MiniAgda by Andreas Abel and Karl Mehltretter
--- opening "Polarities.ma" ---
--- scope checking ---
--- type checking ---
type  Const : ++ Set -> .[Set] -> Set
type  Const = \ A -> [\ X ->] A
type  DNeg : ^ Set -> + Set -> Set
type  DNeg = \ B -> \ A -> (A -> B) -> B
type  Empty : Set
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  Cont' : + Set -> Set
type  Cont' = DNeg Empty
term  cast' : .[i : Size] -> ^ Cont' (Nat i) -> Cont' (Nat #)
term  cast' = [\ i ->] \ x -> x
type  Cont : +(A : Set) -> Set
term  Cont.cont : .[A : Set] -> ^(uncont : DNeg Empty A) -> < Cont.cont uncont : Cont A >
term  uncont : .[A : Set] -> (cont : Cont A) -> DNeg Empty A
{ uncont [A] (Cont.cont #uncont) = #uncont
}
term  cast : .[i : Size] -> ^ Cont (Nat i) -> Cont (Nat #)
term  cast = [\ i ->] \ x -> x
type  Id : Nat # -> ++ Set -> Set
{ Id (Nat.zero [.#]) A = A
; Id (Nat.succ [.#] n) A = A
}
term  kast : .[i : Size] -> .[n : Nat i] -> Id n (Nat i) -> Id n (Nat #)
term  kast = [\ i ->] [\ n ->] \ x -> x
type  Tree : -(B : Set) -> ++(A : Set) -> Set
term  Tree.leaf : .[B : Set] -> .[A : Set] -> < Tree.leaf : Tree B A >
term  Tree.node : .[B : Set] -> .[A : Set] -> ^(y0 : A) -> ^(y1 : B -> Tree B A) -> < Tree.node y0 y1 : Tree B A >
type  STree : -(B : Set) -> ++(A : Set) -> + Size -> Set
term  STree.sleaf : .[B : Set] -> .[A : Set] -> .[s!ze : Size] -> .[i < s!ze] -> STree B A s!ze
term  STree.sleaf : .[B : Set] -> .[A : Set] -> .[i : Size] -> < STree.sleaf i : STree B A $i >
term  STree.snode : .[B : Set] -> .[A : Set] -> .[s!ze : Size] -> .[i < s!ze] -> ^ A -> ^ (B -> STree B A i) -> STree B A s!ze
term  STree.snode : .[B : Set] -> .[A : Set] -> .[i : Size] -> ^(y1 : A) -> ^(y2 : B -> STree B A i) -> < STree.snode i y1 y2 : STree B A $i >
type  Mu : ++(F : ++ Set -> Set) -> Set
term  Mu.inn : .[F : ++ Set -> Set] -> ^(y0 : F (Mu F)) -> < Mu.inn y0 : Mu F >
--- evaluating ---
--- closing "Polarities.ma" ---