Documentation

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

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

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

construction of a 2 argument arrow from a singe argument arrow

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

constructor for a list arrow with 2 arguments

constructor for a const arrow: constA = arr . const

constructor for a const arrow: constL = arrL . const

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

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

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

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

the inverse of listA

 listA af >>> unlistA = af

unlistA is defined as arrL id

the identity arrow, alias for returnA

the zero arrow, alias for zeroArrow

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

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

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"]

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: $<, $<<, $<<<, $<<<<, $<$

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, $<<, $<<<, $<<<<, $<$

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"]

version of $< for arrows with 3 extra parameters

typical usage

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

version of $< for arrows with 4 extra parameters

typical usage

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

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, $<

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

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

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

generalization of arrow combinator <+>

definition: catA = foldl (<+>) none

generalization of arrow combinator >>>

definition: seqA = foldl (>>>) this