-- FILE: natPlus.mod

--> module defining naturals 
--> and plus operator over them
mod! NATplus {
  [ Nat]
  op 0 : -> Nat
  op s_ : Nat -> Nat
  op _+_ : Nat Nat -> Nat

  vars M N : Nat
  eq    0  + N = N .
  eq (s M) + N = s(M + N) .
}

select NATplus
red 0 .
red 0 + s 0 .
red s 0 + 0 .
red s s s s 0 + s s s 0 .

eof

select NATplus
parse 0 .
parse 0 + s 0 .
parse s 0 + 0 .
parse s s s s 0 + s s s 0 .

set verbose on
parse 0 .
parse 0 + s 0 .
parse s 0 + 0 .
parse s s s s 0 + s s s 0 .