false = t
_     = t
true  = t t
id    = a : a
const = a b : 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))

compose = f g x : f (g x)

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

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

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

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

matchPair = a : triage _ _ a

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

or? = (x z : 
  matchBool 
    (matchBool true true z)
    (matchBool true false z)
    x)

xor? = (x z : 
  matchBool 
    (matchBool false true z)
    (matchBool true false z)
    x)

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))))

succ = y (self :
  triage
    1
    t
    (triage
      (t (t t))
      (_ tail : t t (self tail))
      t))