diff --git a/guppylang/checker/expr_checker.py b/guppylang/checker/expr_checker.py
index 8dcbdea3..3d23424a 100644
--- a/guppylang/checker/expr_checker.py
+++ b/guppylang/checker/expr_checker.py
@@ -108,11 +108,15 @@
 from guppylang.tys.builtin import (
     array_type,
     bool_type,
+    float_type,
     get_element_type,
+    int_type,
+    is_array_type,
     is_bool_type,
     is_list_type,
     is_sized_iter_type,
     list_type,
+    nat_type,
 )
 from guppylang.tys.param import ConstParam, TypeParam
 from guppylang.tys.subst import Inst, Subst
@@ -232,6 +236,14 @@ def _synthesize(
         """Invokes the type synthesiser"""
         return ExprSynthesizer(self.ctx).synthesize(node, allow_free_vars)
 
+    def visit_Constant(self, node: ast.Constant, ty: Type) -> tuple[ast.expr, Subst]:
+        act = python_value_to_guppy_type(node.value, node, self.ctx.globals, ty)
+        if act is None:
+            raise GuppyError(IllegalConstant(node, type(node.value)))
+        node, subst, inst = check_type_against(act, ty, node, self.ctx, self._kind)
+        assert inst == [], "Const values are not generic"
+        return node, subst
+
     def visit_Tuple(self, node: ast.Tuple, ty: Type) -> tuple[ast.expr, Subst]:
         if not isinstance(ty, TupleType) or len(ty.element_types) != len(node.elts):
             return self._fail(ty, node)
@@ -318,7 +330,9 @@ def visit_Call(self, node: ast.Call, ty: Type) -> tuple[ast.expr, Subst]:
 
     def visit_PyExpr(self, node: PyExpr, ty: Type) -> tuple[ast.expr, Subst]:
         python_val = eval_py_expr(node, self.ctx)
-        if act := python_value_to_guppy_type(python_val, node.value, self.ctx.globals):
+        if act := python_value_to_guppy_type(
+            python_val, node.value, self.ctx.globals, ty
+        ):
             subst = unify(ty, act, {})
             if subst is None:
                 self._fail(ty, act, node)
@@ -1137,25 +1151,43 @@ def eval_py_expr(node: PyExpr, ctx: Context) -> Any:
     return python_val
 
 
-def python_value_to_guppy_type(v: Any, node: ast.expr, globals: Globals) -> Type | None:
+def python_value_to_guppy_type(
+    v: Any, node: ast.expr, globals: Globals, type_hint: Type | None = None
+) -> Type | None:
     """Turns a primitive Python value into a Guppy type.
 
+    Accepts an optional `type_hint` for the expected expression type that is used to
+    infer a more precise type (e.g. distinguishing between `int` and `nat`). Note that
+    invalid hints are ignored, i.e. no user error are emitted.
+
     Returns `None` if the Python value cannot be represented in Guppy.
     """
     match v:
         case bool():
             return bool_type()
+        # Only resolve `int` to `nat` if the user specifically asked for it
+        case int(n) if type_hint == nat_type() and n >= 0:
+            return nat_type()
+        # Otherwise, default to `int` for consistency with Python
         case int():
-            return cast(TypeDef, globals["int"]).check_instantiate([], globals)
+            return int_type()
         case float():
-            return cast(TypeDef, globals["float"]).check_instantiate([], globals)
+            return float_type()
         case tuple(elts):
-            tys = [python_value_to_guppy_type(elt, node, globals) for elt in elts]
+            hints = (
+                type_hint.element_types
+                if isinstance(type_hint, TupleType)
+                else len(elts) * [None]
+            )
+            tys = [
+                python_value_to_guppy_type(elt, node, globals, hint)
+                for elt, hint in zip(elts, hints, strict=False)
+            ]
             if any(ty is None for ty in tys):
                 return None
             return TupleType(cast(list[Type], tys))
         case list():
-            return _python_list_to_guppy_type(v, node, globals)
+            return _python_list_to_guppy_type(v, node, globals, type_hint)
         case _:
             # Pytket conversion is an experimental feature
             # if pytket and tket2 are installed
@@ -1186,7 +1218,7 @@ def python_value_to_guppy_type(v: Any, node: ast.expr, globals: Globals) -> Type
 
 
 def _python_list_to_guppy_type(
-    vs: list[Any], node: ast.expr, globals: Globals
+    vs: list[Any], node: ast.expr, globals: Globals, type_hint: Type | None
 ) -> OpaqueType | None:
     """Turns a Python list into a Guppy type.
 
@@ -1198,11 +1230,14 @@ def _python_list_to_guppy_type(
 
     # All the list elements must have a unifiable types
     v, *rest = vs
-    el_ty = python_value_to_guppy_type(v, node, globals)
+    elt_hint = (
+        get_element_type(type_hint) if type_hint and is_array_type(type_hint) else None
+    )
+    el_ty = python_value_to_guppy_type(v, node, globals, elt_hint)
     if el_ty is None:
         return None
     for v in rest:
-        ty = python_value_to_guppy_type(v, node, globals)
+        ty = python_value_to_guppy_type(v, node, globals, elt_hint)
         if ty is None:
             return None
         if (subst := unify(ty, el_ty, {})) is None:
diff --git a/guppylang/std/builtins.py b/guppylang/std/builtins.py
index a4027cd3..d9843bc2 100644
--- a/guppylang/std/builtins.py
+++ b/guppylang/std/builtins.py
@@ -106,7 +106,9 @@ def __int__(self: bool) -> int:
     @guppy
     @no_type_check
     def __nat__(self: bool) -> nat:
-        # TODO: Literals should check against `nat`
+        # TODO: Type information doesn't flow through the `if` expression, so we
+        #  have to insert the `nat` coercions by hand.
+        #  See https://github.com/CQCL/guppylang/issues/707
         return nat(1) if self else nat(0)
 
     @guppy.custom(checker=DunderChecker("__bool__"), higher_order_value=False)
diff --git a/guppylang/tys/builtin.py b/guppylang/tys/builtin.py
index 89ffc5c8..86630c28 100644
--- a/guppylang/tys/builtin.py
+++ b/guppylang/tys/builtin.py
@@ -211,6 +211,10 @@ def int_type() -> NumericType:
     return NumericType(NumericType.Kind.Int)
 
 
+def float_type() -> NumericType:
+    return NumericType(NumericType.Kind.Float)
+
+
 def list_type(element_ty: Type) -> OpaqueType:
     return OpaqueType([TypeArg(element_ty)], list_type_def)
 
diff --git a/tests/error/py_errors/negative_nat.err b/tests/error/py_errors/negative_nat.err
new file mode 100644
index 00000000..3cfd76c6
--- /dev/null
+++ b/tests/error/py_errors/negative_nat.err
@@ -0,0 +1,8 @@
+Error: Type mismatch (at $FILE:7:11)
+  | 
+5 | @compile_guppy
+6 | def foo() -> nat:
+7 |     return py(-1)
+  |            ^^^^^^ Expected expression of type `nat`, got `int`
+
+Guppy compilation failed due to 1 previous error
diff --git a/tests/error/py_errors/negative_nat.py b/tests/error/py_errors/negative_nat.py
new file mode 100644
index 00000000..21170653
--- /dev/null
+++ b/tests/error/py_errors/negative_nat.py
@@ -0,0 +1,7 @@
+from guppylang.std.builtins import nat
+from tests.util import compile_guppy
+
+
+@compile_guppy
+def foo() -> nat:
+    return py(-1)
diff --git a/tests/integration/test_arithmetic.py b/tests/integration/test_arithmetic.py
index 33d03914..d8bbc348 100644
--- a/tests/integration/test_arithmetic.py
+++ b/tests/integration/test_arithmetic.py
@@ -42,6 +42,14 @@ def const() -> float:
     validate(const)
 
 
+def test_nat_literal(validate):
+    @compile_guppy
+    def const() -> nat:
+        return 42
+
+    validate(const)
+
+
 def test_aug_assign(validate, run_int_fn):
     module = GuppyModule("test_aug_assign")
 
diff --git a/tests/integration/test_py.py b/tests/integration/test_py.py
index f62d50a5..ac9dce41 100644
--- a/tests/integration/test_py.py
+++ b/tests/integration/test_py.py
@@ -6,7 +6,7 @@
 
 from guppylang.decorator import guppy
 from guppylang.module import GuppyModule
-from guppylang.std.builtins import py, array
+from guppylang.std.builtins import py, array, nat
 from guppylang.std import quantum
 from guppylang.std.quantum import qubit
 from tests.util import compile_guppy
@@ -107,6 +107,16 @@ def foo() -> None:
     validate(foo)
 
 
+def test_nats_from_ints(validate):
+    @compile_guppy
+    def foo() -> None:
+        x: nat = py(1)
+        y: tuple[nat, nat] = py(2, 3)
+        z: array[nat, 3] = py([4, 5, 6])
+
+    validate(foo)
+
+
 @pytest.mark.skipif(not tket2_installed, reason="Tket2 is not installed")
 @pytest.mark.skip("Fails because of extensions in types #343")
 def test_pytket_single_qubit(validate):
diff --git a/tests/integration/test_range.py b/tests/integration/test_range.py
index 092db623..07cfff48 100644
--- a/tests/integration/test_range.py
+++ b/tests/integration/test_range.py
@@ -1,5 +1,5 @@
 from guppylang.decorator import guppy
-from guppylang.std.builtins import nat, range, SizedIter, Range
+from guppylang.std.builtins import nat, range, SizedIter, Range, py
 from guppylang.module import GuppyModule
 from tests.util import compile_guppy
 
@@ -45,6 +45,17 @@ def negative() -> SizedIter[Range, 10]:
     validate(module.compile())
 
 
+def test_py_size(validate):
+    module = GuppyModule("test")
+    n = 10
+
+    @guppy(module)
+    def negative() -> SizedIter[Range, 10]:
+        return range(py(n))
+
+    validate(module.compile())
+
+
 def test_static_generic_size(validate):
     module = GuppyModule("test")
     n = guppy.nat_var("n", module=module)