accept(self)
+            self._write_line("params", last=True)
+            with self._child_level():
+                for i, param in enumerate(type.params):
+                    self._idx = i
+                    if i == len(type.params) - 1:
+                        self._mark_last()
+                    param.accept(self)
+
+    def visit_constraint_type(self, type: m.ConstraintType) -> None:
+        self._write_line("ConstraintType")
+        with self._child_level():
             self._write_line("type")
             with self._child_level(single=True):
-                expr.type.accept(self)
+                type.type.accept(self)
+            self._write_line("constraint", last=True)
+            with self._child_level(single=True):
+                type.constraint.accept(self)
 
-    def visit_type_expr(self, expr: m.TypeExpr):
+    def visit_union_type(self, type: m.UnionType) -> None:
-        self._write_line("TypeExpr")
+        self._write_line("UnionType")
         with self._child_level():
-            self._write_line(f'name: "{expr.name.lexeme}"')
+            self._write_line("types", last=True)
-            self._write_optional_child("template", expr.template)
+            with self._child_level():
-            self._write_line(f"optional: {expr.optional}", last=True)
+                for i, type_ in enumerate(type.types):
+                    self._idx = i
+                    if i == len(type.types) - 1:
+                        self._mark_last()
+                    type_.accept(self)
+
+    def visit_complex_type(self, type: m.ComplexType) -> None:
+        self._write_line("ComplexType")
+        with self._child_level():
+            self._write_line("properties", last=True)
+            with self._child_level():
+                for i, prop in enumerate(type.properties):
+                    self._idx = i
+                    if i == len(type.properties) - 1:
+                        self._mark_last()
+                    prop.accept(self)
 
 
-class MidasPrinter(m.Expr.Visitor[str], m.Stmt.Visitor[str]):
+class MidasPrinter(m.Expr.Visitor[str], m.Stmt.Visitor[str], m.Type.Visitor[str]):
     def __init__(self, indent: int = 4):
         self.indent: int = indent
         self.level: int = 0
@@ -257,29 +287,24 @@ class MidasPrinter(m.Expr.Visitor[str], m.Stmt.Visitor[str]):
         self.level = 0
         return expr.accept(self)
 
-    def visit_simple_type_stmt(self, stmt: m.SimpleTypeStmt):
+    def visit_type_stmt(self, stmt: m.TypeStmt) -> str:
-        template: str = stmt.template.accept(self) if stmt.template is not None else ""
+        template: str = ""
-        res: str = f"type {stmt.name.lexeme}{template}({stmt.base.accept(self)})"
+        if len(stmt.params) != 0:
-        if stmt.constraint is not None:
+            params: list[str] = [
-            res += " where " + stmt.constraint.accept(self)
+                self._print_type_template_param(param) for param in stmt.params
+            ]
+            template = f"[{', '.join(params)}]"
+        res: str = f"type {stmt.name.lexeme}{template} = {stmt.type.accept(self)}"
         return self.indented(res)
 
-    def visit_complex_type_stmt(self, stmt: m.ComplexTypeStmt):
+    def _print_type_template_param(self, param: m.TypeStmt.Param) -> str:
-        template: str = stmt.template.accept(self) if stmt.template is not None else ""
+        res: str = param.name.lexeme
-        res: str = self.indented(f"type {stmt.name.lexeme}{template}")
+        if param.bound is not None:
-        res += " {\n"
+            res += "<:" + param.bound.accept(self)
-        self.level += 1
-        for prop in stmt.properties:
-            res += prop.accept(self)
-            res += "\n"
-        self.level -= 1
-        res += self.indented("}")
         return res
 
     def visit_property_stmt(self, stmt: m.PropertyStmt):
         res: str = f"{stmt.name.lexeme}: {stmt.type.accept(self)}"
-        if stmt.constraint is not None:
-            res += " where " + stmt.constraint.accept(self)
         return self.indented(res)
 
     def visit_extend_stmt(self, stmt: m.ExtendStmt):
@@ -304,9 +329,6 @@ class MidasPrinter(m.Expr.Visitor[str], m.Stmt.Visitor[str]):
         condition: str = stmt.condition.accept(self)
         return self.indented(f"predicate {name}({subject}: {type}) = {condition}")
 
-    def visit_simple_type_expr(self, expr: m.SimpleTypeExpr):
-        return f"{expr.name.lexeme}{'?' if expr.optional else ''}"
-
     def visit_logical_expr(self, expr: m.LogicalExpr):
         left: str = expr.left.accept(self)
         operator: str = expr.operator.lexeme
@@ -342,12 +364,34 @@ class MidasPrinter(m.Expr.Visitor[str], m.Stmt.Visitor[str]):
     def visit_wildcard_expr(self, expr: m.WildcardExpr):
         return "_"
 
-    def visit_template_expr(self, expr: m.TemplateExpr):
+    def visit_named_type(self, type: m.NamedType) -> str:
-        return f"[{expr.type.accept(self)}]"
+        return type.name.lexeme
 
-    def visit_type_expr(self, expr: m.TypeExpr):
+    def visit_generic_type(self, type: m.GenericType) -> str:
-        template: str = expr.template.accept(self) if expr.template is not None else ""
+        res: str = type.type.accept(self)
-        return f"{expr.name.lexeme}{template}{'?' if expr.optional else ''}"
+        if len(type.params) != 0:
+            params: list[str] = [param.accept(self) for param in type.params]
+            res += f"[{', '.join(params)}]"
+        return res
+
+    def visit_constraint_type(self, type: m.ConstraintType) -> str:
+        res: str = type.type.accept(self)
+        res += " where " + type.constraint.accept(self)
+        return res
+
+    def visit_union_type(self, type: m.UnionType) -> str:
+        types: list[str] = [type_.accept(self) for type_ in type.types]
+        return " | ".join(types)
+
+    def visit_complex_type(self, type: m.ComplexType) -> str:
+        res: str = "{\n"
+        self.level += 1
+        for prop in type.properties:
+            res += prop.accept(self)
+            res += "\n"
+        self.level -= 1
+        res += self.indented("}")
+        return res
 
 
 class PythonAstPrinter(

midas/checker/types.py

@@ -9,9 +9,9 @@ class BaseType:
 
 
 @dataclass(frozen=True, kw_only=True)
-class SimpleType:
+class AliasType:
     name: str
-    base: BaseType | SimpleType
+    type: Type
 
 
 @dataclass(frozen=True, kw_only=True)
@@ -39,4 +39,16 @@ class Function:
         required: bool
 
 
-Type = BaseType | SimpleType | UnknownType | UnitType | Function
+@dataclass(frozen=True, kw_only=True)
+class ComplexType:
+    properties: dict[str, Type]
+
+
+@dataclass(frozen=True, kw_only=True)
+class UnionType:
+    alternatives: list[Type]
+
+
+Type = (
+    BaseType | AliasType | UnknownType | UnitType | Function | ComplexType | UnionType
+)

midas/lexer/midas.py

@@ -18,6 +18,8 @@ class MidasLexer(Lexer):
                 self.add_token(TokenType.LEFT_BRACE)
             case "}":
                 self.add_token(TokenType.RIGHT_BRACE)
+            case "|":
+                self.add_token(TokenType.PIPE)
             case "<":
                 self.add_token(
                     TokenType.LESS_EQUAL if self.match("=") else TokenType.LESS
@@ -40,8 +42,8 @@ class MidasLexer(Lexer):
                 self.add_token(TokenType.AND)
             case "?":
                 self.add_token(TokenType.QMARK)
-            # case ",":
+            case ",":
-            #     self.add_token(TokenType.COMMA)
+                self.add_token(TokenType.COMMA)
             case "_" if not self.is_identifier_char(self.peek_next(), start=False):
                 self.add_token(TokenType.UNDERSCORE)
             case "-" if self.match(">"):

midas/lexer/token.py

@@ -17,12 +17,13 @@ class TokenType(Enum):
     LEFT_BRACE = auto()
     RIGHT_BRACE = auto()
     COLON = auto()
-    # COMMA = auto()
+    COMMA = auto()
     UNDERSCORE = auto()
     ARROW = auto()
     AND = auto()
     QMARK = auto()
     DOT = auto()
+    PIPE = auto()
 
     # Operators
     # PLUS = auto()

midas/parser/midas.py

@@ -3,22 +3,24 @@ from typing import Optional
 from midas.ast.location import Location
 from midas.ast.midas import (
     BinaryExpr,
-    ComplexTypeStmt,
+    ComplexType,
+    ConstraintType,
     Expr,
     ExtendStmt,
+    GenericType,
     GetExpr,
     GroupingExpr,
     LiteralExpr,
     LogicalExpr,
+    NamedType,
     OpStmt,
     PredicateStmt,
     PropertyStmt,
-    SimpleTypeExpr,
-    SimpleTypeStmt,
     Stmt,
-    TemplateExpr,
+    Type,
-    TypeExpr,
+    TypeStmt,
     UnaryExpr,
+    UnionType,
     VariableExpr,
     WildcardExpr,
 )
@@ -81,7 +83,7 @@ class MidasParser(Parser):
             self.synchronize()
             return None
 
-    def type_declaration(self) -> SimpleTypeStmt | ComplexTypeStmt:
+    def type_declaration(self) -> TypeStmt:
         """Parse a type declaration
 
         A type declaration can either be a simple type alias or a new complex type.
@@ -107,33 +109,22 @@ class MidasParser(Parser):
         """
         keyword: Token = self.previous()
         name: Token = self.consume(TokenType.IDENTIFIER, "Expected type name")
-        template: Optional[TemplateExpr] = None
+        params: list[TypeStmt.Param] = []
         if self.check(TokenType.LEFT_BRACKET):
-            template = self.template_expr()
+            params = self.type_stmt_params()
 
-        if self.match(TokenType.LEFT_PAREN):
+        self.consume(TokenType.EQUAL, "Expected '=' before type definition")
-            base: TypeExpr = self.type_expr()
+
-            self.consume(TokenType.RIGHT_PAREN, "Unclosed base type parenthesis")
+        type: Type = self.type_expr()
-            constraint: Optional[Expr] = None
+
-            if self.match(TokenType.WHERE):
+        return TypeStmt(
-                constraint = self.constraint()
-            return SimpleTypeStmt(
             location=keyword.location_to(self.previous()),
             name=name,
-                template=template,
+            params=params,
-                base=base,
+            type=type,
-                constraint=constraint,
-            )
-        else:
-            properties: list[PropertyStmt] = self.type_properties()
-            return ComplexTypeStmt(
-                location=keyword.location_to(self.previous()),
-                name=name,
-                template=template,
-                properties=properties,
         )
 
-    def template_expr(self) -> TemplateExpr:
+    def type_stmt_params(self) -> list[TypeStmt.Param]:
         """Parse a generic template expression
 
         A template is written `[TypeExpr]`
@@ -141,16 +132,27 @@ class MidasParser(Parser):
         Returns:
             TemplateExpr: the parsed template expression
         """
-        left: Token = self.consume(
+        self.consume(TokenType.LEFT_BRACKET, "Missing '[' before template expression")
-            TokenType.LEFT_BRACKET, "Missing '[' before template expression"
+        params: list[TypeStmt.Param] = []
+        while not self.is_at_end() and not self.check(TokenType.RIGHT_BRACKET):
+            name: Token = self.consume(TokenType.IDENTIFIER, "Expected type variable")
+            bound: Optional[Type] = None
+            if self.match(TokenType.LESS):
+                self.consume(TokenType.COLON, "Expected ':' after '<'")
+                bound = self.type_expr()
+            params.append(
+                TypeStmt.Param(
+                    location=name.location_to(self.previous()),
+                    name=name,
+                    bound=bound,
                 )
-        type: TypeExpr = self.type_expr()
-        right: Token = self.consume(
-            TokenType.RIGHT_BRACKET, "Missing ']' after template expression"
             )
-        return TemplateExpr(location=left.location_to(right), type=type)
+            if not self.match(TokenType.COMMA):
+                break
+        self.consume(TokenType.RIGHT_BRACKET, "Missing ']' after template expression")
+        return params
 
-    def type_expr(self) -> TypeExpr:
+    def type_expr(self) -> Type:
         """Parse a type expression
 
         A type is an identifier, optionally followed by a template expression.
@@ -159,30 +161,93 @@ class MidasParser(Parser):
         Returns:
             TypeExpr: the parsed type expression
         """
-        name: Token = self.consume(TokenType.IDENTIFIER, "Expected type name")
+        return self.union_type()
-        template: Optional[TemplateExpr] = None
+
-        if self.check(TokenType.LEFT_BRACKET):
+    def union_type(self) -> Type:
-            template = self.template_expr()
+        types: list[Type] = [self.constraint_type()]
-        optional: bool = self.match(TokenType.QMARK)
+        while self.match(TokenType.PIPE):
-        return TypeExpr(
+            types.append(self.constraint_type())
-            location=name.location_to(self.previous()),
+        if len(types) == 1:
-            name=name,
+            return types[0]
-            template=template,
+        return UnionType(
-            optional=optional,
+            location=Location.span(types[0].location, types[-1].location),
+            types=types,
         )
 
-    def simple_type_expr(self) -> SimpleTypeExpr:
+    def constraint_type(self) -> Type:
-        """Parse a simple type expression
+        type: Type = self.base_type()
+        if self.match(TokenType.WHERE):
+            constraint: Expr = self.constraint()
+            return ConstraintType(
+                location=Location.span(type.location, constraint.location),
+                type=type,
+                constraint=constraint,
+            )
+        return type
 
-        A simple type is just an identifier optionally followed by a '?'
+    def base_type(self) -> Type:
+        if self.match(TokenType.LEFT_PAREN):
+            type: Type = self.type_expr()
+            self.consume(TokenType.RIGHT_PAREN, "Unclosed parenthesis")
+            return type
+
+        if self.check(TokenType.LEFT_BRACE):
+            return self.complex_type()
+
+        return self.generic_type()
+
+    def generic_type(self) -> Type:
+        type: Type = self.named_type()
+        if self.check(TokenType.LEFT_BRACKET):
+            params: list[Type] = self.type_params()
+            return GenericType(
+                location=Location.span(type.location, self.previous().get_location()),
+                type=type,
+                params=params,
+            )
+        return type
+
+    def type_params(self) -> list[Type]:
+        params: list[Type] = []
+        self.consume(TokenType.LEFT_BRACKET, "Missing '[' before generic parameters")
+        while not self.is_at_end() and not self.check(TokenType.RIGHT_BRACKET):
+            params.append(self.type_expr())
+            if not self.match(TokenType.COMMA):
+                break
+        self.consume(TokenType.RIGHT_BRACKET, "Missing ']' after generic parameters")
+        return params
+
+    def named_type(self) -> Type:
+        name: Token = self.consume(TokenType.IDENTIFIER, "Expected type name")
+        return NamedType(
+            location=name.get_location(),
+            name=name,
+        )
+
+    def complex_type(self) -> Type:
+        """Parse a type definition body
+
+        A type definition body is a set of whitespace-separated
+        property statements enclosed in curly braces
 
         Returns:
-            SimpleTypeExpr: the parsed simple type expression
+            list[PropertyStmt]: the parsed type properties
         """
-        name: Token = self.consume(TokenType.IDENTIFIER, "Expected type name")
+        left: Token = self.consume(
-        optional: bool = self.match(TokenType.QMARK)
+            TokenType.LEFT_BRACE, "Expected '{' to start type body"
-        return SimpleTypeExpr(
+        )
-            location=name.location_to(self.previous()), name=name, optional=optional
+        properties: list[PropertyStmt] = []
+        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)
+        right: Token = self.consume(TokenType.RIGHT_BRACE, "Unclosed type body")
+        return ComplexType(
+            location=left.location_to(right),
+            properties=properties,
         )
 
     def constraint(self) -> Expr:
@@ -308,27 +373,6 @@ class MidasParser(Parser):
 
         raise self.error(self.peek(), "Expected expression")
 
-    def type_properties(self) -> list[PropertyStmt]:
-        """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
-        """
-        self.consume(TokenType.LEFT_BRACE, "Expected '{' to start type body")
-        properties: list[PropertyStmt] = []
-        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)
-        self.consume(TokenType.RIGHT_BRACE, "Unclosed type body")
-        return properties
-
     def property_stmt(self) -> PropertyStmt:
         """Parse a property statement
 
@@ -339,15 +383,11 @@ class MidasParser(Parser):
         """
         name: Token = self.consume(TokenType.IDENTIFIER, "Expected property name")
         self.consume(TokenType.COLON, "Expected ':' after property name")
-        type: TypeExpr = self.type_expr()
+        type: Type = self.type_expr()
-        constraint: Optional[Expr] = None
-        if self.match(TokenType.WHERE):
-            constraint = self.constraint()
         return PropertyStmt(
             location=name.location_to(self.previous()),
             name=name,
             type=type,
-            constraint=constraint,
         )
 
     def extend_declaration(self) -> ExtendStmt:
@@ -359,7 +399,7 @@ class MidasParser(Parser):
             ExtendStmt: the parsed extension statement
         """
         keyword: Token = self.previous()
-        type: TypeExpr = self.type_expr()
+        type: Type = self.type_expr()
         self.consume(TokenType.LEFT_BRACE, "Expected '{' to start extend body")
         operations: list[OpStmt] = []
         while not self.is_at_end() and not self.check(TokenType.RIGHT_BRACE):
@@ -380,11 +420,11 @@ class MidasParser(Parser):
 
         name: Token = self.consume(TokenType.IDENTIFIER, "Expected operation name")
         self.consume(TokenType.LEFT_PAREN, "Expected '(' before operand type")
-        operand: TypeExpr = self.type_expr()
+        operand: Type = self.type_expr()
         self.consume(TokenType.RIGHT_PAREN, "Expected ')' after operand type")
 
         self.consume(TokenType.ARROW, "Expected '->' before result type")
-        result: TypeExpr = self.type_expr()
+        result: Type = self.type_expr()
 
         return OpStmt(
             location=keyword.location_to(self.previous()),
@@ -406,7 +446,7 @@ class MidasParser(Parser):
         self.consume(TokenType.LEFT_PAREN, "Expected '(' before predicate subject")
         subject: Token = self.consume(TokenType.IDENTIFIER, "Expected subject name")
         self.consume(TokenType.COLON, "Expected ':' after subject name")
-        type: TypeExpr = self.type_expr()
+        type: Type = self.type_expr()
         self.consume(TokenType.RIGHT_PAREN, "Expected ')' after predicate subject")
         self.consume(TokenType.EQUAL, "Expected '=' after predicate subject")
         condition: Expr = self.constraint()

midas/resolver/midas.py

@@ -1,11 +1,15 @@
 from typing import Optional
 
 import midas.ast.midas as m
-from midas.checker.types import BaseType, SimpleType, Type
+from midas.checker.types import (
+    Type,
+    UnionType,
+    UnknownType,
+)
 from midas.resolver.builtin import define_builtins
 
 
-class MidasResolver(m.Stmt.Visitor[None], m.Expr.Visitor[Type]):
+class MidasResolver(m.Stmt.Visitor[None], m.Expr.Visitor[None], m.Type.Visitor[Type]):
     """A resolver which evaluates Midas type definitions and build a registry"""
 
     def __init__(self) -> None:
@@ -94,20 +98,12 @@ class MidasResolver(m.Stmt.Visitor[None], m.Expr.Visitor[Type]):
         for stmt in stmts:
             stmt.accept(self)
 
-    def visit_simple_type_stmt(self, stmt: m.SimpleTypeStmt) -> None:
+    def visit_type_stmt(self, stmt: m.TypeStmt) -> None:
-        # TODO generics, optional, constraint
+        type: Type = stmt.type.accept(self)
-        base: Type = self.get_type(stmt.base.name.lexeme)
+        for param in stmt.params:
-        match base:
+            if param.bound is not None:
-            case BaseType() | SimpleType():
+                param.bound.accept(self)
-                type = SimpleType(
+        self.define_type(stmt.name.lexeme, type)
-                    name=stmt.name.lexeme,
-                    base=base,
-                )
-                self.define_type(type.name, type)
-            case _:
-                raise TypeError(f"Invalid base {base} for simple type")
-
-    def visit_complex_type_stmt(self, stmt: m.ComplexTypeStmt) -> None: ...
 
     def visit_property_stmt(self, stmt: m.PropertyStmt) -> None: ...
 
@@ -127,27 +123,44 @@ class MidasResolver(m.Stmt.Visitor[None], m.Expr.Visitor[Type]):
 
     def visit_predicate_stmt(self, stmt: m.PredicateStmt) -> None: ...
 
-    def visit_simple_type_expr(self, expr: m.SimpleTypeExpr) -> Type:
+    def visit_logical_expr(self, expr: m.LogicalExpr) -> None: ...
-        return self.get_type(expr.name.lexeme)
 
-    def visit_logical_expr(self, expr: m.LogicalExpr) -> Type: ...
+    def visit_binary_expr(self, expr: m.BinaryExpr) -> None: ...
 
-    def visit_binary_expr(self, expr: m.BinaryExpr) -> Type: ...
+    def visit_unary_expr(self, expr: m.UnaryExpr) -> None: ...
 
-    def visit_unary_expr(self, expr: m.UnaryExpr) -> Type: ...
+    def visit_get_expr(self, expr: m.GetExpr) -> None: ...
 
-    def visit_get_expr(self, expr: m.GetExpr) -> Type: ...
+    def visit_variable_expr(self, expr: m.VariableExpr) -> None: ...
 
-    def visit_variable_expr(self, expr: m.VariableExpr) -> Type: ...
+    def visit_grouping_expr(self, expr: m.GroupingExpr) -> None:
-
-    def visit_grouping_expr(self, expr: m.GroupingExpr) -> Type:
         return expr.expr.accept(self)
 
-    def visit_literal_expr(self, expr: m.LiteralExpr) -> Type: ...
+    def visit_literal_expr(self, expr: m.LiteralExpr) -> None: ...
 
-    def visit_wildcard_expr(self, expr: m.WildcardExpr) -> Type: ...
+    def visit_wildcard_expr(self, expr: m.WildcardExpr) -> None: ...
 
-    def visit_template_expr(self, expr: m.TemplateExpr) -> Type: ...
+    def visit_named_type(self, type: m.NamedType) -> Type:
+        return self.get_type(type.name.lexeme)
 
-    def visit_type_expr(self, expr: m.TypeExpr) -> Type:
+    def visit_generic_type(self, type: m.GenericType) -> Type:
-        return self.get_type(expr.name.lexeme)
+        type_: Type = type.type.accept(self)
+        params: list[Type] = [param.accept(self) for param in type.params]
+        # TODO
+        return UnknownType()
+
+    def visit_constraint_type(self, type: m.ConstraintType) -> Type:
+        type_: Type = type.type.accept(self)
+        type.constraint.accept(self)
+        # TODO
+        return UnknownType()
+
+    def visit_union_type(self, type: m.UnionType) -> Type:
+        types: list[Type] = [type_.accept(self) for type_ in type.types]
+        return UnionType(alternatives=types)
+
+    def visit_complex_type(self, type: m.ComplexType) -> Type:
+        for prop in type.properties:
+            prop.accept(self)
+        # TODO
+        return UnknownType()