From 522eb40ab39800f75daa704ae56c18953c4885e7 Mon Sep 17 00:00:00 2001
From: Greg Brown <greg.brown01@ed.ac.uk>
Date: Tue, 6 Dec 2022 13:22:10 +0000
Subject: Migrate to use idris-setoid library.

---
 src/Data/Morphism/Indexed.idr | 13 ----------
 src/Data/Setoid.idr           | 55 -------------------------------------------
 src/Data/Setoid/Either.idr    | 37 -----------------------------
 src/Data/Setoid/Indexed.idr   | 48 -------------------------------------
 4 files changed, 153 deletions(-)
 delete mode 100644 src/Data/Morphism/Indexed.idr
 delete mode 100644 src/Data/Setoid.idr
 delete mode 100644 src/Data/Setoid/Either.idr
 delete mode 100644 src/Data/Setoid/Indexed.idr

(limited to 'src/Data')

diff --git a/src/Data/Morphism/Indexed.idr b/src/Data/Morphism/Indexed.idr
deleted file mode 100644
index c271c90..0000000
--- a/src/Data/Morphism/Indexed.idr
+++ /dev/null
@@ -1,13 +0,0 @@
-module Data.Morphism.Indexed
-
-import Data.Setoid.Indexed
-
-public export
-IFunc : {a : Type} -> (x, y : a -> Type) -> Type
-IFunc {a} x y = (i : a) -> x i -> y i
-
-public export
-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)
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
diff --git a/src/Data/Setoid/Either.idr b/src/Data/Setoid/Either.idr
deleted file mode 100644
index 682ac5a..0000000
--- a/src/Data/Setoid/Either.idr
+++ /dev/null
@@ -1,37 +0,0 @@
-module Data.Setoid.Either
-
-import public Data.Setoid
-
-public export
-data Either : (0 r : Rel a) -> (0 s : Rel b) -> Rel (Either a b) where
-  Left  : forall r, s . r x y -> Either r s (Left x) (Left y)
-  Right : forall r, s . s x y -> Either r s (Right x) (Right y)
-
-public export
-[eitherRefl] Reflexive a rel => Reflexive b rel' => Reflexive (Either a b) (Either rel rel') where
-  reflexive {x = (Left x)}  = Left reflexive
-  reflexive {x = (Right x)} = Right reflexive
-
-public export
-[eitherSym] Symmetric a rel => Symmetric b rel' => Symmetric (Either a b) (Either rel rel') where
-  symmetric (Left eq)  = Left $ symmetric eq
-  symmetric (Right eq) = Right $ symmetric eq
-
-public export
-[eitherTrans] Transitive a rel => Transitive b rel'
-  => Transitive (Either a b) (Either rel rel') where
-  transitive (Left eq)  (Left eq')  = Left $ transitive eq eq'
-  transitive (Right eq) (Right eq') = Right $ transitive eq eq'
-
-public export
-EitherEquivalence : Setoid.Equivalence a rel -> Setoid.Equivalence b rel'
-  -> Setoid.Equivalence (Either a b) (Either rel rel')
-EitherEquivalence eq eq' = MkEquivalence
-  { refl  = MkReflexive $ reflexive @{eitherRefl @{eq.refl} @{eq'.refl}}
-  , sym   = MkSymmetric $ symmetric @{eitherSym @{eq.sym} @{eq'.sym}}
-  , trans = MkTransitive $ transitive @{eitherTrans @{eq.trans} @{eq'.trans}}
-  }
-
-public export
-EitherSetoid : Setoid -> Setoid -> Setoid
-EitherSetoid x y = MkSetoid _ _ $ EitherEquivalence x.equivalence y.equivalence
diff --git a/src/Data/Setoid/Indexed.idr b/src/Data/Setoid/Indexed.idr
deleted file mode 100644
index a04b647..0000000
--- a/src/Data/Setoid/Indexed.idr
+++ /dev/null
@@ -1,48 +0,0 @@
-module Data.Setoid.Indexed
-
-import public Data.Setoid
-
-%default total
-
-public export
-IRel : {a : Type} -> (a -> Type) -> Type
-IRel {a = a} x = (i : a) -> x i -> x i -> Type
-
-public export
-IReflexive : {a : Type} -> (x : a -> Type) -> IRel x -> Type
-IReflexive x rel = (i : a) -> Reflexive (x i) (rel i)
-
-public export
-ISymmetric : {a : Type} -> (x : a -> Type) -> IRel x -> Type
-ISymmetric x rel = (i : a) -> Symmetric (x i) (rel i)
-
-public export
-ITransitive : {a : Type} -> (x : a -> Type) -> IRel x -> Type
-ITransitive x rel = (i : a) -> Transitive (x i) (rel i)
-
-public export
-IEquivalence : {a : Type} -> (x : a -> Type) -> IRel x -> Type
-IEquivalence x rel = (i : a) -> Setoid.Equivalence (x i) (rel i)
-
-public export
-record ISetoid (a : Type) where
-  constructor MkISetoid
-  0 U         : a -> Type
-  0 relation  : IRel U
-  equivalence : IEquivalence U relation
-
-public export
-fromIndexed : (a -> Setoid) -> ISetoid a
-fromIndexed x = MkISetoid (\i => (x i).U) (\i => (x i).relation) (\i => (x i).equivalence)
-
-public export
-(.index) : ISetoid a -> a -> Setoid
-(.index) x i = MkSetoid (x.U i) (x.relation i) (x.equivalence i)
-
-public export
-reindex : (a -> b) -> ISetoid b -> ISetoid a
-reindex f x = MkISetoid (x.U . f) (\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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