Tacit programming: Difference between revisions

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{{Short description|Programming paradigm}}

'''Tacit programming''', also called '''point-free style''', is a [[programming paradigm]] in which function definitions do not identify the [[parameter (computer science)|arguments]] (or "points") on which they operate. Instead the definitions merely [[function composition (computer science)|compose]] other functions, among which are [[Combinatory logic|combinators]] that manipulate the arguments. Tacit programming is of theoretical interest, because the strict use of composition results in programs that are well adapted for [[Equational logic|equational]] reasoning.<ref name="cunha2005">{{cite thesis |last1=Cunha |first1=Manuel Alcino Pereira da Cunha (|year=2005) [http|url=https://hdl.handle.net/1822/2869 |title=Point-free Program Calculation |degree=PhD |publisher=[[University of Minho]]}}</ref> It is also the natural style of certainsome [[programming languageslanguage]]s, including [[APL (programming language)|APL]] and its derivatives,<ref>W.{{cite Nevillebook |editor1-last=Holmes, ed|editor1-first=W. (Neville |year=2006) ''|title=Computers and People''}}</ref> and [[concatenative programming language|concatenative languages]] such as [[Forth (programming language)|Forth]]. The lack of argument naming gives point-free style a reputation of being unnecessarilyneedlessly obscure, hence the [[epithet]] "pointless style".<ref name="cunha2005"/>

[[Unix]] [[Command-line interface|scripting]] uses the paradigm with [[Pipeline (Unix)|pipes]].

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return baz(bar(foo(x)))

</syntaxhighlight>

... can be written in point-free style as the composition of a sequence of functions, without parameters:<ref>{{cite web | url=http://concatenative.org/wiki/view/Concatenative%20language/Name%20code%20not%20values | title=Name code not values | publisher=Concatenative.org | accessdateaccess-date=13 September 2013}}</ref>

<syntaxhighlight lang="python">

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</syntaxhighlight>

For a more complex example, the [[Haskell]] code {{<code|1=>p = ((.) f) . g}}</code> can be translated as:

<syntaxhighlight lang="python">

p = partial(compose, partial(compose, f), g)

</syntaxhighlight>

===Functional programming===

A simple example (in [[Haskell (programming language)|Haskell]]) is a program which computes the sum of a list of numbers. We can define the sum function recursively using a ''pointed'' style (cf. [[value-level programming|''value''-level programming]]) as:

<syntaxhighlight lang="haskell">sum [] = 0

sum (x:xs) = x + sum xs</syntaxhighlight>

sum [] = 0

</syntaxhighlight>

However, using a [[fold (higher-order function)|fold]], wethis can replacebe thisreplaced with:

<syntaxhighlight lang="haskell">

sum xs = foldr (+) 0 xs

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</syntaxhighlight>

The following Haskell-like pseudo-code[[pseudocode]] exposes how to reduce a function definition to its point-free equivalent:

<syntaxhighlight lang="haskell" line highlight="5">

p = \x -> \y -> \z -> f (g x y) z

= \x -> \y -> f (g x y)

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<syntaxhighlight lang="haskell">

mf = (. map) . (.) . filter

</syntaxhighlight>NoteAs that, as statedsuggested previouslyalready, the points in ''point-free'' refer to the arguments, not to the use of dots; a common misconception.<ref>{{Cite web |url=https://wiki.haskell.org/Pointfree#But_pointfree_has_more_points.21 |title=Pointfree - HaskellWiki|website=wiki.haskellHaskell.org Wiki |access-date=2016-06-05}}</ref>

A few programs have been written to automatically convert a Haskell expression to a point-free form.

===APL family===

In the language [[J (programming language)|J]], the same sort of point-free code occurs in a function made to compute the average of a list (array) of numbers:

<syntaxhighlight lang=j>avg=: +/ % #</syntaxhighlight>

<code>+/</code> sums the items of the array by mapping (<code>/</code>) summation (<code>+</code>) to the array. <code>%</code> divides the sum by the number of elements (<code>#</code>) in the array.

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===Pipelines===

====Unix pipeline====

{{mainFurther|Pipeline (Unix)}}

In Unix scripting the functions are computer programs which receive data from [[Standard streams|standard input]] and send the results to [[Standard streams|standard output]]. For example,

<syntaxhighlight lang="bash">

sort | uniq -c | sort -rn

</syntaxhighlight>

is a tacit or point-free composition which returns the counts of its arguments and the arguments, in the order of decreasing counts. The 'sort' and 'uniq' are the functions, the '-c' and '-rn' control the functions, but the arguments are not mentioned. The pipe '|' is the composition operator.

sort | uniq -c | sort -rn

Due to the way pipelines work, it is only normally possible to pass one "argument" at a time in the form of a pair of standard input/output stream. Although extra [[file descriptor]]s can be opened from [[named pipe]]s, this no longer constitutes a point-free style.

is a tacit or point-free composition which returns the counts of its arguments and the arguments, in the order of decreasing counts. The '{{mono|sort'}} and '{{mono|uniq'}} are the functions, the '{{Code|-c'}} and '{{Code|-rn'}} control the functions, but the arguments are not mentioned. The pipe '<Code>|'</code> is the composition operator.

Due to the way pipelines work, it is only normally possible only to pass one "''argument"'' at a time in the form of a pair of standard [[input/output]] stream. Although extra [[file descriptor]]s can be opened from [[named pipe]]s, this no longer constitutes a point-free style.

====jq====

[[jq (programming language)|jq]] is a [[JSON]]-oriented programming language in which the <code>|</code> symbol is used to connect filters to form a pipeline in a familiar way. For example:

the '|' symbol is used to connect filters to form a pipeline

in a familiar way. For example:

[1,2] | add

evaluates to 3. (Yes, the JSON array is a jq filter that evaluates to an array.)

Although similar to Unix pipelines, jq pipelines allow the incoming data to be sent to more than one recipient on the RHS of the <code>|</code> as though in parallel. For example, the program <code>add/length</code> will compute the average of the numbers in an array, so that:

incoming data to be sent to more than one recipient on the

RHS of the '|' as though in parallel. For example, the program `add/length`

will compute the average of the numbers in an array, so that:

[1,2] | add/length

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evaluates to [2,3,1.5]

A dot ('<code>.'</code>) can be used to define an attachment point on the RHS, e.g.:

1 | [., .]

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2 | pow(.; .)

evaluates to 4 since <code>pow(x;y)</code> is x to the power y.

=====Fibonacci sequence=====

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[0,1] | recurse( [last, add] ) | first

Here, <code>[0,1]</code> is the initial pair to be taken as the first two items

in the Fibonacci sequence. (The pair <code>[1,1]</code> could likewise be used for

the variant definition.)

The alphabetic tokens are built-in filters: `first` and `last`

emit the first and last elements of their input arrays respectively;

and `<code>recurse(f)`</code> applies a filter, f, to its input recursively.

jq also allows new filters to be defined in a tacit style, e.g.:

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</syntaxhighlight>

In point-free style, this couldcan be written in Python as:

<syntaxhighlight lang="python">

example = compose(foo, bar, baz)

</syntaxhighlight>

In jq, the equivalent point-free definition would be:

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[[Category:Programming paradigms]]

[[Category:Programming language comparisons]]

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