--
--
-- Base
--
--

-- | Type class for equality
class Eq a where
  (==) (x: a) (y: a) : Bool
  (/=) (x: a) (y: a) : Bool

-- | Eq instances for basic types
instance Eq Integer where
  (==) x y := x = y
  (/=) x y := not (x == y)

instance Eq Float where
  (==) x y := x = y
  (/=) x y := not (x == y)

instance Eq String where
  (==) x y := x = y
  (/=) x y := not (x == y)

instance Eq Bool where
  (==) x y := x = y
  (/=) x y := not (x == y)

instance Eq Char where
  (==) x y := x = y
  (/=) x y := not (x == y)

instance {Eq a} Eq (Tensor a) where
  (==) t1 t2 := t1 = t2
  (/=) t1 t2 := not (t1 == t2)

def eq {Eq a} : Matcher a :=
  matcher
    | #$val as () with
      | $tgt -> if val == tgt then [()] else []
    | $ as something with
      | $tgt -> [tgt]

def bool : Matcher Bool := eq
def char : Matcher Char := eq
def integer : Matcher Integer := eq
def float : Matcher Float := eq

class Num a where
  (+) (x: a) (y: a) : a
  (-) (x: a) (y: a) : a
  (*) (x: a) (y: a) : a
  (/) (x: a) (y: a) : a

--instance Num Integer where
--  (+) x y := i.+ x y
--  (-) x y := i.- x y
--  (*) x y := i.* x y
--  (/) x y := i./ x y
instance Num MathExpr where
  (+) x y := plusForMathExpr x y
  (-) x y := minusForMathExpr x y
  (*) x y := multForMathExpr x y
  (/) x y := divForMathExpr x y

instance Num Float where
  (+) x y := f.+ x y
  (-) x y := f.- x y
  (*) x y := f.* x y
  (/) x y := f./ x y

--
-- Utility
--

def id {a} (x: a) : a := x

def fst {a, b} (x: a, _: b) : a := x
def snd {a, b} (_: a, y: b) : b := y

def ($) {a, b} (f: a -> b) (x: a) : b := f x

def compose {a, b, c} (f: a -> b) (g: b -> c) : a -> c := \x -> g (f x)

def flip {a, b, c} (fn: a -> b -> c) : b -> a -> c := \x y -> fn y x

def eqAs {Eq a} (m: Matcher a) (x: a) (y: a) : Bool :=
  match x as m with
    | #y -> True
    | _ -> False

def curry {a, b, c} (f: (a, b) -> c) (x: a) (y: b) : c := f (x, y)
def uncurry {a, b, c} (f: a -> b -> c) (x: a, y: b) : c := f x y

--
-- Boolean
--

def (&&) (b1: Bool) (b2: Bool) : Bool := if b1 then b2 else False
def (||) (b1: Bool) (b2: Bool) : Bool := if b1 then True else b2

def not (b: Bool) : Bool := if b then False else True

--
-- Unordered Pair
--

def unorderedPair {a} (m: Matcher a) : Matcher (a, a) :=
  matcher
    | ($, $) as (m, m) with
      | ($x, $y) -> [(x, y), (y, x)]
    | $ as something with
      | $tgt -> [tgt]