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Functions to operate with So of conjunctions #4788

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Functions to operate with So of conjunctions #4788

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30 changes: 28 additions & 2 deletions libs/base/Data/So.idr
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Original file line number Diff line number Diff line change
Expand Up @@ -23,14 +23,40 @@ choose : (b : Bool) -> Either (So b) (So (not b))
choose True = Left Oh
choose False = Right Oh

--------------------------------------------------------------------------------
-- Absurd- and negation-related properties
--------------------------------------------------------------------------------

||| Absurd when you have proof that both `b` and `not b` is true.
export
soAbsurd : So b -> So (not b) -> Void
soAbsurd sb snb with (sb)
| Oh = uninhabited snb
soAbsurd Oh = uninhabited

||| Absurd when you have a proof of both `b` and `not b` (with something else).
export
soConjAbsurd : So b -> So (not b && c) -> Void
soConjAbsurd Oh = uninhabited

||| Transmission between usage of value-level `not` and type-level `Not`.
export
soNotToNotSo : So (not b) -> Not (So b)
soNotToNotSo = flip soAbsurd

--------------------------------------------------------------------------------
--- Operations for `So` of conjunction
--------------------------------------------------------------------------------

||| Given proofs of two properties you have a proof of a conjunction.
export
(&&) : So b -> So c -> So (b && c)
Oh && Oh = Oh

||| A proof of the right side of a conjunction given a proof of the left side.
export
takeSoConjPart : So b -> So (b && c) -> So c
takeSoConjPart Oh Oh = Oh

||| Splits the proof of a conjunction to a pair of proofs for each part.
export
splitSoConj : So (b && c) -> (So b, So c)
splitSoConj {b=True} Oh = (Oh, Oh)