Joy (Programming Language)

The Joy programming language incomputer science is a purely functional programming language that was produced by Manfred von Thun ofLa Trobe University inMelbourne,Australia. Joy is based on composition of functions rather thanlambda calculus. It has turned out to have many similarities toForth, due not to design but to a sort of parallel evolution and convergence. It was also inspired by the function-level programming style ofJohn Backus'sFP.

How it works [ edit ]

Joy is unusual (except for function-level programming languages and some esoteric ones, such asunlambda) in its lack of alambda operator, and therefore lack offormal parameters. To illustrate this with a common example, here is how the square function might be defined in an imperative programming language (C):

int square(int x)
{
    return x * x;
}

The variable x is a formal parameter which is replaced by the actual value to be squared when the function is called. In afunctional language (Scheme) the same function could be defined:

(define square
  (lambda (x) 
    (* x x)))

This is different in many ways, but it still uses the formal parameter x in the same way. In Joy the square function is defined:

DEFINE square == dup * .

In Joy, everything is a function that takes astack as an argument and returns a stack as a result. For instance, the numeral '5' does not represent an integer constant, but instead a short program that pushes the number 5 onto the stack.

• The dup operator simply duplicates the top element of the stack by pushing a copy of it.
• The * operator pops two numbers off the stack and pushes their product.

So the square function makes a copy of the top element, and then multiplies the two top elements of the stack, leaving the square of the original top element at the top of the stack, with no need for a formal parameter. This makes Joy concise, as illustrated by this definition ofquicksort:

DEFINE qsort ==
   [small]
   []
   [uncons [>] split]
   [enconcat]
   binrec.

"binrec" is one of Joy's manyrecursive combinators, implementing binary recursion. It expects four quoted programs on top of the stack which represent:

• the termination condition (if a list is "small" (1 or 0 elements) it is already sorted),
• what to do if the termination condition is met (in this case nothing),
• what to do by default (split the list into two halves by comparing each element with the pivot), and finally
• what to do at the end (insert the pivot between the two sorted halves).

Mathematical purity [ edit ]

In Joy, themeaning function is ahomomorphism from thesyntactic monoid onto thesemantic monoid. That is, the syntactic relation ofconcatenation ofsymbols maps directly onto the semantic relation ofcomposition offunctions. It is ahomomorphism rather than anisomorphism, because it isonto but notone-to-one; that is, no symbol has more than one meaning, but some sequences of symbols have the same meaning (e.g. "dup +" and "2 *").

Joy is a concatenative programming language : "The concatenation of two programs denotes the composition of the functions denoted by the two programs".

Its library routines mirror those of ISOC, though the current implementation is not easily extensible with functions written in C.

See also [ edit ]