countConstructors.golden

MiniAgda by Andreas Abel and Karl Mehltretter
--- opening "countConstructors.ma" ---
--- scope checking ---
--- type checking ---
type  Nat : Set
term  Nat.zero : < Nat.zero : Nat >
term  Nat.succ : ^(y0 : Nat) -> < Nat.succ y0 : Nat >
term  plus : Nat -> Nat -> Nat
{}
term  f1 : Nat -> Nat
term  g1 : Nat -> Nat
{ f1 Nat.zero = Nat.zero
; f1 (Nat.succ Nat.zero) = Nat.zero
; f1 (Nat.succ (Nat.succ n)) = g1 n
}
{ g1 Nat.zero = Nat.zero
; g1 (Nat.succ n) = f1 (Nat.succ (Nat.succ n))
}
term  f : Nat -> Nat
term  g : Nat -> Nat
{ f Nat.zero = Nat.zero
; f (Nat.succ Nat.zero) = Nat.zero
; f (Nat.succ (Nat.succ n)) = g n
}
{ g Nat.zero = Nat.zero
; g (Nat.succ n) = plus (f n) (plus (f (Nat.succ n)) (f (Nat.succ (Nat.succ n))))
}
--- evaluating ---
--- closing "countConstructors.ma" ---