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Diffstat (limited to 'src/Inky/Decidable/Either.idr')
-rw-r--r-- | src/Inky/Decidable/Either.idr | 111 |
1 files changed, 0 insertions, 111 deletions
diff --git a/src/Inky/Decidable/Either.idr b/src/Inky/Decidable/Either.idr deleted file mode 100644 index bea3364..0000000 --- a/src/Inky/Decidable/Either.idr +++ /dev/null @@ -1,111 +0,0 @@ -module Inky.Decidable.Either - -import Data.So -import Data.These - -public export -Union : Type -> Type -> Bool -> Type -Union a b False = b -Union a b True = a - -public export -record LazyEither (0 a, b : Type) where - constructor Because - does : Bool - reason : Lazy (Union a b does) - -%name LazyEither p, q - -namespace Union - public export - map : {tag : Bool} -> (a -> c) -> (b -> d) -> Union a b tag -> Union c d tag - map {tag = False} f g x = g x - map {tag = True} f g x = f x - - public export - not : {tag : Bool} -> Union a b tag -> Union b a (not tag) - not {tag = False} x = x - not {tag = True} x = x - - public export - both : - {tag1 : Bool} -> {tag2 : Lazy Bool} -> - Union a b tag1 -> Lazy (Union c d tag2) -> - Union (a, c) (Either b d) (tag1 && tag2) - both {tag1 = True, tag2 = True} x y = (x, y) - both {tag1 = True, tag2 = False} x y = Right y - both {tag1 = False} x y = Left x - - public export - first : - {tag1 : Bool} -> {tag2 : Lazy Bool} -> - Union a b tag1 -> Lazy (Union c d tag2) -> - Union (Either a c) (b, d) (tag1 || tag2) - first {tag1 = True} x y = Left x - first {tag1 = False, tag2 = True} x y = Right y - first {tag1 = False, tag2 = False} x y = (x, y) - - public export - all : - {tag1, tag2 : Bool} -> - Union a b tag1 -> Union c d tag2 -> - Union (a, c) (These b d) (tag1 && tag2) - all {tag1 = True, tag2 = True} x y = (x, y) - all {tag1 = True, tag2 = False} x y = That y - all {tag1 = False, tag2 = True} x y = This x - all {tag1 = False, tag2 = False} x y = Both x y - - public export - any : - {tag1, tag2 : Bool} -> - Union a b tag1 -> Union c d tag2 -> - Union (These a c) (b, d) (tag1 || tag2) - any {tag1 = True, tag2 = True} x y = Both x y - any {tag1 = True, tag2 = False} x y = This x - any {tag1 = False, tag2 = True} x y = That y - any {tag1 = False, tag2 = False} x y = (x, y) - -public export -map : (a -> c) -> (b -> d) -> LazyEither a b -> LazyEither c d -map f g p = p.does `Because` Union.map f g p.reason - -public export -not : LazyEither a b -> LazyEither b a -not p = not p.does `Because` Union.not p.reason - -public export -both : LazyEither a b -> Lazy (LazyEither c d) -> LazyEither (a, c) (Either b d) -both p q = p.does && q.does `Because` Union.both p.reason q.reason - -public export -first : LazyEither a b -> Lazy (LazyEither c d) -> LazyEither (Either a c) (b, d) -first p q = p.does || q.does `Because` Union.first p.reason q.reason - -public export -all : LazyEither a b -> Lazy (LazyEither c d) -> LazyEither (a, c) (These b d) -all p q = p.does && q.does `Because` Union.all p.reason q.reason - -public export -any : LazyEither a b -> Lazy (LazyEither c d) -> LazyEither (These a c) (b, d) -any p q = p.does || q.does `Because` Union.any p.reason q.reason - -public export -so : (b : Bool) -> LazyEither (So b) (So $ not b) -so b = b `Because` if b then Oh else Oh - -export autobind infixr 0 >=> - -public export -andThen : - {0 p, q : a -> Type} -> - LazyEither a b -> ((x : a) -> LazyEither (p x) (q x)) -> - LazyEither (x ** p x) (Either b (x ** q x)) -andThen (True `Because` x) f = map (\px => (x ** px)) (\qx => Right (x ** qx)) (f x) -andThen (False `Because` y) f = False `Because` (Left y) - -public export -(>=>) : - {0 p, q : a -> Type} -> - LazyEither a b -> ((x : a) -> LazyEither (p x) (q x)) -> - LazyEither (x ** p x) (Either b (x ** q x)) -(>=>) = andThen |