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"binrec" is one of joy'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 beautiful aspects of joy is this: the [[meaning]] function is a [[homomorphism]] from the [[syntax|syntactic]] [[monoid]] onto the [[semantics|semantic]] [[monoid]]. 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 is the purest implementation of the [[lambda calculus]] as a programming language, but it still manages to be practical and potentially useful, unlike the otherwise similar [[unlambda]].
== External link ==
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