!import "base.tri" !Local

matchList = a b : triage a _ b

emptyList? = matchList true (_ _ : false)
head = matchList t (head _ : head)
tail = matchList t (_ tail : tail)

append = y (self : matchList
  (k : k)
  (h r k : pair h (self r k)))

lExist? = y (self x : matchList
  false
  (h z : or? (equal? x h) (self x z)))

map_ = y (self :
  matchList
    (_ : t)
    (head tail f : pair (f head) (self tail f)))
map = f l : map_ l f

filter_ = y (self : matchList
  (_ : t)
  (head tail f : matchBool (t head) id (f head) (self tail f)))
filter  = f l : filter_ l f

foldl_ = y (self f l x : matchList (acc : acc) (head tail acc : self f tail (f acc head)) l x)
foldl  = f x l : foldl_ f l x

foldr_ = y (self x f l : matchList x (head tail : f (self x f tail) head) l)
foldr  = f x l : foldr_ x f l

length = y (self : matchList
  0
  (_ tail : succ (self tail)))

reverse = y (self : matchList
  t
  (head tail : append (self tail) (pair head t)))

snoc = y (self x : matchList
  (pair x t)
  (h z : pair h (self x z)))

count = y (self x : matchList
  0
  (h z : matchBool
    (succ (self x z))
    (self x z)
    (equal? x h)))

last = y (self : matchList
  t
  (hd tl : matchBool
    hd
    (self tl)
    (emptyList? tl)))

all? = y (self pred : matchList
  true
  (h z : and? (pred h) (self pred z)))

any? = y (self pred : matchList
  false
  (h z : or? (pred h) (self pred z)))

intersect = xs ys : filter (x : lExist? x ys) xs