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[haskell/symantic-base.git] / src / Symantic / Base / Permutable.hs
1 {-# LANGUAGE TypeFamilyDependencies #-}
2 {-# LANGUAGE UndecidableInstances #-}
3 module Symantic.Base.Permutable where
4
5 import Data.Function ((.))
6 import Data.Maybe (Maybe(..), fromJust)
7
8 import Symantic.Base.Composable
9 import Symantic.Base.Algebrable
10
11 -- * Class 'Permutable'
12 class Permutable repr where
13 -- Use @TypeFamilyDependencies@ to help type-inference infer @(repr)@.
14 type Permutation (repr:: * -> * -> *) = (r :: * -> * -> *) | r -> repr
15 type Permutation repr = Permutation (UnTrans repr)
16 permutable :: Permutation repr (a->k) k -> repr (a->k) k
17 perm :: repr (a->k) k -> Permutation repr (a->k) k
18 noPerm :: Permutation repr k k
19 permWithDefault :: a -> repr (a->k) k -> Permutation repr (a->k) k
20 optionalPerm ::
21 Eitherable repr => Dimapable repr => Permutable repr =>
22 repr (a->k) k -> Permutation repr (Maybe a -> k) k
23 optionalPerm = permWithDefault Nothing . dimap Just fromJust
24
25 (<&>) ::
26 Permutable repr =>
27 Tupable (Permutation repr) =>
28 repr (a->k) k ->
29 Permutation repr (b->k) k ->
30 Permutation repr ((a,b)->k) k
31 x <&> y = perm x <:> y
32
33 (<?&>) ::
34 Eitherable repr =>
35 Dimapable repr =>
36 Permutable repr =>
37 Tupable (Permutation repr) =>
38 repr (a->k) k ->
39 Permutation repr (b->k) k ->
40 Permutation repr ((Maybe a,b)->k) k
41 x <?&> y = optionalPerm x <:> y
42
43 (<*&>) ::
44 Eitherable repr =>
45 Repeatable repr =>
46 Dimapable repr =>
47 Permutable repr =>
48 Tupable (Permutation repr) =>
49 repr (a->k) k ->
50 Permutation repr (b->k) k ->
51 Permutation repr (([a],b)->k) k
52 x <*&> y = permWithDefault [] (many1 x) <:> y
53
54 (<+&>) ::
55 Eitherable repr =>
56 Repeatable repr =>
57 Dimapable repr =>
58 Permutable repr =>
59 Tupable (Permutation repr) =>
60 repr (a->k) k ->
61 Permutation repr (b->k) k ->
62 Permutation repr (([a],b)->k) k
63 x <+&> y = perm (many1 x) <:> y
64
65 infixr 4 <&>
66 infixr 4 <?&>
67 infixr 4 <*&>
68 infixr 4 <+&>
69
70 {-# INLINE (<&>) #-}
71 {-# INLINE (<?&>) #-}
72 {-# INLINE (<*&>) #-}
73 {-# INLINE (<+&>) #-}