def test_compose_associative(x: int, y: int, z: int):
"""Rearranging the parentheses in an expression will not change the result."""
fn: Func = lambda a: a + x
gn: Func = lambda b: b - y
hn: Func = lambda c: c * z
cn = compose(fn, gn, hn)
cn_: Func = lambda x: hn(gn(fn(x)))
rn = compose(fn, compose(gn, hn))
# right associative
rn_: Func = lambda x: (lambda b: hn(gn(b)))(fn(x)) # type: ignore
ln = compose(compose(fn, gn), hn)
# left associative
ln_: Func = lambda x: hn((lambda b: gn(fn(b)))(x)) # type: ignore
assert cn(x) == cn_(x) == rn(x) == rn_(x) == ln(x) == ln_(x)
def test_compose_many(x: int):
fn: Func = lambda x: x + 42
gn: Func = lambda x: x - 3
hn: Func = lambda x: x * 2
cn = compose(fn, gn, hn, fn, hn, gn, fn)
assert cn(x) == fn(gn(hn(fn(hn(gn(fn(x)))))))
def test_compose_left_identity(x: int):
fn: Func = lambda x: x + 42
cn: Func = compose(identity, fn)
assert cn(x) == fn(x)
def test_compose_rigth_identity(x: int):
fn: Func = lambda x: x + 42
cn = compose(fn, identity)
assert cn(x) == fn(x)
def test_compose_2(x: int):
fn: Func = lambda x: x + 42
gn: Func = lambda x: x - 3
hn = compose(fn, gn)
assert hn(x) == gn(fn(x))
def test_compose_1(x: int):
fn: Callable[[int], int] = lambda x: x + 42
gn = compose(fn)
assert gn(x) == fn(x) == x + 42
def test_compose_identity(x: int):
fn: Func = compose(identity)
assert fn(x) == x
def test_compose_identity_implicit(x: int):
fn = compose()
assert fn(x) == x