Add assocl and assocr functions to Data.Tensor

Data/Profunctor/Costrong.idr

@@ -33,7 +33,7 @@ import Data.Profunctor.Types
 ||| * `costrongl = costrongr . dimap swap swap`
 ||| * `costrongl . dimap unitr.rightToLeft unitr.leftToRight = id`
 ||| * `costrongl . lmap (mapSnd f) = costrongl . rmap (mapSnd f)`
-||| * `costrongr . costrongr = costrongr . dimap assoc.leftToRight assoc.rightToLeft`
+||| * `costrongr . costrongr = costrongr . dimap assocl assocr`
 |||
 ||| @ ten The tensor product of the monoidal structure
 public export

Data/Profunctor/Strong.idr

@@ -30,7 +30,7 @@ import Data.Profunctor.Types
 ||| * `strongl = dimap swap swap . strongr`
 ||| * `dimap unitr.rightToLeft unitr.leftToRight . strongl = id`
 ||| * `lmap (mapSnd f) . strongl = rmap (mapSnd f) . strongl`
-||| * `strongr . strongr = dimap assoc.rightToLeft assoc.leftToRight . strongr`
+||| * `strongr . strongr = dimap assocr assocl . strongr`
 |||
 ||| @ ten The tensor product of the monoidal structure
 public export
@@ -156,13 +156,13 @@ ProfunctorFunctor (GenTambara ten) where
 export
 Tensor ten i => ProfunctorComonad (GenTambara ten) where
   proextract (MkTambara p) = dimap unitr.rightToLeft unitr.leftToRight p
-  produplicate (MkTambara p) = MkTambara $ MkTambara $ dimap assoc.rightToLeft assoc.leftToRight p
+  produplicate (MkTambara p) = MkTambara $ MkTambara $ dimap assocr assocl p
 
 export
 Associative ten => Symmetric ten => Profunctor p => GenStrong ten (GenTambara ten p) where
-  strongl (MkTambara p) = MkTambara $ dimap assoc.rightToLeft assoc.leftToRight p
+  strongl (MkTambara p) = MkTambara $ dimap assocr assocl p
-  strongr (MkTambara p) = MkTambara $ dimap (assoc.rightToLeft . mapFst swap)
+  strongr (MkTambara p) = MkTambara $ dimap (assocr . mapFst swap)
-                                            (mapFst swap . assoc.leftToRight) p
+                                            (mapFst swap . assocl) p
 
 export
 Bifunctor ten => Profunctor p => Functor (GenTambara ten p a) where
@@ -223,10 +223,10 @@ export
   projoin (MkPastro {x=x',y=y',z=z'} l' (MkPastro {x,y,z} l m r) r') = MkPastro ll m rr
     where
       ll : y `ten` (z' `ten` z) -> b
-      ll = l' . mapFst l . assoc.leftToRight . mapSnd swap
+      ll = l' . mapFst l . assocl . mapSnd swap
 
       rr : a -> x `ten` (z' `ten` z)
-      rr = mapSnd swap . assoc.rightToLeft . mapFst r . r'
+      rr = mapSnd swap . assocr . mapFst r . r'
 
 export
 ProfunctorAdjunction (GenPastro ten) (GenTambara ten) where
@@ -238,15 +238,15 @@ export
   strongl (MkPastro {x,y,z} l m r) = MkPastro l' m r'
     where
       l' : y `ten` (z `ten` c) -> b `ten` c
-      l' = mapFst l . assoc.leftToRight
+      l' = mapFst l . assocl
       r' : a `ten` c -> x `ten` (z `ten` c)
-      r' = assoc.rightToLeft . mapFst r
+      r' = assocr . mapFst r
   strongr (MkPastro {x,y,z} l m r) = MkPastro l' m r'
     where
       l' : y `ten` (c `ten` z) -> c `ten` b
-      l' = swap . mapFst l . assoc.leftToRight . mapSnd swap
+      l' = swap . mapFst l . assocl . mapSnd swap
       r' : c `ten` a -> x `ten` (c `ten` z)
-      r' = mapSnd swap . assoc.rightToLeft . mapFst r . swap
+      r' = mapSnd swap . assocr . mapFst r . swap
 
 
 ||| The monad generated by the reflective subcategory of profunctors that

Data/Tensor.idr

@@ -15,10 +15,18 @@ module Data.Tensor
 ||| associative up to isomorphism.
 |||
 ||| Laws:
-||| * `mapFst assoc.rightToLeft . assoc.leftToRight . assoc.leftToRight = assoc.leftToRight . mapSnd assoc.leftToRight`
+||| * `mapFst assocl . assocl . assocl = assocl . mapSnd assocl`
 public export
 interface Bifunctor ten => Associative ten where
+  assocl : a `ten` (b `ten` c) -> (a `ten` b) `ten` c
+  assocl = assoc.leftToRight
+
+  assocr : (a `ten` b) `ten` c -> a `ten` (b `ten` c)
+  assocr = assoc.rightToLeft
+
   assoc : a `ten` (b `ten` c) <=> (a `ten` b) `ten` c
+  assoc = MkEquivalence assocl assocr
+
 
 ||| A bifunctor that admits a swap map, i.e. a bifunctor that is
 ||| symmetric up to isomorphism.
@@ -38,7 +46,7 @@ interface Bifunctor ten => Symmetric ten where
 ||| monoidal category.
 |||
 ||| Laws:
-||| * `mapSnd unitl.leftToRight = mapFst unitr.leftToRight . assoc.leftToRight`
+||| * `mapSnd unitl.leftToRight = mapFst unitr.leftToRight . assocl`
 public export
 interface Associative ten => Tensor ten i | ten where
   unitl : i `ten` a <=> a
@@ -52,7 +60,8 @@ interface Associative ten => Tensor ten i | ten where
 
 export
 Associative Pair where
-  assoc = MkEquivalence (\(x,(y,z)) => ((x,y),z)) (\((x,y),z) => (x,(y,z)))
+  assocl (x,(y,z)) = ((x,y),z)
+  assocr ((x,y),z) = (x,(y,z))
 
 export
 Symmetric Pair where
@@ -71,17 +80,13 @@ Tensor Pair () where
 
 export
 Associative Either where
-  assoc = MkEquivalence f b
+  assocl (Left x) = Left (Left x)
-    where
+  assocl (Right (Left x)) = Left (Right x)
-      f : forall a,b,c. Either a (Either b c) -> Either (Either a b) c
+  assocl (Right (Right x)) = Right x
-      f (Left x) = Left (Left x)
-      f (Right (Left x)) = Left (Right x)
-      f (Right (Right x)) = Right x
 
-      b : forall a,b,c. Either (Either a b) c -> Either a (Either b c)
+  assocr (Left (Left x)) = Left x
-      b (Left (Left x)) = Left x
+  assocr (Left (Right x)) = Right (Left x)
-      b (Left (Right x)) = Right (Left x)
+  assocr (Right x) = Right (Right x)
-      b (Right x) = Right (Right x)
 
 export
 Symmetric Either where