@tuple
class Vec[T]:
    x: T
    y: T

    @pure
    def __abs__(self):
        return ((self.x * self.x) + (self.y * self.y)) ** 0.5

    @pure
    @commutative
    @associative
    def __add__(self, other: Vec[T]):
        print 'vec add', self, other
        return Vec[T](self.x + other.x, self.y + other.y)

    @pure
    @commutative
    @associative
    def __add__(self, other: T):
        print 'vec add', self, other
        return Vec[T](self.x + other, self.y + other)

    @pure
    def __sub__(self, other: Vec[T]):
        print 'vec sub', self, other
        return Vec[T](self.x - other.x, self.y - other.y)

    @pure
    def __sub__(self, other: T):
        print 'vec sub', self, other
        return Vec[T](self.x - other, self.y - other)

    @pure
    @commutative
    @associative
    @distributive
    def __mul__(self, other: Vec[T]):
        print 'vec mul', self, other
        return Vec[T](self.x * other.x, self.y * other.y)

    @pure
    @commutative
    @associative
    @distributive
    def __mul__(self, other: T):
        print 'vec mul', self, other
        return Vec[T](self.x * other, self.y * other)

    @pure
    @commutative
    def __eq__(self, other: Vec[T]):
        print 'vec eq', self, other
        return abs(self) == abs(other)

    @pure
    @commutative
    def __ne__(self, other: Vec[T]):
        print 'vec ne', self, other
        return abs(self) != abs(other)

    @pure
    def __lt__(self, other: Vec[T]):
        print 'vec lt', self, other
        return abs(self) < abs(other)

    @pure
    def __le__(self, other: Vec[T]):
        print 'vec le', self, other
        return abs(self) <= abs(other)

    @pure
    def __gt__(self, other: Vec[T]):
        print 'vec gt', self, other
        return abs(self) > abs(other)

    @pure
    def __ge__(self, other: Vec[T]):
        print 'vec ge', self, other
        return abs(self) >= abs(other)

@test
def test_op_chain_canon():
    @pure
    def f(a): return a

    a = Vec(1, 2)
    b = Vec(3, 4)
    c = a + f(b)  # -> f(b) + a
    assert (c.x, c.y) == (4, 6)
    # EXPECT: vec add (x: 3, y: 4) (x: 1, y: 2)

    a = Vec(1, 2)
    b = Vec(3, 4)
    c = Vec(5, 6)
    d = f(a + f(b) + f(f(c)))  # -> f(f(f(c)) + f(b) + a)
    assert (d.x, d.y) == (9, 12)
    # EXPECT: vec add (x: 5, y: 6) (x: 3, y: 4)
    # EXPECT: vec add (x: 8, y: 10) (x: 1, y: 2)

    a = Vec(1, 2)
    b = Vec(3, 4)
    c = Vec(5, 6)
    d = f(a + (f(b) + f(f(c))))  # -> f(f(f(c)) + f(b) + a)
    assert (d.x, d.y) == (9, 12)
    # EXPECT: vec add (x: 5, y: 6) (x: 3, y: 4)
    # EXPECT: vec add (x: 8, y: 10) (x: 1, y: 2)

    a = Vec(1, 2)
    b = Vec(3, 4)
    c = a - f(b)  # -> no change
    assert (c.x, c.y) == (-2, -2)
    # EXPECT: vec sub (x: 1, y: 2) (x: 3, y: 4)

    # don't canon float ops
    assert f(1e100) + f(f(-1e100)) + f(f(f(1.))) == 1.
test_op_chain_canon()

class C:
    n: int

    def __lt__(self: C, other: C):
        return self.n < other.n

@test
def test_inequality_canon():
    @pure
    def f(a): return a

    a = Vec(1,1)
    b = Vec(2,2)

    assert not (f(a) == b)
    assert f(a) != b
    assert f(a) < b
    assert f(a) <= b
    assert not (f(a) > b)
    assert not (f(a) >= b)
    # EXPECT: vec eq (x: 1, y: 1) (x: 2, y: 2)
    # EXPECT: vec ne (x: 1, y: 1) (x: 2, y: 2)
    # EXPECT: vec lt (x: 1, y: 1) (x: 2, y: 2)
    # EXPECT: vec le (x: 1, y: 1) (x: 2, y: 2)
    # EXPECT: vec gt (x: 1, y: 1) (x: 2, y: 2)
    # EXPECT: vec ge (x: 1, y: 1) (x: 2, y: 2)

    assert not (a == f(b))
    assert a != f(b)
    assert a < f(b)
    assert a <= f(b)
    assert not (a > f(b))
    assert not (a >= f(b))
    # EXPECT: vec eq (x: 2, y: 2) (x: 1, y: 1)
    # EXPECT: vec ne (x: 2, y: 2) (x: 1, y: 1)
    # EXPECT: vec gt (x: 2, y: 2) (x: 1, y: 1)
    # EXPECT: vec ge (x: 2, y: 2) (x: 1, y: 1)
    # EXPECT: vec lt (x: 2, y: 2) (x: 1, y: 1)
    # EXPECT: vec le (x: 2, y: 2) (x: 1, y: 1)

    c1 = C(1)
    c2 = C(2)
    # ensure we don't use missing ops
    assert c1 < f(c2)
test_inequality_canon()

@test
def test_add_mul_canon():
    @pure
    def f(a): return a

    a = Vec(1,1)
    b = Vec(2,2)
    c = Vec(3,3)
    d = (a*f(b) + c*a)  # -> (f(b) + c) * a
    assert (d.x, d.y) == (5, 5)
    # EXPECT: vec add (x: 2, y: 2) (x: 3, y: 3)
    # EXPECT: vec mul (x: 5, y: 5) (x: 1, y: 1)

    d = (a + c*a)  # -> (c + 1) * a
    assert (d.x, d.y) == (4, 4)
    # EXPECT: vec add (x: 3, y: 3) 1
    # EXPECT: vec mul (x: 4, y: 4) (x: 1, y: 1)

    d = (c*a + a)  # -> (c + 1) * a
    assert (d.x, d.y) == (4, 4)
    # EXPECT: vec add (x: 3, y: 3) 1
    # EXPECT: vec mul (x: 4, y: 4) (x: 1, y: 1)

    a = Vec(1,1)
    b = a + a + a + a + a
    assert (b.x, b.y) == (5, 5)
    # EXPECT: vec mul (x: 1, y: 1) 5

    a = Vec(1,1)
    b = a + a*2 + a*3 + a*4 + a*5
    assert (b.x, b.y) == (15, 15)
    # EXPECT: vec mul (x: 1, y: 1) 15

    x = f(100.)  # don't distribute float ops
    assert (x * 0.1) + (x * 0.2) == 30.
test_add_mul_canon()