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1−-- | Collection of type families on type lists. This module differs
2−-- from __Data.Singletons.Prelude.List__ because works with __[*]__
3−-- and relies on GHC's type equality (~). The rest of required
4−-- operations like 'Reverse' or '(:++:)' you could find in singletons
6−module TypeFun.Data.List
7− ( -- * Primitive operations on lists
27− -- * Operations with lists
39− -- * Uniqueness checking
51−import TypeFun.Data.Eq
52−import TypeFun.Data.Maybe
53−import TypeFun.Data.Peano
56−------------------------------------------------------------------------
57−-- NOTE: Errors type classes. These type classes are not in separate --
58−-- module because in this case user could import them and instantiate --
59−-- by mistake. The name of typeclass is an error message in fact. We --
60−-- have not any way to fail constraint explicitly, so this hack was --
62−------------------------------------------------------------------------
64−class ElementNotFoundInList a s
66−class ElementIsInList a s
68−class ListIsNotPrefixOf a b
70−class ListIsPrefixOf a b
72−class ElementIsNotUniqInList a s
74−class IndexNotFoundInList a s
76−----------------------
77−-- main module code --
78−----------------------
81−type family Length (a :: [k]) :: N where
83− Length (a ': as) = 'S (Length as)
85−type family Drop (c :: N) (s :: [k]) :: [k] where
87− Drop ('S c) '[] = '[]
88− Drop ('S c) (a ': as) = Drop c as
90−type family Take (c :: N) (s :: [k]) :: [k] where
92− Take ('S c) '[] = '[]
93− Take ('S c) (a ': as) = a ': (Take c as)
95−-- | Remove first argument type from anywhere in a list.
96−type family Delete (a :: k) (s :: [k]) :: [k] where
98− Delete a (a ': as) = Delete a as
99− Delete a (b ': as) = b ': (Delete a as)
101−-- | Remove index from the list
102−type family Remove (i :: N) (a :: [k]) :: [k] where
104− Remove 'Z (a ': as) = as
105− Remove ('S i) (a ': as) = a ': (Remove i as)
107−type family (:++:) (a :: [k]) (b :: [k]) :: [k] where
109− (a ': as) :++: b = a ': (as :++: b)
114− -> (l ~ (l :++: '[]) => r)
116−appendId = unsafeCoerce id
118−type IndexOf a s = FromJust (IndexOfMay a s)
120−type IndexOfMay a s = IndexOfMay' Z a s
122−type family IndexOfMay' (acc :: N) (a :: k) (s :: [k]) :: Maybe N where
123− IndexOfMay' acc a '[] = 'Nothing
124− IndexOfMay' acc a (a ': as) = 'Just acc
125− IndexOfMay' acc a (b ': as) = IndexOfMay' (S acc) a as
127−type family IndicesOfMay (a :: [k]) (b :: [k]) :: [Maybe N] where
128− IndicesOfMay '[] bs = '[]
129− IndicesOfMay (a ': as) bs = (IndexOfMay a bs) ': (IndicesOfMay as bs)
131−type family IndicesOf (a :: [k]) (b :: [k]) :: [N] where
132− IndicesOf '[] bs = '[]
133− IndicesOf (a ': as) bs = (IndexOf a bs) ': (IndicesOf as bs)
135−type Index idx s = FromJust (IndexMay idx s)
137−type family IndexMay (idx :: N) (s :: [k]) :: Maybe k where
138− IndexMay idx '[] = 'Nothing
139− IndexMay Z (a ': as) = 'Just a
140− IndexMay (S idx) (a ': as) = IndexMay idx as
142−type family IndicesMay (idxs :: [N]) (a :: [k]) :: [Maybe k] where
143− IndicesMay '[] as = '[]
144− IndicesMay (i ': idxs) as = (IndexMay i as) ': (IndicesMay idxs as)
146−type family Indices (idxs :: [N]) (a :: [k]) :: [k] where
147− Indices '[] as = '[]
148− Indices (i ': idxs) as = (Index i as) ': (Indices idxs as)
150−-- | Generates unresolvable constraint if fists element is not
151−-- contained inside of second
152−type Elem a s = NothingToConstr (IndexOfMay a s)
153− (ElementNotFoundInList a s)
155−-- | Reverse of 'Elem'
156−type NotElem a s = JustToConstr (IndexOfMay a s)
157− (ElementIsInList a s)
159−-- | Count elements in a list
160−type family Count (a :: k) (s :: [k]) :: N where
162− Count a (a ': as) = 'S (Count a as)
163− Count a (b ': as) = Count a as
165−-- | Constanints that first argument is a sublist of second. Reduces
166−-- to __(Elem a1 b, Elem a2 b, Elem a3 b, ...)__
167−type family SubList (a :: [k]) (b :: [k]) :: Constraint where
169− SubList (a ': as) bs = (Elem a bs, SubList as bs)
174− -> (SubList l l => r) -> r
175−subListId _ = unsafeCoerce id
177−type family NotSubList (a :: [k]) (b :: [k]) :: Constraint where
178− NotSubList '[] bs = ()
179− NotSubList (a ': as) bs = (NotElem a bs, NotSubList as bs)
181−type IsPrefixOf a b = ( If (IsPrefixOfBool a b)
183− (ListIsNotPrefixOf a b)
186−type IsNotPrefixOf a b = If (IsPrefixOfBool a b)
187− (ListIsPrefixOf a b)
190−-- | First argument is prefix of second
191−type family IsPrefixOfBool (a :: [k]) (b :: [k]) :: Bool where
192− IsPrefixOfBool '[] b = 'True
193− IsPrefixOfBool (a ': as) (a ': bs) = IsPrefixOfBool as bs
194− IsPrefixOfBool as bs = 'False
196−-- | Appends elements from first list to second if they are not
198−type family Union (a :: [k]) (b :: [k]) :: [k] where
200− Union (a ': as) bs = Union as (AppendUniq a bs)
202−type family UnionList (l :: [[k]]) :: [k] where
204− UnionList (a ': as) = Union a (UnionList as)
206−-- | Append element to list if element is not already presented in
207−type family AppendUniq (a :: k) (s :: [k]) :: [k] where
208− AppendUniq a (a ': bs) = a ': bs
209− AppendUniq a (b ': bs) = b ': (AppendUniq a bs)
210− AppendUniq a '[] = '[a]
212−-- | Calculates intersection between two lists. Order of elements is
213−-- taken from first list
214−type Intersect a b = (Indices (CatMaybes (IndicesOfMay a b)) b)
216−-- | Removes from first list all elements occured in second
217−type family Substract (a :: [k]) (b :: [k]) :: [k] where
218− Substract '[] b = '[]
220− Substract a (b ': bs) = Substract (Delete b a) bs
222−-- | Checks that element 'a' occurs in a list just once
223−type ElementIsUniq a s = If (Equal (S Z) (Count a s))
225− (ElementIsNotUniqInList a s)
227−-- | Checks that all elements in list are unique
228−type UniqElements a = UniqElements' a a
230−type family UniqElements' (a :: [k]) (self :: [k]) :: Constraint where
231− UniqElements' '[] self = ()
232− UniqElements' (a ': as) self = (ElementIsUniq a self, UniqElements' as self)