MiniAgda by Andreas Abel and Karl Mehltretter
--- opening "Prelude.ma" ---
--- scope checking ---
--- type checking ---
type  Empty : Set
type  Unit : Set
term  Unit.unit : < Unit.unit : Unit >
type  Bool : Set
term  Bool.true : < Bool.true : Bool >
term  Bool.false : < Bool.false : Bool >
type  If : (b : Bool) -> ++(A : Set) -> ++(B : Set) -> Set
{ If Bool.true A B = A
; If Bool.false A B = B
}
type  Either : ++(A : Set) -> ++(B : Set) -> Set
type  Either = \ A -> \ B -> (b : Bool) & If b B A
pattern left a = (false, a)
pattern right b = (true, b)
type  Maybe : ++(A : Set) -> Set
type  Maybe = \ A -> Either Unit A
pattern nothing = left unit
pattern just a = right a
type  Nat : + Size -> Set
{ Nat i = .[j < i] & Maybe (Nat j)
}
pattern zero j = (j, nothing)
pattern succ j n = (j, just n)
term  zer : .[i : Size] -> Nat $i
term  zer = [\ i ->] ([0] , (Bool.false , Unit.unit))
term  suc : .[i < #] -> (n : Nat i) -> Nat $i
term  suc = [\ i ->] \ n -> ([i] , (Bool.true , n))
term  suc : .[i : Size] -> (n : Nat i) -> Nat $i
{ suc [i] ([i' < i], m) = ([$i'] , (Bool.true , ([i'] , m)))
}
term  plus : .[i : Size] -> (n : Nat i) -> .[j : Size] -> (m : Nat j) -> Nat (i + j)
{ plus [i] ([i' < i], (Bool.false, un!t)) [j] m = m
; plus [i] ([i' < i], (Bool.true, n)) [j] m = suc [i' + j] (plus [i'] n [j] m)
}
--- evaluating ---
--- closing "Prelude.ma" ---