Tacit programming

Tacit programming is a programming paradigm in which a function definition does not include information regarding its arguments, using combinators and function composition (but not λ-abstraction) instead of variables. The simplicity behind this idea allows its use on several programming languages, such as J programming language and APL and especially in stack or concatenative languages, such as PostScript, Forth, Joy, and Factor. Outside of the APL and J communities, tacit programming is referred to as point-free style, or more pithily as pointless programming. This is because of the relation between how definitions are done in pointless topology and how they are done in this style.

The key idea in tacit programming is to assist in operating at the appropriate level of abstraction. That is, to translate the natural transformation given by currying:

$\hom(A\times B,C)\equiv \hom(A,\hom(B,C))$

into computer functions, where the left represents the uncurried form of a function and the right the curried. hom(X,Y) denotes the homomorphisms from X to Y while, A x B denotes the Cartesian product of A and B.

Examples

Functional programming

A simple example (in Haskell) is a program which takes a sum of a list. A programmer might define a sum recursively using a pointed (cf. value-level programming) method as:

sum (x:xs) = x + sum xs
sum [] = 0

However by noting this is a fold the programmer could replace this with:

sum xs = foldr (+) 0 xs

and then the argument is not needed so this can be replaced with

sum  = foldr (+) 0

which is point-free.

Another example is the use of the dot operator:

p x y z = f (g x y) z

we can simply group

f (g x y) z ≡ f ((g x) y) z ≡ (f .) (g x) y z ≡ ((f .) . g) x y z

so

p = (f .) . g

Finally to see a complex example imagine a map filter program which takes a list, applies a function to it, and then filters the elements based on a criterion

mf criteria operator list = filter criteria (map operator list)

can be expressed point-free as

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

APL family

In J one can see the same sort of point-free code in a function designed to compute the average of a list (array) of numbers:

 avg=: +/ % #

# counts the number of items in the array. +/ sums the items of the array. % divides the sum by the number of items

Stack-based

In stack-oriented programming languages (and concatenative ones, most of which are stack based), point-free methods are commonly used. For example a procedure to compute the Fibonacci numbers might look like:

/fib
{
   dup dup 1 eq exch 0 eq or not
   {
      dup 1 sub fib
      exch 2 sub fib
      add
   } if
} def

See also

• Combinatory logic
• Concatenative programming language
• Function-level programming
• Joy (programming language), modern highly tacit language

External links

• Pure Functions in APL and J How to use tacit programming in any APL-like language