false = t
_     = t
true  = t t
k     = t t
i     = t (t k) t
s     = t (t (k t)) t
m     = s i i
b     = s (k s) k
c     = s (s (k s) (s (k k) s)) (k k)
id    = \a : a
pair  = t
if    = \cond then else : t (t else (t t then)) t cond

y = ((\mut wait fun : wait mut (\x : fun (wait mut x)))
     (\x : x x)
     (\a0 a1 a2 : t (t a0) (t t a2) a1))

triage = \leaf stem fork : t (t leaf stem) fork
test   = triage "Leaf" (\_ : "Stem") (\_ _ : "Fork")

matchBool = (\ot of : triage
  of
  (\_ : ot)
  (\_ _ : ot)
)

matchList = \a b : triage a _ b

matchPair = \a   : triage _ _ a

not? = matchBool false true
and? = matchBool id (\_ : false)
emptyList? = matchList true (\_ _ : false)

head = matchList t (\head _ : head)
tail = matchList t (\_ tail : tail)

lconcat = y (\self : matchList
  (\k : k)
  (\h r k : pair h (self r k)))

lAnd = (triage
  (\_     : false)
  (\_ x   : x)
  (\_ _ x : x))

lOr = (triage
  (\x     : x)
  (\_ _   : true)
  (\_ _ _ : true))

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

equal? = y (\self : triage
  (triage
    true
    (\_   : false)
    (\_ _ : false))
  (\ax :
    triage
      false
      (self ax)
      (\_ _ : false))
  (\ax ay :
    triage
      false
      (\_ : false)
      (\bx by : lAnd (self ax bx) (self ay by))))

filter_ = y (\self : matchList
  (\_ : t)
  (\head tail f : matchBool (t head) i (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