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mirror of https://github.com/idris-lang/Idris2.git synced 2024-12-26 05:01:34 +03:00
Idris2/libs/base/Data/So.idr
2022-06-17 19:52:35 +01:00

75 lines
1.8 KiB
Idris

module Data.So
import Data.Bool
%default total
||| Ensure that some run-time Boolean test has been performed.
|||
||| This lifts a Boolean predicate to the type level. See the function `choose`
||| if you need to perform a Boolean test and convince the type checker of this
||| fact.
|||
||| If you find yourself using `So` for something other than primitive types,
||| it may be appropriate to define a type of evidence for the property that you
||| care about instead.
public export
data So : Bool -> Type where
Oh : So True
export
Uninhabited (So False) where
uninhabited Oh impossible
||| Perform a case analysis on a Boolean, providing clients with a `So` proof
export
choose : (b : Bool) -> Either (So b) (So (not b))
choose True = Left Oh
choose False = Right Oh
export
decSo : (b : Bool) -> Dec (So b)
decSo True = Yes Oh
decSo False = No uninhabited
export
eqToSo : b = True -> So b
eqToSo Refl = Oh
export
soToEq : So b -> b = True
soToEq Oh = Refl
||| If `b` is True, `not b` can't be True
export
soToNotSoNot : So b -> Not (So (not b))
soToNotSoNot Oh = uninhabited
||| If `not b` is True, `b` can't be True
export
soNotToNotSo : So (not b) -> Not (So b)
soNotToNotSo = flip soToNotSoNot
export
soAnd : {a : Bool} -> So (a && b) -> (So a, So b)
soAnd soab with (choose a)
soAnd {a=True} soab | Left Oh = (Oh, soab)
soAnd {a=True} soab | Right prf = absurd prf
soAnd {a=False} soab | Right prf = absurd soab
export
andSo : (So a, So b) -> So (a && b)
andSo (Oh, Oh) = Oh
export
soOr : {a : Bool} -> So (a || b) -> Either (So a) (So b)
soOr soab with (choose a)
soOr {a=True} _ | Left Oh = Left Oh
soOr {a=False} soab | Right Oh = Right soab
export
orSo : Either (So a) (So b) -> So (a || b)
orSo (Left Oh) = Oh
orSo (Right Oh) = rewrite orTrueTrue a in
Oh