PredDepType.golden

MiniAgda by Andreas Abel and Karl Mehltretter
--- opening "PredDepType.ma" ---
--- scope checking ---
--- type checking ---
type  Nat : + Size -> Set
term  Nat.zero : .[s!ze : Size] -> .[i < s!ze] -> Nat s!ze
term  Nat.zero : .[i : Size] -> < Nat.zero i : Nat $i >
term  Nat.succ : .[s!ze : Size] -> .[i < s!ze] -> ^ Nat i -> Nat s!ze
term  Nat.succ : .[i : Size] -> ^(y1 : Nat i) -> < Nat.succ i y1 : Nat $i >
type  Pred : (i : Size) -> (x : Nat $i) -> Set
{ Pred i (Nat.succ [.i] n) = Nat i
; Pred i (Nat.zero [.i]) = Nat $i
}
term  pred : .[i : Size] -> (x : Nat $i) -> Pred i x
{ pred [i] (Nat.succ [.i] n) = n
; pred [i] (Nat.zero [.i]) = Nat.zero [i]
}
--- evaluating ---
--- closing "PredDepType.ma" ---