diff --git a/midas/checker/types.py b/midas/checker/types.py
index 71765ad..ea94b45 100644
--- a/midas/checker/types.py
+++ b/midas/checker/types.py
@@ -10,15 +10,8 @@ class BaseType:
 
 @dataclass(frozen=True, kw_only=True)
 class SimpleType:
-    base: BaseType
-
-
-@dataclass(frozen=True, kw_only=True)
-class Operation:
-    left: Type
-    operator: str
-    right: Type
-    result: Type
+    name: str
+    base: BaseType | SimpleType
 
 
 @dataclass(frozen=True, kw_only=True)
diff --git a/midas/resolver/midas.py b/midas/resolver/midas.py
new file mode 100644
index 0000000..66c3152
--- /dev/null
+++ b/midas/resolver/midas.py
@@ -0,0 +1,114 @@
+from typing import Optional
+
+import midas.ast.midas as m
+from midas.checker.types import BaseType, SimpleType, Type
+
+
+class MidasResolver(m.Stmt.Visitor[None], m.Expr.Visitor[Type]):
+    def __init__(self) -> None:
+        self._types: dict[str, Type] = {}
+        self._operations: dict[tuple[Type, str, Type], Type] = {}
+
+        self._define_builtin()
+
+    def get_type(self, name: str) -> Type:
+        type: Optional[Type] = self._types.get(name)
+        if type is None:
+            raise NameError(f"Undefined type {name}")
+        return type
+
+    def get_operation_result(self, left: Type, operator: str, right: Type) -> Type:
+        operation: tuple[Type, str, Type] = (left, operator, right)
+        result: Optional[Type] = self._operations.get(operation)
+        if result is None:
+            raise ValueError(
+                f"Undefined operation {operator} between {left} and {right}"
+            )
+        return result
+
+    def _define_builtin(self):
+        self.define_type("int", BaseType(name="int"))
+        self.define_type("float", BaseType(name="float"))
+        self.define_type("bool", BaseType(name="bool"))
+        self.define_operation(
+            left=self.get_type("int"),
+            operator="__add__",
+            right=self.get_type("int"),
+            result=self.get_type("int"),
+        )
+
+    def define_type(self, name: str, type: Type) -> Type:
+        if name in self._types:
+            raise ValueError(f"Type {name} already defined")
+        self._types[name] = type
+        return type
+
+    def define_operation(self, left: Type, operator: str, right: Type, result: Type):
+        operation: tuple[Type, str, Type] = (left, operator, right)
+        if operation in self._operations:
+            raise ValueError(
+                f"Operation {operator} already defined between {left} and {right}"
+            )
+        self._operations[operation] = result
+
+    def resolve(self, stmts: list[m.Stmt]):
+        for stmt in stmts:
+            stmt.accept(self)
+
+    def visit_simple_type_stmt(self, stmt: m.SimpleTypeStmt) -> None:
+        # TODO generics, optional, constraint
+        base: Type = self.get_type(stmt.base.name.lexeme)
+        match base:
+            case BaseType() | SimpleType():
+                type = SimpleType(
+                    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: ...
+
+    def visit_extend_stmt(self, stmt: m.ExtendStmt) -> None:
+        base: Type = stmt.type.accept(self)
+        for op in stmt.operations:
+            right: Type = op.operand.accept(self)
+            result: Type = op.result.accept(self)
+            self.define_operation(
+                left=base,
+                operator=op.name.lexeme,
+                right=right,
+                result=result,
+            )
+
+    def visit_op_stmt(self, stmt: m.OpStmt) -> None: ...
+
+    def visit_predicate_stmt(self, stmt: m.PredicateStmt) -> None: ...
+
+    def visit_simple_type_expr(self, expr: m.SimpleTypeExpr) -> Type:
+        return self.get_type(expr.name.lexeme)
+
+    def visit_logical_expr(self, expr: m.LogicalExpr) -> Type: ...
+
+    def visit_binary_expr(self, expr: m.BinaryExpr) -> Type: ...
+
+    def visit_unary_expr(self, expr: m.UnaryExpr) -> Type: ...
+
+    def visit_get_expr(self, expr: m.GetExpr) -> Type: ...
+
+    def visit_variable_expr(self, expr: m.VariableExpr) -> Type: ...
+
+    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_wildcard_expr(self, expr: m.WildcardExpr) -> Type: ...
+
+    def visit_template_expr(self, expr: m.TemplateExpr) -> Type: ...
+
+    def visit_type_expr(self, expr: m.TypeExpr) -> Type:
+        return self.get_type(expr.name.lexeme)