def typeof(obj):
"""Returns the type of an object within the internal type system.
:param obj: the object to inspect.
:returns: An object representing the type in the internal type system
language (i.e., a
`~hask3.lang.hindley_milner.TypeOperator`:class: or
`~hask3.lang.hindley_milner.TypeVariable`:class:).
"""
from hask3.hack import is_python_function
from hask3.lang.hindley_milner import TypeVariable, TypeOperator, Tuple
# XXX: WTF?
TypeVariable.next_var_name = 'a'
if isinstance(obj, Hask):
return obj.__type__()
elif isinstance(obj, tuple):
return Tuple([typeof(o) for o in obj])
elif obj is None:
return TypeOperator(None, [])
elif is_python_function(obj):
return TypeOperator(PyFunc, [])
else:
return TypeOperator(type(obj), [])
def build_sig_arg(arg, cons, var_dict):
"""Covert a type signature argument into its internal representation.
:param arg: The argument (a string, a Python type, etc) to convert.
:param cons: A dictionary of typeclass constraints for the type
signature.
:param var_dict: a dictionary of bound type variables.
:returns: A TypeVariable or TypeOperator representing the `arg`.
:raises TypeSignatureError: if the argument cannot be converted.
"""
from hask3.lang.hindley_milner import TypeVariable, TypeOperator
from hask3.lang.hindley_milner import Tuple, ListType
if isinstance(arg, str):
if arg.islower():
if arg not in var_dict:
kw = {'constraints': cons[arg]} if arg in cons else {}
var_dict[arg] = TypeVariable(**kw)
res = var_dict[arg]
else:
res = None
# sub-signature, e.g. H/ (H/ int >> int) >> int >> int
elif isinstance(arg, TypeSignature):
res = make_fn_type(build_sig(arg, var_dict))
# HKT, e.g. t(Maybe "a") or t("m", "a", "b")
elif isinstance(arg, TypeSignatureHKT):
if type(arg.tcon) == str:
hkt = build_sig_arg(arg.tcon, cons, var_dict)
else:
hkt = arg.tcon
types = [build_sig_arg(a, cons, var_dict) for a in arg.params]
res = TypeOperator(hkt, types)
# None (the unit type)
elif arg is None:
res = TypeOperator(None, [])
# Tuples: ("a", "b"), (int, ("a", float)), etc.
elif isinstance(arg, tuple):
f = lambda x: build_sig_arg(x, cons, var_dict)
res = Tuple([f(x) for x in arg])
# Lists: ["a"], [int], etc.
elif isinstance(arg, list):
if len(arg) == 1:
res = ListType(build_sig_arg(arg[0], cons, var_dict))
else:
res = None
# any other type, builtin or user-defined
elif isinstance(arg, type):
res = TypeOperator(arg, [])
else:
res = None
if res is not None:
return res
else:
raise TypeSignatureError(f"Invalid item in type signature: {arg}")
def __type__(self):
args = [
typeof(self[fields.index(p)])
if p in fields else TypeVariable()
for p in type_constructor.__params__
]
return TypeOperator(type_constructor, args)
def setUp(self):
"""Create some basic types and polymorphic typevars, a toy environment,
and some AST nodes
"""
self.var1 = TypeVariable()
self.var2 = TypeVariable()
self.var3 = TypeVariable()
self.var4 = TypeVariable()
self.Pair = TypeOperator("*", (self.var1, self.var2))
self.Bool = TypeOperator("bool", [])
self.Integer = TypeOperator("int", [])
self.NoneT = TypeOperator("None", [])
# toy environment
self.env = {
"pair":
Function(self.var1, Function(self.var2, self.Pair)),
"True":
self.Bool,
"None":
self.NoneT,
"id":
Function(self.var4, self.var4),
"cond":
Function(self.Bool,
Function(self.var3, Function(self.var3, self.var3))),
"zero":
Function(self.Integer, self.Bool),
"pred":
Function(self.Integer, self.Integer),
"times":
Function(self.Integer, Function(self.Integer, self.Integer)),
"4":
self.Integer,
"1":
self.Integer
}
# some expressions to play around with
self.compose = Lam(
"f", Lam("g", Lam("arg", App(Var("g"), App(Var("f"),
Var("arg"))))))
self.pair = App(App(Var("pair"), App(Var("f"), Var("1"))),
App(Var("f"), Var("True")))
def make_type_const(name, typeargs):
"""Build a new type constructor given a name and the type parameters.
:param name: the name of the new type constructor to be created.
:param typeargs: the type parameters to the constructor.
:returns: A new class that acts as a type constructor.
"""
from hask3.lang.hindley_milner import TypeVariable, TypeOperator
def raise_fn(err):
raise err
default_attrs = {"__params__": tuple(typeargs), "__constructors__": ()}
cls = type(name, (ADT, ), default_attrs)
cls.__type__ = lambda self: \
TypeOperator(cls, [TypeVariable() for i in cls.__params__])
# Unless typeclass instances are provided or derived, ADTs do not support
# any of these attributes, and trying to use one is a TypeError
magic = {
'iter', 'contains', 'add', 'radd', 'rmul', 'mul', 'lt', 'gt', 'le',
'ge', 'eq', 'ne'
}
magic = {f'__{op}__' for op in magic} | {'count', 'index'}
for attr in magic:
setattr(cls, attr, lambda self: raise_fn(TypeError))
# Unless Show is instantiated/derived, use object's `repr` method
cls.__repr__ = object.__repr__
cls.__str__ = object.__str__
return cls
def test_signature_build(self):
"""Make sure type signatures are built correctly"""
# int -> int
self.unified(make_fn_type(build_sig((H / int >> int).sig)),
Function(TypeOperator(int, []), TypeOperator(int, [])))
# a -> a
a = TypeVariable()
self.unified(make_fn_type(build_sig((H / "a" >> "a").sig)),
Function(a, a))
# a -> b
a, b = TypeVariable(), TypeVariable()
self.unified(make_fn_type(build_sig((H / "a" >> "b").sig)),
Function(a, b))
# (int -> int) -> int -> int
self.unified(
make_fn_type(build_sig((H / (H / int >> int) >> int >> int).sig)),
Function(Function(TypeOperator(int, []), TypeOperator(int, [])),
Function(TypeOperator(int, []), TypeOperator(int, []))))
def test_typecheck_builtins(self):
"""Make sure builtin types typecheck correctly"""
# 1 :: int
self.unified(typeof(1), TypeOperator(int, []))
# "a" :: str
self.unified(typeof("a"), TypeOperator(str, []))
# Nothing :: Maybe a
self.unified(typeof(Nothing), TypeOperator(Maybe, [TypeVariable()]))
# Just(1) :: Maybe int
self.unified(typeof(Just(1)),
TypeOperator(Maybe, [TypeOperator(int, [])]))
# Just(Just(Nothing)) :: Maybe (Maybe (Maybe a))
self.unified(
typeof(Just(Just(Nothing))),
TypeOperator(
Maybe,
[TypeOperator(Maybe, [TypeOperator(Maybe, [TypeVariable()])])
]))
# Right("error") :: Either a str
self.unified(
typeof(Right("error")),
TypeOperator(
Either, [TypeVariable(), TypeOperator(str, [])]))
# Left(2.0) :: Either float a
self.unified(
typeof(Left(2.0)),
TypeOperator(Either, [TypeOperator(float, []),
TypeVariable()]))
def test_build_sig_item(self):
"""Test type signature building internals - make sure that types are
translated in a reasonable way"""
class example:
pass
# type variables
self.assertTrue(isinstance(build_sig_arg("a", {}, {}), TypeVariable))
self.assertTrue(isinstance(build_sig_arg("abc", {}, {}), TypeVariable))
# builtin/non-ADT types
self.unified(build_sig_arg(str, {}, {}), TypeOperator(str, []))
self.unified(build_sig_arg(int, {}, {}), TypeOperator(int, []))
self.unified(build_sig_arg(float, {}, {}), TypeOperator(float, []))
self.unified(build_sig_arg(list, {}, {}), TypeOperator(list, []))
self.unified(build_sig_arg(set, {}, {}), TypeOperator(set, []))
self.unified(build_sig_arg(example, {}, {}), TypeOperator(example, []))
# unit type (None)
self.unified(build_sig_arg(None, {}, {}), TypeOperator(None, []))
# tuple
self.unified(build_sig_arg((int, int), {}, {}),
Tuple([TypeOperator(int, []),
TypeOperator(int, [])]))
self.unified(
build_sig_arg((None, (None, int)), {}, {}),
Tuple([
TypeOperator(None, []),
Tuple([TypeOperator(None, []),
TypeOperator(int, [])])
]))
a = TypeVariable()
self.unified(build_sig_arg(("a", "a", "a"), {}, {}), Tuple([a, a, a]))
# list
self.unified(typeof(L[[]]), build_sig_arg(["a"], {}, {}))
self.unified(typeof(L[1, 1]), build_sig_arg([int], {}, {}))
self.unified(typeof(L[[L[1, 1]]]), build_sig_arg([[int]], {}, {}))
# adts
self.unified(typeof(Nothing), build_sig_arg(t(Maybe, "a"), {}, {}))
self.unified(typeof(Just(1)), build_sig_arg(t(Maybe, int), {}, {}))
self.unified(typeof(Just(Just(Nothing))),
build_sig_arg(t(Maybe, t(Maybe, t(Maybe, "a"))), {}, {}))
self.unified(typeof(Right("error")),
build_sig_arg(t(Either, str, "a"), {}, {}))
self.unified(typeof(Left(2.0)),
build_sig_arg(t(Either, "a", int), {}, {}))
self.unified(typeof(Just(__ + 1)),
build_sig_arg(t(Maybe, "a"), {}, {}))
self.unified(typeof(Just(__ + 1)),
build_sig_arg(t(Maybe, (H / "a" >> "b")), {}, {}))
def test_type_checking(self):
"""Basic type checking in our toy environment"""
# 1 :: Integer
self.typecheck(Var("1"), self.Integer)
# 1 :: Bool ==> TypeError
self.not_typecheck(Var("1"), self.Bool)
# (\x -> x) :: (a -> a)
v = TypeVariable()
self.typecheck(Lam("n", Var("n")), Function(v, v))
# type(id) == type(\x -> x)
self.typecheck(Lam("n", Var("n")), self.env["id"])
# (\x -> x) :: (a -> b)
self.typecheck(Lam("n", Var("n")),
Function(TypeVariable(), TypeVariable()))
# (id 1) :: Integer
self.typecheck(App(Var("id"), Var("1")), self.Integer)
# (id 1) :: Bool ==> TypeError
self.not_typecheck(App(Var("id"), Var("1")), self.Bool)
# pred :: (Integer -> Integer)
self.typecheck(Var("pred"), Function(self.Integer, self.Integer))
# (pred 4) :: Integer
self.typecheck(App(Var("pred"), Var("1")), self.Integer)
# ((pair 1) 4) :: (a, b)
self.typecheck(
App(App(Var("pair"), Var("1")), Var("4")),
TypeOperator("*", [TypeVariable(), TypeVariable()]))
# (*) :: (Integer -> Integer -> Integer)
self.typecheck(
Var("times"),
Function(self.Integer, Function(self.Integer, self.Integer)))
# (* 4) :: (Integer -> Integer)
self.typecheck(App(Var("times"), Var("4")),
Function(self.Integer, self.Integer))
# (* 4) :: (Bool -> Integer) ==> TypeError
self.not_typecheck(App(Var("times"), Var("4")),
Function(self.Bool, self.Integer))
# (* 4) :: (Integer -> a) ==> TypeError
self.not_typecheck(App(Var("times"), Var("4")),
Function(self.Integer, TypeVariable))
# ((* 1) 4) :: Integer
self.typecheck(App(App(Var("times"), Var("1")), Var("4")),
self.Integer)
# ((* 1) 4) :: Bool ==> TypeError
self.not_typecheck(App(App(Var("times"), Var("1")), Var("4")),
self.Bool)
# let g = (\f -> 5) in (g g) :: Integer
self.typecheck(Let("g", Lam("f", Var("4")), App(Var("g"), Var("g"))),
self.Integer)
# (.) :: (a -> b) -> (b -> c) -> (a -> c)
a, b, c = TypeVariable(), TypeVariable(), TypeVariable()
self.typecheck(
self.compose,
Function(Function(a, b), Function(Function(b, c), Function(a, c))))
# composing `id` with `id` == `id`
# ((. id) id) :: (a -> a)
d = TypeVariable()
self.typecheck(App(App(self.compose, Var("id")), Var("id")),
Function(d, d))
# composing `id` with `times 4`
# ((. id) (* 2)) :: (int -> int)
self.typecheck(
App(App(self.compose, Var("id")), App(Var("times"), Var("4"))),
Function(self.Integer, self.Integer))
# composing `times 4` with `id`
# ((. (* 2)) id) :: (int -> int)
self.typecheck(
App(App(self.compose, App(Var("times"), Var("4"))), Var("id")),
Function(self.Integer, self.Integer))
# basic closure
# ((\x -> (\y -> ((* x) y))) 1) :: (Integer -> Integer)
self.typecheck(
App(Lam("x", Lam("y", App(App(Var("times"), Var("x")), Var("y")))),
Var("1")), Function(self.Integer, self.Integer))
# lambdas have lexical scope
# (((\x -> (\x -> x)) True) None) :: NoneT
self.typecheck(
App(App(Lam("x", Lam("x", Var("x"))), Var("True")), Var("None")),
self.NoneT)
# basic let expression
# let a = times in ((a 1) 4) :: Integer
self.typecheck(
Let("a", Var("times"), App(App(Var("a"), Var("1")), Var("4"))),
self.Integer)
# let has lexical scope
# let a = 1 in (let a = None in a) :: NoneT
self.typecheck(Let("a", Var("1"), Let("a", Var("None"), Var("a"))),
self.NoneT)
# let polymorphism
# let f = (\x -> x) in ((f 4), (f True)) :: (Integer, Bool)
self.typecheck(Let("f", Lam("x", Var("x")), self.pair),
TypeOperator("*", [self.Integer, self.Bool]))
# recursive let
# (factorial 4) :: Integer
self.typecheck(
Let(
"factorial", # letrec factorial =
Lam(
"n", # fn n =>
App(
App( # cond (zero n) 1
App(
Var("cond"), # cond (zero n)
App(Var("zero"), Var("n"))),
Var("1")),
App( # times n
App(Var("times"), Var("n")),
App(Var("factorial"),
App(Var("pred"), Var("n")))))), # in # noqa
App(Var("factorial"), Var("4"))),
self.Integer)