{-# OPTIONS_HADDOCK show-extensions #-}
-- |
-- Module : Languages.UniquenessPeriods.Array.Constraints
-- Copyright : (c) OleksandrZhabenko 2020
-- License : MIT
-- Stability : Experimental
-- Maintainer : olexandr543@yahoo.com
--
-- Provides several the most important variants of constraints for the
-- permutations. All the 'Array'
-- here must consists of unique 'Int' starting from 0 to n and the 'Int'
-- arguments must be in the range [0..n] though these inner constraints are
-- not checked. It is up to user to check them.
-- Uses arrays instead of vectors.
{-# LANGUAGE BangPatterns, FlexibleContexts #-}
module Languages.UniquenessPeriods.Array.Constraints (
-- * Basic predicate
unsafeOrderIJ
-- * Functions to work with permutations with basic constraints ('Array'-based)
, filterOrderIJ
, unsafeTriples
, unsafeQuadruples
-- ** With multiple elements specified
, unsafeSeveralA
, unsafeSeveralB
) where
import Data.Maybe (fromJust)
import Data.SubG (InsertLeft(..),filterG)
import GHC.Arr
import Data.Foldable (foldl')
-- | Being given the data satisfying the constraints in the module header checks whether in the 'Array' the first argument stands before the second one.
unsafeOrderIJ :: Int -> Int -> Array Int Int -> Bool
unsafeOrderIJ i j = (\(_,_,r) -> if r == 0 then True else False) . foldl' helpG (i,j,0)
helpG (t,u,n) z
| z == t = (t,u,1)
| z == u =
case n of
0 -> (t,u,2)
_ -> (t,u,n - 1)
| otherwise = (t,u,n)
{-# INLINE helpG #-}
-- | Being given the data satisfying the constraints in the module header returns the elements that satisfy 'unsafeOrderIJ' as a predicate.
filterOrderIJ :: (InsertLeft t (Array Int Int), Monoid (t (Array Int Int))) => Int -> Int -> t (Array Int Int) -> t (Array Int Int)
filterOrderIJ i j = filterG (unsafeOrderIJ i j)
-- | Being given the data satisfying the constraints in the module header reduces the number of further computations in the foldable structure of
-- the permutations each one being represented as 'Array' 'Int' 'Int' where the elements are all the numbers in the range [0..n] without duplication if the
-- arguments are the indeces of the duplicated words or their concatenated combinations in the corresponding line.
-- The first three arguments
-- are the indices of the the triple duplicated elements (words or their concatenated combinations in the @phonetic-languages@ series of packages).
unsafeTriples :: (InsertLeft t (Array Int Int), Monoid (t (Array Int Int))) => Int -> Int -> Int -> t (Array Int Int) -> t (Array Int Int)
unsafeTriples i j k = filterG (\v -> unsafeOrderIJ i j v && unsafeOrderIJ j k v)
-- | Being given the data satisfying the constraints in the module header reduces the number of further computations in the foldable structure of
-- the permutations each one being represented as 'Array' 'Int' 'Int' where the elements are all the numbers in the range [0..n] without duplication if the
-- arguments are the indeces of the duplicated words or their concatenated combinations in the corresponding line.
-- The first four arguments
-- are the indices of the the quadruple duplicated elements (words or their concatenated combinations in the @phonetic-languages@ series of packages).
unsafeQuadruples :: (InsertLeft t (Array Int Int), Monoid (t (Array Int Int))) => Int -> Int -> Int -> Int -> t (Array Int Int) -> t (Array Int Int)
unsafeQuadruples i j k l = filterG (\v -> unsafeOrderIJ i j v && unsafeOrderIJ j k v && unsafeOrderIJ k l v)
-- | Being given the data satisfying the constraints in the module header reduces the number of further computations in the foldable structure of
-- the permutations each one being represented as 'Array' 'Int' 'Int' where the elements are all the numbers in the range [0..n] without duplication.
-- The first argument
-- is the index of the the element (a word or their concatenated combination in the @phonetic-languages@ series of packages), the second argument
-- is 'Array' 'Int' of indices that are in the range [0..n]. Filters (and reduces further complex computtions) the permutations so that only the
-- variants with the indices in the second argument all stand AFTER the element with the index equal to the first argument.
unsafeSeveralA :: (InsertLeft t (Array Int Int), Monoid (t (Array Int Int))) => Int -> Array Int Int -> t (Array Int Int) -> t (Array Int Int)
unsafeSeveralA !i0 arr x = filterG (g i0 arr) x
where g !i0 !arr1 arr2 = all id . amap (\k -> unsafeOrderIJ i0 k arr2) $ arr1
-- | Being given the data satisfying the constraints in the module header reduces the number of further computations in the foldable structure of
-- the permutations each one being represented as 'Array' 'Int' 'Int' where the elements are all the numbers in the range [0..n] without duplication.
-- The first argument
-- is the index of the the element (a word or their concatenated combination in the @phonetic-languages@ series of packages), the second argument
-- is 'Array' of indices that are in the range [0..n]. Filters (and reduces further complex computtions) the permutations so that only the
-- variants with the indices in the second argument all stand BEFORE the element with the index equal to the first argument.
unsafeSeveralB :: (InsertLeft t (Array Int Int), Monoid (t (Array Int Int))) => Int -> Array Int Int -> t (Array Int Int) -> t (Array Int Int)
unsafeSeveralB !i0 arr x = filterG (g i0 arr) x
where g !i0 !arr1 arr2 = all id . amap (\k -> unsafeOrderIJ k i0 arr2) $ arr1