right object 1 with ! is
end object;

right object prod(a,b) with pair is
  pi1: prod -> a
  pi2: prod -> b
end object;

right object exp(a,b) with curry is
  eval: prod(exp,a) -> b
end object;

left object nat with pr is
  0: 1 -> nat
  s: nat -> nat
end object;

let times=eval.prod(pr(curry(curry(pi2)), curry(curry(eval.pair(eval.pi1,eval.pair(pi2.pi1,pi2))))),I);
let ack_0=curry(s.pi2);
let ack_s=curry(eval.pair(times.pair(s.pi2,pi1),s.0.!));
let ack=eval.prod(pr(ack_0,ack_s),I);

#show aexp eval.prod(pr(curry(curry(pi2)), curry(curry(eval.pair(eval.pi1,eval.pair(pi2.pi1,pi2))))),I);
#show aexp curry(s.pi2);
#show aexp curry(eval.pair(times.pair(s.pi2,pi1),s.0.!));
#show aexp eval.prod(pr(ack_0,ack_s),I);

simp full ack.pair(s.s.s.0,s.s.s.0);

# time ~/cpl/cpl/bin/cpl.rb ack.cpl
# cpl.rb (An implementation of Categorical Programming Language)
# version 0.0.4
# Type help for help
# right object 1 defined
# right object prod(+,+) defined
# right object exp(-,+) defined
# left object nat defined
# times : prod(nat,exp(*a,*a)) -> exp(*a,*a)  defined
# ack_0 : *a -> exp(nat,nat)  defined
# ack_s : exp(nat,nat) -> exp(nat,nat)  defined
# ack : prod(nat,nat) -> nat  defined
# s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.s.0.!
#     : *a -> nat
# 
# real	21m17.567s
# user	20m43.233s
# sys	0m0.296s


# Haskell”Ĺ
# real	0m9.230s
# user	0m0.031s
# sys	0m0.000s