@@ -243,7 +243,7 @@ type Trivial a = FromNat (Count a) ~ a
243243-- class.
244244instance (Num e) => Category (Matrix e) where
245245 type Object (Matrix e) a = (FL a a, Countable a)
246− id = iden
246+ id = iden
247247 (.) = comp
248248
249249instance NFData e => NFData (Matrix e cols rows) where
@@ -259,7 +259,6 @@ instance Eq e => Eq (Matrix e cols rows) where
259259 x@(Join _ _) == y@(Fork _ _) = abideJF x == y
260260
261261instance Num e => Num (Matrix e cols rows) where
262−
263262 a + b = zipWithM (+) a b
264263
265264 a - b = zipWithM (-) a b
@@ -326,7 +325,8 @@ instance (FromLists cols ()) => FromLists (Either () cols) () where
326325 fromLists [h : t] = Join (One h) (fromLists [t])
327326 fromLists _ = error "Wrong dimensions"
328327
329−instance {-# OVERLAPPABLE #-} (FromLists a (), FromLists b (), Countable a) => FromLists (Either a b) () where
328+instance {-# OVERLAPPABLE #-}
329+ (FromLists a (), FromLists b (), Countable a) => FromLists (Either a b) () where
330330 fromLists [l] =
331331 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))
332332 in Join (fromLists [take rowsA l]) (fromLists [drop rowsA l])
@@ -336,13 +336,15 @@ instance (FromLists () rows) => FromLists () (Either () rows) where
336336 fromLists ([h] : t) = Fork (One h) (fromLists t)
337337 fromLists _ = error "Wrong dimensions"
338338
339−instance {-# OVERLAPPABLE #-} (FromLists () a, FromLists () b, Countable a) => FromLists () (Either a b) where
339+instance {-# OVERLAPPABLE #-}
340+ (FromLists () a, FromLists () b, Countable a) => FromLists () (Either a b) where
340341 fromLists l@([_] : _) =
341342 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))
342343 in Fork (fromLists (take rowsA l)) (fromLists (drop rowsA l))
343344 fromLists _ = error "Wrong dimensions"
344345
345−instance (FromLists (Either a b) c, FromLists (Either a b) d, Countable c) => FromLists (Either a b) (Either c d) where
346+instance (FromLists (Either a b) c, FromLists (Either a b) d, Countable c)
347+ => FromLists (Either a b) (Either c d) where
346348 fromLists l@(h : t) =
347349 let lh = length h
348350 rowsC = fromInteger (natVal (Proxy :: Proxy (Count c)))
@@ -369,16 +371,15 @@ matrixBuilder' f =
369371matrixBuilder ::
370372 forall e a b.
371373 ( FLN a b,
372− CountableN b,
373374 Enum a,
374375 Enum b,
375376 Bounded a,
376377 Bounded b,
377378 Eq a,
378− CountableDimsN a b
379+ Countable b
379380 ) => ((a, b) -> e) -> Matrix e (Normalize a) (Normalize b)
380381matrixBuilder f =
381− let r = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))
382+ let r = fromInteger $ natVal (Proxy :: Proxy (Count b))
382383 positions = [(a, b) | a <- [minBound .. maxBound], b <- [minBound .. maxBound]]
383384 in fromLists . map (map f) . transpose . buildList r $ positions
384385 where
@@ -434,24 +435,7 @@ fromF ::
434435 ) =>
435436 (a -> b) ->
436437 Matrix e (Normalize a) (Normalize b)
437−fromF f =
438− let minA = minBound @a
439− maxA = maxBound @a
440− minB = minBound @b
441− maxB = maxBound @b
442− ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))
443− rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))
444− elementsA = take ccols [minA .. maxA]
445− elementsB = take rrows [minB .. maxB]
446− combinations = (,) <$> elementsA <*> elementsB
447− combAp = map snd . sort . map (\(a, b) -> if f a == b
448− then ((fromEnum a, fromEnum b), 1)
449− else ((fromEnum a, fromEnum b), 0)) $ combinations
450− mList = buildList combAp rrows
451− in tr $ fromLists mList
452− where
453− buildList [] _ = []
454− buildList l r = take r l : buildList (drop r l) r
438+fromF = fromF'
455439
456440-- Conversion
457441
@@ -947,24 +931,7 @@ fromFRel' ::
947931 ) =>
948932 (a -> b) ->
949933 Relation cols rows
950−fromFRel' f =
951− let minA = minBound @a
952− maxA = maxBound @a
953− minB = minBound @b
954− maxB = maxBound @b
955− ccols = fromInteger $ natVal (Proxy :: Proxy (Count cols))
956− rrows = fromInteger $ natVal (Proxy :: Proxy (Count rows))
957− elementsA = take ccols [minA .. maxA]
958− elementsB = take rrows [minB .. maxB]
959− combinations = (,) <$> elementsA <*> elementsB
960− combAp = map snd . sort . map (\(a, b) -> if f a == b
961− then ((fromEnum a, fromEnum b), nat 1)
962− else ((fromEnum a, fromEnum b), nat 0)) $ combinations
963− mList = buildList combAp rrows
964− in tr $ fromLists mList
965− where
966− buildList [] _ = []
967− buildList l r = take r l : buildList (drop r l) r
934+fromFRel' = fromF'
968935
969936-- | Lifts functions to relations with dimensions matching @a@ and @b@
970937-- cardinality's.
@@ -972,28 +939,11 @@ fromFRel ::
972939 forall a b.
973940 ( Liftable Boolean a b,
974941 CountableDimsN a b,
975− FL (Normalize b) (Normalize a)
942+ FLN b a
976943 ) =>
977944 (a -> b) ->
978945 Relation (Normalize a) (Normalize b)
979−fromFRel f =
980− let minA = minBound @a
981− maxA = maxBound @a
982− minB = minBound @b
983− maxB = maxBound @b
984− ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))
985− rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))
986− elementsA = take ccols [minA .. maxA]
987− elementsB = take rrows [minB .. maxB]
988− combinations = (,) <$> elementsA <*> elementsB
989− combAp = map snd . sort . map (\(a, b) -> if f a == b
990− then ((fromEnum a, fromEnum b), nat 1)
991− else ((fromEnum a, fromEnum b), nat 0)) $ combinations
992− mList = buildList combAp rrows
993− in tr $ fromLists mList
994− where
995− buildList [] _ = []
996− buildList l r = take r l : buildList (drop r l) r
946+fromFRel = fromFRel'
997947
998948-- | Lifts a relation function to a Boolean Matrix
999949toRel ::
@@ -1003,7 +953,7 @@ toRel ::
1003953 Enum a,
1004954 Enum b,
1005955 Eq b,
1006− CountableDimsN a b,
956+ CountableDims a b,
1007957 FLN b a
1008958 )
1009959 => (a -> b -> Bool) -> Relation (Normalize a) (Normalize b)
@@ -1012,8 +962,8 @@ toRel f =
1012962 maxA = maxBound @a
1013963 minB = minBound @b
1014964 maxB = maxBound @b
1015− ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))
1016− rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))
965+ ccols = fromInteger $ natVal (Proxy :: Proxy (Count a))
966+ rrows = fromInteger $ natVal (Proxy :: Proxy (Count b))
1017967 elementsA = take ccols [minA .. maxA]
1018968 elementsB = take rrows [minB .. maxB]
1019969 combinations = (,) <$> elementsA <*> elementsB