Control.Arrow.ArrowList

hxt-9.3.1.22: A collection of tools for processing XML with Haskell.

Copyright | Copyright (C) 2005 Uwe Schmidt
License | MIT
Maintainer | Uwe Schmidt (uwe\@fh-wedel.de)
Stability | experimental
Portability | portable
Safe Haskell | Safe-Inferred
Language | Haskell2010

Control.Arrow.ArrowList

Description

The list arrow class

This module defines the interface for list arrows.

A list arrow is a function that gives a list of results for a given argument. A single element result represents a normal function. An empty list often indicates that the function is undefined for the given argument. The empty list may also represent False, non-empty lists True. A list with more than one element gives all results for a so called nondeterministic function.

Synopsis

- class (Arrow a, ArrowPlus a, ArrowZero a, ArrowApply a) => ArrowList (a :: Type -> Type -> Type) where
  - arr2 :: (b1 -> b2 -> c) -> a (b1, b2) c
  - arr3 :: (b1 -> b2 -> b3 -> c) -> a (b1, (b2, b3)) c
  - arr4 :: (b1 -> b2 -> b3 -> b4 -> c) -> a (b1, (b2, (b3, b4))) c
  - arr2A :: (b -> a c d) -> a (b, c) d
  - arrL :: (b -> [c]) -> a b c
  - arr2L :: (b -> c -> [d]) -> a (b, c) d
  - constA :: c -> a b c
  - constL :: [c] -> a b c
  - isA :: (b -> Bool) -> a b b
  - (>>.) :: a b c -> ([c] -> [d]) -> a b d
  - (>.) :: a b c -> ([c] -> d) -> a b d
  - listA :: a b c -> a b [c]
  - unlistA :: a [b] b
  - this :: a b b
  - none :: a b c
  - withDefault :: a b c -> c -> a b c
  - single :: a b c -> a b c
  - applyA :: a b (a b c) -> a b c
  - ($<) :: (c -> a b d) -> a b c -> a b d
  - ($<<) :: (c1 -> c2 -> a b d) -> a b (c1, c2) -> a b d
  - ($<<<) :: (c1 -> c2 -> c3 -> a b d) -> a b (c1, (c2, c3)) -> a b d
  - ($<<<<) :: (c1 -> c2 -> c3 -> c4 -> a b d) -> a b (c1, (c2, (c3, c4))) -> a b d
  - ($<$) :: (c -> a b b) -> a b c -> a b b
  - mergeA :: (a (a1, b1) a1 -> a (a1, b1) b1 -> a (a1, b1) c) -> a (a1, b1) c
  - perform :: a b c -> a b b
  - catA :: [a b c] -> a b c
  - seqA :: [a b b] -> a b b

# Documentation

class (Arrow a, ArrowPlus a, ArrowZero a, ArrowApply a) => ArrowList (a :: Type -> Type -> Type) where #

The interface for list arrows

Only `mkA`, `isA` `(>>.)` don't have default implementations

Minimal complete definition

arrL, isA, (>>.)

Methods

arr2 :: (b1 -> b2 -> c) -> a (b1, b2) c #

construction of a 2 argument arrow from a binary function | | example: `a1 &&& a2 >>> arr2 f`

arr3 :: (b1 -> b2 -> b3 -> c) -> a (b1, (b2, b3)) c #

construction of a 3 argument arrow from a 3-ary function | | example: `a1 &&& a2 &&& a3 >>> arr3 f`

arr4 :: (b1 -> b2 -> b3 -> b4 -> c) -> a (b1, (b2, (b3, b4))) c #

construction of a 4 argument arrow from a 4-ary function | | example: `a1 &&& a2 &&& a3 &&& a4 >>> arr4 f`

arr2A :: (b -> a c d) -> a (b, c) d #

construction of a 2 argument arrow from a singe argument arrow

arrL :: (b -> [c]) -> a b c #

constructor for a list arrow from a function with a list as result

arr2L :: (b -> c -> [d]) -> a (b, c) d #

constructor for a list arrow with 2 arguments

constA :: c -> a b c #

constructor for a const arrow: `constA = arr . const`

constL :: [c] -> a b c #

constructor for a const arrow: `constL = arrL . const`

isA :: (b -> Bool) -> a b b #

builds an arrow from a predicate. If the predicate holds, the single list containing the input is returned, else the empty list

(>>.) :: a b c -> ([c] -> [d]) -> a b d infixl 8 #

combinator for converting the result of a list arrow into another list

example: `foo >>. reverse` reverses the the result of foo

example: `foo >>. take 1` constructs a deterministic version of foo by deleting all further results

(>.) :: a b c -> ([c] -> d) -> a b d infixl 8 #

combinator for converting the result of an arrow into a single element result

listA :: a b c -> a b [c] #

combinator for converting an arrow into a determinstic version with all results collected in a single element list

     listA af = af >>. (:[])

this is useful when the list of results computed by an arrow must be manipulated (e.g. sorted)

example for sorting the results of a filter

    collectAndSort         :: a b c -> a b c

    collectAndSort collect = listA collect >>> arrL sort

unlistA :: a [b] b #

the inverse of `listA`

     listA af >>> unlistA = af

unlistA is defined as `arrL id`

this :: a b b #

the identity arrow, alias for returnA

none :: a b c #

the zero arrow, alias for zeroArrow

withDefault :: a b c -> c -> a b c #

converts an arrow, that may fail, into an arrow that always succeeds

example: `withDefault none "abc"` is equivalent to `constA "abc"`

single :: a b c -> a b c #

makes a list arrow deterministic, the number of results is at most 1

definition

    single f = f >>. take 1

examples with strings:

    runLA ( single none ) "x" == []
    runLA ( single this ) "x" == ["x"]
    runLA ( single
            (constA "y"
             <+> this ) ) "x" == ["y"]

applyA :: a b (a b c) -> a b c #

compute an arrow from the input and apply the arrow to this input

definition: `(f &&& this) >>> app`

in a point free style, there is no way to use an argument in 2 places, this is a combinator for simulating this. first the argument is used to compute an arrow, then this new arrow is applied to the input

applyA coresponds to: `apply f x = let g = f x in g x`

see also: `$<`, `$<<`, `$<<<`, `$<<<<`, `$<$`

($<) :: (c -> a b d) -> a b c -> a b d infixl 2 #

compute the parameter for an arrow with extra parameters from the input and apply the arrow for all parameter values to the input

a kind of "function call" for arrows, useful for joining arrows

    infixl 2 ($<)

definition:

    g $< f = applyA (f >>> arr g)

if `f` fails, the whole arrow fails, e.g. `g $< none == none`

if `f` computes n values and `g` is deterministic, the whole arrow computes n values

examples with simple list arrows with strings

    prefixString   :: String -> a String String
    prefixString s =  arr (s++)

    runLA ( prefixString $< none           ) "x" == []
    runLA ( prefixString $< constA "y"     ) "x" == ["yx"]
    runLA ( prefixString $< this           ) "x" == ["xx"]
    runLA ( prefixString $< constA "y"
                            <+> constA "z" ) "x" == ["yx","zx"]
    runLA ( prefixString $< constA "y"
                            <+> this
                            <+> constA "z" ) "x" == ["yx","xx","zx"]

see also: `applyA`, `$<<`, `$<<<`, `$<<<<`, `$<$`

($<<) :: (c1 -> c2 -> a b d) -> a b (c1, c2) -> a b d infixl 2 #

binary version of `$<`

example with simple list arrows with strings

    infixString    :: String -> String -> a String String
    infixString s1 s2
                   = arr (\ s -> s1 ++ s ++ s2)

    runLA ( infixString $<< constA "y" &&& constA "z" ) "x" = ["yxz"]
    runLA ( infixString $<< this &&& this             ) "x" = ["xxx"]
    runLA ( infixString $<< constA "y"
                            &&& (constA "z" <+> this) ) "x" = ["yxz", "yxx"]

($<<<) :: (c1 -> c2 -> c3 -> a b d) -> a b (c1, (c2, c3)) -> a b d infixl 2 #

version of `$<` for arrows with 3 extra parameters

typical usage

    f $<<< g1 &&& g2 &&& g3

($<<<<) :: (c1 -> c2 -> c3 -> c4 -> a b d) -> a b (c1, (c2, (c3, c4))) -> a b d infixl 2 #

version of `$<` for arrows with 4 extra parameters

typical usage

    f $<<<< g1 &&& g2 &&& g3 &&& g4

($<$) :: (c -> a b b) -> a b c -> a b b infixl 2 #

compute the parameter for an arrow `f` with an extra parameter by an arrow `g` and apply all the results from `g` sequentially to the input

    infixl 2 ($<$)

typical usage:

    g :: a b c
    g = ...

    f :: c -> a b b
    f x = ... x ...

    f $<$ g

`f` computes the extra parameters for `g` from the input of type `b` and `g` is applied with this parameter to the input. This allows programming in a point wise style in `g`, which becomes neccessary, when a value is needed more than once.

this combinator is useful, when transforming a single value (document) step by step, with `g` for collecting the data for all steps, and `f` for transforming the input step by step

if `g` is deterministic (computes exactly one result), `g $<$ f == g $< f` holds

if `g` fails, `f $<$ g == this`

if `g` computes more than one result, `f` is applied sequentially to the input for every result from `g`

examples with simple list arrows with strings

    prefixString   :: String -> a String String
    prefixString s =  arr (s++)

    runLA ( prefixString $<$ none                      ) "x" == ["x"]
    runLA ( prefixString $<$ constA "y"                ) "x" == ["yx"]
    runLA ( prefixString $<$ constA "y" <+> constA "z" ) "x" == ["zyx"]
    runLA ( prefixString $<$ constA "y" <+> this
                             <+> constA "z"            ) "x" == ["zxyx"]

example with two extra parameter

    g1 :: a b c1
    g2 :: a b c2

    f          :: (c1, c2) -> a b b
    f (x1, x2) =  ... x1 ... x2 ...

    f $<$ g1 &&& g2

see also: `applyA`, `$<`

mergeA :: (a (a1, b1) a1 -> a (a1, b1) b1 -> a (a1, b1) c) -> a (a1, b1) c #

merge the result pairs of an arrow with type `a a1 (b1, b2)` by combining the tuple components with the `op` arrow

examples with simple list arrows working on strings and XmlTrees

        a1 :: a String (XmlTree, XmlTree)
        a1 = selem "foo" [this >>> mkText]
             &&&
             selem "bar" [arr (++"0") >>> mkText]

        runLA (a1 >>> mergeA (<+>) >>> xshow this) "42" == ["<foo>42</foo>","<bar>420</bar>"]
        runLA (a1 >>> mergeA (+=)  >>> xshow this) "42" == ["<foo>42<bar>420</bar></foo>"]

see also: `applyA`, `$<` and `+=` in class `ArrowXml`

perform :: a b c -> a b b #

useful only for arrows with side effects: perform applies an arrow to the input ignores the result and returns the input

example: `... >>> perform someTraceArrow >>> ...`

catA :: [a b c] -> a b c #

generalization of arrow combinator `<+>`

definition: `catA = foldl (<+>) none`

seqA :: [a b b] -> a b b #

generalization of arrow combinator `>>>`

definition: `seqA = foldl (>>>) this`

#### Instances

Instances details

ArrowList IOLA # |
Instance details Defined in Control.Arrow.IOListArrow Methods arr2 :: (b1 -> b2 -> c) -> IOLA (b1, b2) c # arr3 :: (b1 -> b2 -> b3 -> c) -> IOLA (b1, (b2, b3)) c # arr4 :: (b1 -> b2 -> b3 -> b4 -> c) -> IOLA (b1, (b2, (b3, b4))) c # arr2A :: (b -> IOLA c d) -> IOLA (b, c) d # arrL :: (b -> [c]) -> IOLA b c # arr2L :: (b -> c -> [d]) -> IOLA (b, c) d # constA :: c -> IOLA b c # constL :: [c] -> IOLA b c # isA :: (b -> Bool) -> IOLA b b # (>>.) :: IOLA b c -> ([c] -> [d]) -> IOLA b d # (>.) :: IOLA b c -> ([c] -> d) -> IOLA b d # listA :: IOLA b c -> IOLA b [c] # unlistA :: IOLA [b] b # this :: IOLA b b # none :: IOLA b c # withDefault :: IOLA b c -> c -> IOLA b c # single :: IOLA b c -> IOLA b c # applyA :: IOLA b (IOLA b c) -> IOLA b c # ($<) :: (c -> IOLA b d) -> IOLA b c -> IOLA b d # ($<<) :: (c1 -> c2 -> IOLA b d) -> IOLA b (c1, c2) -> IOLA b d # ($<<<) :: (c1 -> c2 -> c3 -> IOLA b d) -> IOLA b (c1, (c2, c3)) -> IOLA b d # ($<<<<) :: (c1 -> c2 -> c3 -> c4 -> IOLA b d) -> IOLA b (c1, (c2, (c3, c4))) -> IOLA b d # ($<$) :: (c -> IOLA b b) -> IOLA b c -> IOLA b b # mergeA :: (IOLA (a1, b1) a1 -> IOLA (a1, b1) b1 -> IOLA (a1, b1) c) -> IOLA (a1, b1) c # perform :: IOLA b c -> IOLA b b # catA :: [IOLA b c] -> IOLA b c # seqA :: [IOLA b b] -> IOLA b b #
ArrowList LA # |
Instance details Defined in Control.Arrow.ListArrow Methods arr2 :: (b1 -> b2 -> c) -> LA (b1, b2) c # arr3 :: (b1 -> b2 -> b3 -> c) -> LA (b1, (b2, b3)) c # arr4 :: (b1 -> b2 -> b3 -> b4 -> c) -> LA (b1, (b2, (b3, b4))) c # arr2A :: (b -> LA c d) -> LA (b, c) d # arrL :: (b -> [c]) -> LA b c # arr2L :: (b -> c -> [d]) -> LA (b, c) d # constA :: c -> LA b c # constL :: [c] -> LA b c # isA :: (b -> Bool) -> LA b b # (>>.) :: LA b c -> ([c] -> [d]) -> LA b d # (>.) :: LA b c -> ([c] -> d) -> LA b d # listA :: LA b c -> LA b [c] # unlistA :: LA [b] b # this :: LA b b # none :: LA b c # withDefault :: LA b c -> c -> LA b c # single :: LA b c -> LA b c # applyA :: LA b (LA b c) -> LA b c # ($<) :: (c -> LA b d) -> LA b c -> LA b d # ($<<) :: (c1 -> c2 -> LA b d) -> LA b (c1, c2) -> LA b d # ($<<<) :: (c1 -> c2 -> c3 -> LA b d) -> LA b (c1, (c2, c3)) -> LA b d # ($<<<<) :: (c1 -> c2 -> c3 -> c4 -> LA b d) -> LA b (c1, (c2, (c3, c4))) -> LA b d # ($<$) :: (c -> LA b b) -> LA b c -> LA b b # mergeA :: (LA (a1, b1) a1 -> LA (a1, b1) b1 -> LA (a1, b1) c) -> LA (a1, b1) c # perform :: LA b c -> LA b b # catA :: [LA b c] -> LA b c # seqA :: [LA b b] -> LA b b #
ArrowList (IOSLA s) # |
Instance details Defined in Control.Arrow.IOStateListArrow Methods arr2 :: (b1 -> b2 -> c) -> IOSLA s (b1, b2) c # arr3 :: (b1 -> b2 -> b3 -> c) -> IOSLA s (b1, (b2, b3)) c # arr4 :: (b1 -> b2 -> b3 -> b4 -> c) -> IOSLA s (b1, (b2, (b3, b4))) c # arr2A :: (b -> IOSLA s c d) -> IOSLA s (b, c) d # arrL :: (b -> [c]) -> IOSLA s b c # arr2L :: (b -> c -> [d]) -> IOSLA s (b, c) d # constA :: c -> IOSLA s b c # constL :: [c] -> IOSLA s b c # isA :: (b -> Bool) -> IOSLA s b b # (>>.) :: IOSLA s b c -> ([c] -> [d]) -> IOSLA s b d # (>.) :: IOSLA s b c -> ([c] -> d) -> IOSLA s b d # listA :: IOSLA s b c -> IOSLA s b [c] # unlistA :: IOSLA s [b] b # this :: IOSLA s b b # none :: IOSLA s b c # withDefault :: IOSLA s b c -> c -> IOSLA s b c # single :: IOSLA s b c -> IOSLA s b c # applyA :: IOSLA s b (IOSLA s b c) -> IOSLA s b c # ($<) :: (c -> IOSLA s b d) -> IOSLA s b c -> IOSLA s b d # ($<<) :: (c1 -> c2 -> IOSLA s b d) -> IOSLA s b (c1, c2) -> IOSLA s b d # ($<<<) :: (c1 -> c2 -> c3 -> IOSLA s b d) -> IOSLA s b (c1, (c2, c3)) -> IOSLA s b d # ($<<<<) :: (c1 -> c2 -> c3 -> c4 -> IOSLA s b d) -> IOSLA s b (c1, (c2, (c3, c4))) -> IOSLA s b d # ($<$) :: (c -> IOSLA s b b) -> IOSLA s b c -> IOSLA s b b # mergeA :: (IOSLA s (a1, b1) a1 -> IOSLA s (a1, b1) b1 -> IOSLA s (a1, b1) c) -> IOSLA s (a1, b1) c # perform :: IOSLA s b c -> IOSLA s b b # catA :: [IOSLA s b c] -> IOSLA s b c # seqA :: [IOSLA s b b] -> IOSLA s b b #
ArrowList (SLA s) # |
Instance details Defined in Control.Arrow.StateListArrow Methods arr2 :: (b1 -> b2 -> c) -> SLA s (b1, b2) c # arr3 :: (b1 -> b2 -> b3 -> c) -> SLA s (b1, (b2, b3)) c # arr4 :: (b1 -> b2 -> b3 -> b4 -> c) -> SLA s (b1, (b2, (b3, b4))) c # arr2A :: (b -> SLA s c d) -> SLA s (b, c) d # arrL :: (b -> [c]) -> SLA s b c # arr2L :: (b -> c -> [d]) -> SLA s (b, c) d # constA :: c -> SLA s b c # constL :: [c] -> SLA s b c # isA :: (b -> Bool) -> SLA s b b # (>>.) :: SLA s b c -> ([c] -> [d]) -> SLA s b d # (>.) :: SLA s b c -> ([c] -> d) -> SLA s b d # listA :: SLA s b c -> SLA s b [c] # unlistA :: SLA s [b] b # this :: SLA s b b # none :: SLA s b c # withDefault :: SLA s b c -> c -> SLA s b c # single :: SLA s b c -> SLA s b c # applyA :: SLA s b (SLA s b c) -> SLA s b c # ($<) :: (c -> SLA s b d) -> SLA s b c -> SLA s b d # ($<<) :: (c1 -> c2 -> SLA s b d) -> SLA s b (c1, c2) -> SLA s b d # ($<<<) :: (c1 -> c2 -> c3 -> SLA s b d) -> SLA s b (c1, (c2, c3)) -> SLA s b d # ($<<<<) :: (c1 -> c2 -> c3 -> c4 -> SLA s b d) -> SLA s b (c1, (c2, (c3, c4))) -> SLA s b d # ($<$) :: (c -> SLA s b b) -> SLA s b c -> SLA s b b # mergeA :: (SLA s (a1, b1) a1 -> SLA s (a1, b1) b1 -> SLA s (a1, b1) c) -> SLA s (a1, b1) c # perform :: SLA s b c -> SLA s b b # catA :: [SLA s b c] -> SLA s b c # seqA :: [SLA s b b] -> SLA s b b #