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Diffstat (limited to 'src/Data/Setoid.idr')
-rw-r--r-- | src/Data/Setoid.idr | 55 |
1 files changed, 0 insertions, 55 deletions
diff --git a/src/Data/Setoid.idr b/src/Data/Setoid.idr deleted file mode 100644 index 8014bac..0000000 --- a/src/Data/Setoid.idr +++ /dev/null @@ -1,55 +0,0 @@ -module Data.Setoid - -import public Control.Relation - -%default total - -public export -record Equivalence a (rel : Rel a) where - constructor MkEquivalence - refl : Reflexive a rel - sym : Symmetric a rel - trans : Transitive a rel - -public export -record Setoid where - constructor MkSetoid - 0 U : Type - 0 relation : Rel U - equivalence : Data.Setoid.Equivalence U relation - -public export -equiv : Control.Relation.Equivalence a rel => Data.Setoid.Equivalence a rel -equiv = MkEquivalence (MkReflexive reflexive) (MkSymmetric symmetric) (MkTransitive transitive) - -public export -[refl'] (eq : Data.Setoid.Equivalence a rel) => Reflexive a rel where - reflexive = reflexive @{eq.refl} - -public export -[sym'] (eq : Data.Setoid.Equivalence a rel) => Symmetric a rel where - symmetric = symmetric @{eq.sym} - -public export -[trans'] (eq : Data.Setoid.Equivalence a rel) => Transitive a rel where - transitive = transitive @{eq.trans} - -public export -[equiv'] Data.Setoid.Equivalence a rel => Control.Relation.Equivalence a rel - using refl' sym' trans' where - -public export -(.reflexive) : Data.Setoid.Equivalence a rel -> {x : a} -> rel x x -(.reflexive) eq = reflexive @{eq.refl} - -public export -(.symmetric) : Data.Setoid.Equivalence a rel -> {x, y : a} -> rel x y -> rel y x -(.symmetric) eq = symmetric @{eq.sym} - -public export -(.transitive) : Data.Setoid.Equivalence a rel -> {x, y, z : a} -> rel x y -> rel y z -> rel x z -(.transitive) eq = transitive @{eq.trans} - -public export -(.equalImpliesEq) : Data.Setoid.Equivalence a rel -> {x, y : a} -> x = y -> rel x y -(.equalImpliesEq) eq Refl = eq.reflexive |