diff --git a/phasm/ourlang.py b/phasm/ourlang.py
index 5f19d2e..3338ce4 100644
--- a/phasm/ourlang.py
+++ b/phasm/ourlang.py
@@ -21,18 +21,22 @@ from .typing import (
     TypeTuple, TypeTupleMember,
     TypeStaticArray, TypeStaticArrayMember,
     TypeStruct, TypeStructMember,
+
+    TypeVar,
 )
 
 class Expression:
     """
     An expression within a statement
     """
-    __slots__ = ('type', )
+    __slots__ = ('type', 'type_var', )
 
     type: TypeBase
+    type_var: Optional[TypeVar]
 
     def __init__(self, type_: TypeBase) -> None:
         self.type = type_
+        self.type_var = None
 
 class Constant(Expression):
     """
diff --git a/phasm/typer.py b/phasm/typer.py
new file mode 100644
index 0000000..d21f823
--- /dev/null
+++ b/phasm/typer.py
@@ -0,0 +1,71 @@
+"""
+Type checks and enriches the given ast
+"""
+from math import ceil, log2
+
+from . import ourlang
+
+from .typing import Context, TypeConstraintBitWidth, TypeConstraintSigned, TypeVar
+
+def phasm_type(inp: ourlang.Module) -> None:
+    module(inp)
+
+def constant(ctx: 'Context', inp: ourlang.Constant) -> 'TypeVar':
+    if getattr(inp, 'value', int):
+        result = ctx.new_var()
+
+        # Need at least this many bits to store this constant value
+        result.add_constraint(TypeConstraintBitWidth(minb=len(bin(inp.value)) - 2)) # type: ignore
+        # Don't dictate anything about signedness - you can use a signed
+        # constant in an unsigned variable if the bits fit
+        result.add_constraint(TypeConstraintSigned(None))
+
+        result.add_location(str(inp.value)) # type: ignore
+
+        inp.type_var = result
+
+        return result
+
+    raise NotImplementedError(constant, inp)
+
+def expression(ctx: 'Context', inp: ourlang.Expression) -> 'TypeVar':
+    if isinstance(inp, ourlang.Constant):
+        return constant(ctx, inp)
+
+    if isinstance(inp, ourlang.BinaryOp):
+        left = expression(ctx, inp.left)
+        right = expression(ctx, inp.right)
+        ctx.unify(left, right)
+        return left
+
+    raise NotImplementedError(expression, inp)
+
+def function(ctx: 'Context', inp: ourlang.Function) -> None:
+    bctx = ctx.clone() # Clone whenever we go into a block
+
+    assert len(inp.statements) == 1 # TODO
+
+    assert isinstance(inp.statements[0], ourlang.StatementReturn)
+    typ = expression(ctx, inp.statements[0].value)
+
+    ctx.unify(_convert_old_type(ctx, inp.returns), typ)
+    return
+
+def module(inp: ourlang.Module) -> None:
+    ctx = Context()
+
+    for func in inp.functions.values():
+        function(ctx, func)
+
+from . import typing
+
+def _convert_old_type(ctx: Context, inp: typing.TypeBase) -> TypeVar:
+    result = ctx.new_var()
+
+    if isinstance(inp, typing.TypeUInt32):
+        result.add_constraint(TypeConstraintBitWidth(maxb=32))
+        result.add_constraint(TypeConstraintSigned(False))
+        result.add_location('u32')
+        return result
+
+    raise NotImplementedError(_convert_old_type, inp)
diff --git a/phasm/typing.py b/phasm/typing.py
index e56f7a9..0cb213d 100644
--- a/phasm/typing.py
+++ b/phasm/typing.py
@@ -1,7 +1,7 @@
 """
 The phasm type system
 """
-from typing import Optional, List
+from typing import Dict, Optional, List, Type
 
 class TypeBase:
     """
@@ -200,3 +200,133 @@ class TypeStruct(TypeBase):
             x.type.alloc_size()
             for x in self.members
         )
+
+## NEW STUFF BELOW
+
+class TypingError(Exception):
+    pass
+
+class TypingNarrowProtoError(TypingError):
+    pass
+
+class TypingNarrowError(TypingError):
+    def __init__(self, l: 'TypeVar', r: 'TypeVar', msg: str) -> None:
+        super().__init__(
+            f'Cannot narrow types {l} and {r}: {msg}'
+        )
+
+class TypeConstraintBase:
+    def narrow(self, other: 'TypeConstraintBase') -> 'TypeConstraintBase':
+        raise NotImplementedError('narrow', self, other)
+
+class TypeConstraintSigned(TypeConstraintBase):
+    __slots__ = ('signed', )
+
+    signed: Optional[bool]
+
+    def __init__(self, signed: Optional[bool]) -> None:
+        self.signed = signed
+
+    def narrow(self, other: 'TypeConstraintBase') -> 'TypeConstraintSigned':
+        if not isinstance(other, TypeConstraintSigned):
+            raise Exception('Invalid comparison')
+
+        if other.signed is None:
+            return TypeConstraintSigned(self.signed)
+        if self.signed is None:
+            return TypeConstraintSigned(other.signed)
+
+        if self.signed is not other.signed:
+            raise TypeError()
+
+        return TypeConstraintSigned(self.signed)
+
+    def __repr__(self) -> str:
+        return f'Signed={self.signed}'
+
+class TypeConstraintBitWidth(TypeConstraintBase):
+    __slots__ = ('minb', 'maxb', )
+
+    minb: int
+    maxb: int
+
+    def __init__(self, *, minb: int = 1, maxb: int = 64) -> None:
+        assert minb is not None or maxb is not None
+        assert maxb <= 64 # For now, support up to 64 bits values
+
+        self.minb = minb
+        self.maxb = maxb
+
+    def narrow(self, other: 'TypeConstraintBase') -> 'TypeConstraintBitWidth':
+        if not isinstance(other, TypeConstraintBitWidth):
+            raise Exception('Invalid comparison')
+
+        if self.minb > other.maxb:
+            raise TypingNarrowProtoError('Min bitwidth exceeds other max bitwidth')
+
+        if other.minb > self.maxb:
+            raise TypingNarrowProtoError('Other min bitwidth exceeds max bitwidth')
+
+        return TypeConstraintBitWidth(
+            minb=max(self.minb, other.minb),
+            maxb=min(self.maxb, other.maxb),
+        )
+
+    def __repr__(self) -> str:
+        return f'BitWidth={self.minb}..{self.maxb}'
+
+class TypeVar:
+    def __init__(self, ctx: 'Context') -> None:
+        self.context = ctx
+        self.constraints: Dict[Type[TypeConstraintBase], TypeConstraintBase] = {}
+        self.locations: List[str] = []
+
+    def add_constraint(self, newconst: TypeConstraintBase) -> None:
+        if newconst.__class__ in self.constraints:
+            self.constraints[newconst.__class__] = self.constraints[newconst.__class__].narrow(newconst)
+        else:
+            self.constraints[newconst.__class__] = newconst
+
+    def add_location(self, ref: str) -> None:
+        self.locations.append(ref)
+
+    def __repr__(self) -> str:
+        return (
+            'TypeVar<'
+            + '; '.join(map(repr, self.constraints.values()))
+            + '; locations: '
+            + ', '.join(self.locations)
+            + '>'
+        )
+
+class Context:
+    def clone(self) -> 'Context':
+        return self # TODO: STUB
+
+    def new_var(self) -> TypeVar:
+        return TypeVar(self)
+
+    def unify(self, l: 'TypeVar', r: 'TypeVar') -> None:
+        newtypevar = self.new_var()
+
+        try:
+            for const in l.constraints.values():
+                newtypevar.add_constraint(const)
+            for const in r.constraints.values():
+                newtypevar.add_constraint(const)
+        except TypingNarrowProtoError as ex:
+            raise TypingNarrowError(l, r, str(ex)) from None
+
+        newtypevar.locations.extend(l.locations)
+        newtypevar.locations.extend(r.locations)
+
+        # Make pointer locations to the constraints and locations
+        # so they get linked together throughout the unification
+
+        l.constraints = newtypevar.constraints
+        l.locations = newtypevar.locations
+
+        r.constraints = newtypevar.constraints
+        r.locations = newtypevar.locations
+
+        return
diff --git a/tests/integration/runners.py b/tests/integration/runners.py
index fd3a53e..57d2adb 100644
--- a/tests/integration/runners.py
+++ b/tests/integration/runners.py
@@ -5,6 +5,7 @@ from typing import Any, Callable, Dict, Iterable, Optional, TextIO
 
 import ctypes
 import io
+import warnings
 
 import pywasm.binary
 import wasm3
@@ -13,6 +14,7 @@ import wasmtime
 
 from phasm.compiler import phasm_compile
 from phasm.parser import phasm_parse
+from phasm.typer import phasm_type
 from phasm import ourlang
 from phasm import wasm
 
@@ -40,6 +42,10 @@ class RunnerBase:
         Parses the Phasm code into an AST
         """
         self.phasm_ast = phasm_parse(self.phasm_code)
+        try:
+            phasm_type(self.phasm_ast)
+        except NotImplementedError as exc:
+            warnings.warn(f'phash_type throws an NotImplementedError on this test: {exc}')
 
     def compile_ast(self) -> None:
         """