diff options
Diffstat (limited to 'src/Data')
| -rw-r--r-- | src/Data/Morphism/Indexed.idr | 8 | ||||
| -rw-r--r-- | src/Data/Setoid/Indexed.idr | 7 |
2 files changed, 15 insertions, 0 deletions
diff --git a/src/Data/Morphism/Indexed.idr b/src/Data/Morphism/Indexed.idr index c271c90..6737275 100644 --- a/src/Data/Morphism/Indexed.idr +++ b/src/Data/Morphism/Indexed.idr @@ -11,3 +11,11 @@ record IFunction {a : Type} (x, y : ISetoid a) where constructor MkIFunction func : IFunc x.U y.U cong : (i : a) -> {u, v : x.U i} -> x.relation i u v -> y.relation i (func i u) (func i v) + +public export +ifunc : IFunc x y -> IFunction (isetoid x) (isetoid y) +ifunc f = MkIFunction f (\i => cong (f i)) + +public export +compFunc : IFunction b c -> IFunction a b -> IFunction a c +compFunc f g = MkIFunction (\i => f.func i . g.func i) (\i => f.cong i . g.cong i) diff --git a/src/Data/Setoid/Indexed.idr b/src/Data/Setoid/Indexed.idr index 7277932..db5fb07 100644 --- a/src/Data/Setoid/Indexed.idr +++ b/src/Data/Setoid/Indexed.idr @@ -40,5 +40,12 @@ public export (.index) x i = MkSetoid (x.U i) (x.relation i) (x.equivalence i) public export +(.reindex) : ISetoid b -> (f : a -> b) -> ISetoid a +(.reindex) x f = MkISetoid + (\i => x.U $ f i) + (\i => x.relation $ f i) + (\i => x.equivalence $ f i) + +public export isetoid : (a -> Type) -> ISetoid a isetoid u = MkISetoid u (\_ => Equal) (\_ => equiv) |