From 2bd69bf893b7e1ebe4186639526451caf2083b12 Mon Sep 17 00:00:00 2001
From: Greg Brown <greg.brown01@ed.ac.uk>
Date: Fri, 2 Dec 2022 14:14:44 +0000
Subject: WIP: Frex is free

---
 src/Data/Morphism/Indexed.idr | 8 ++++++++
 src/Data/Setoid/Indexed.idr   | 7 +++++++
 2 files changed, 15 insertions(+)

(limited to 'src/Data')

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
@@ -39,6 +39,13 @@ public export
 (.index) : ISetoid a -> a -> Setoid
 (.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)
-- 
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