mmsyn2-0.3.2.0: The library that can be used for multiple (Ord a) => a -> b transformations

CaseBi

Description

A library that can be used as a case ... of constuction analogue for the multiple Ord a => a -> b transformations and data representation.

Synopsis

# Function that can be used instead of case ... of construction

Arguments

 :: Ord a => (b, Vector (a, b)) b is a default value that can be substituted if there is no correspendence in the set of (a, b) tuples (the otherwise or irrefutable pattern analogue). Vector of the (a, b) tuples that must be sorted in ascending order for the first argument. If there are several pairs (a, b) with the same a, the function gives a resulting b as if there is only the first one -> a an element for which the corresponding resulting b must be found -> b the result

The function that can be used instead of the 'case ... of' function

case var of
a1 -> b1
a2 -> b2
a3 -> b3
...
an -> bn
_  -> defaultValue

If we follow a lot of teaching materials that explain the workflow of the construction we think that the complexity of it is about O(n) for the transformation of a to b here. David Feuer (david.feuer (at) gmail.com) said that 'case ... of' is already optimized in GHC. Some benchmarks show that its behaviour tends to be about of O(log n) complexity, the same as the proposed function getBFst'. Nevertheless, the last one shows better performance in some situations, is rather general and can be used for another data representation. Therefore, it can be preferred in some situations. getBFst' uses binary search algorithm and a Vector (a, b) as somewhat like a complicated filter or like a special sieve. The Vector (a, b) must be sorted in ascending order here for the algorithm to be used correctly. For this you can use the following functions sortFst and sortFstV.

b before Vector (a, b) in the tuple in the type definition of the getBFst must be a defaultValue for 'case' above.

Vector (a, b) corresponds to

 a1 -> b1
a2 -> b2
a3 -> b3
...
an -> bn

Arguments

 :: Ord a => Vector (a, b) Vector of the (a, b) tuples that must be sorted in ascending order for the first argument -> b a default value that can be substituted if there is no correspendence in the set of (a, b) tuples (the otherwise or irrefutable pattern analogue) -> [a] a list of values needed to be transformed accordingly to the correct (a, b) tuple pairs -> [b] the resulting list

The function that uses special kind of bisection to effectively transform the [a] to [b] instead of simply use

case var of
a1 -> b1
a2 -> b2
a3 -> b3
...
an -> bn
_  -> defaultValue

A Vector (a, b) must be sorted in ascending order here for the algorithm to be used correctly. For this you can use the following functions sortFst and sortFstV. The function can be used to simplify the procedure for optimizing the code for transformation of the list data or to represent the data in another way.

b after the Vector (a, b) in the type definition of the getBFst must be a defaultValue for case ... of above.

Vector (a, b) corresponds to

 a1 -> b1
a2 -> b2
a3 -> b3
...
an -> bn

Arguments

 :: Ord a => Vector (a, b) Vector of the (a, b) tuples that are sorted in ascending order for the first argument -> b a default value that can be substituted if there is no correspendence in the set of (a, b) tuples (the otherwise or irrefutable pattern analogue) -> Vector a a Vector needed to be transformed accordingly to the correct (a, b) tuple pairs -> Vector b the resulting Vector

The function that uses special realization of the binary search to effectively transform the Vector a to Vector b instead of simply use

case var of
a1 -> b1
a2 -> b2
a3 -> b3
...
an -> bn
_  -> defaultValue

The Vector (a, b) must be sorted in ascending order here for the algorithm to be used correctly. For this you can use the following functions sortFst and sortFstV. it can be used to simplify the procedure for optimizing the code for transformation of the Vector data.

b after Vector (a, b) in the type definition of the getBFstV must be a defaultValue for case ... of above.

Vector (a, b) corresponds to

 a1 -> b1
a2 -> b2
a3 -> b3
...
an -> bn

# Additional functions that are used to sort a list of pairs (which can be obtained e. g. by zip)

sortFst :: Ord a => [(a, b)] -> [(a, b)] Source #

Function that sorts a list of (a, b) tuples by the first argument and is inspired by sort function (the last one can be used for sorting the (a, b) tuples where both the types of a and b have instances of the class Ord). It is inspired by the work: https://wiki.haskell.org/Introduction

Arguments

 :: Ord a => [(a, b)] The list of conditions that is then converted to the corresponding Vector -> Vector (a, b) the resulting sorted Vector that can be used further in getBFst' and its successors.

Function that prepares the list of (a, b) tuples representing the

case var of
a1 -> b1
a2 -> b2
a3 -> b3
...
an -> bn
_  -> defaultValue

for usage in the getBFst and getBFstV functions.

The resulting Vector has for every a only one element, which was the first in the list of tuples (a, b) after sorting by sortFst function.

## Function that can be used for changing the Vector (a, b) during its creation

Arguments

 :: Ord a => ((a, b) -> Bool) The predicate p used to select the only one value of b in the pairs (a, b) with the same a. ^ If there are several pairs (a, b) for the same a that satisfies a predicate then the first one is used. For large [(a, b)] ^ it can be rather complex. -> [(a, b)] The list of (a, b) sorted in the ascending order by the first element a (e. g. by the sortFst function) -> Vector (a, b) The resulting filtered Vector (a, b) that can be used for getFstB' and its successor functions.Example: filterP (\(t, w) -> (t == "1") || (w > 'f')) . sortFst \$ [("1",'a'),("4a",'k'),("4a",'b'),("4a",'c'),("4a",'d'),("4a",'e'),("b7",'c'),("b7",'k')] = [("1",'a'),("4a",'k'),("b7",'k')]

Is used to filter [(a, b)] of the corresponding values for getFstB' to obtain the Vector (a, b) such that the b element for the sequence of pairs (a, b) with the same a is selected by the predicate p and is not necessarily the first one as it is for the getFstB' function and its successors by default.