This is different in many ways, but it still uses the formal parameter x in the same way. Now here is how the square function would be defined in joyJoy:
DEFINE square == dup * .
ThatTo probably requires some explanation.explain: In joyJoy, everything is a function that takes a [[stack (computing)|stack]] as an argument and returns a stack as a result. For instance, the number 5 is not, as it might appear to be, an integer constant, but instead a short program that pushes the number 5 onto the stack. The + operator pops two numbers off the stack and pushes their sum. The dup operator simply duplicates the top element of the stack by pushing a copy of it. So this definition of the square function says to make a copy of the top element and then multiply the two top elements, leaving the square of the original top element on top of the stack. There is no need for a formal parameter at all. This design makesgives joyJoy one of the most powerfulconciseness and concise languagespower, as illustrated by this definition of [[quicksort]]:
<pre>
Line 30:
</pre>
"binrec" is one of joyJoy's many [[recursion|recursive]] [[combinator|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 ==
One of the most beautifulappealing aspects of joyJoy is this: the [[meaning]] function is a [[homomorphism]] from the [[syntax|syntactic]] [[monoid]] onto the [[semantics|semantic]] [[monoid]]. That is, the syntactic relation of [[concatenation]] of [[symbol|symbols]] maps directly onto the semantic relation of [[Function composition|composition]] of [[function (mathematics)|functions]]. It is a [[homomorphism]] instead of an [[isomorphism]] because it is [[onto]] but not [[one-to-one]], that is, some sequences of symbols have the same meaning (e.g. "dup +" and "2 *") but no symbol has more than one meaning.
Joy manages to be practical and potentially useful, unlike the otherwise similar [[unlambda]]. Its library routines mirror those of ISO [[C programming language|C]], though the current implementation is not easily extensible with functions written in C.
