Joy (programming language): Difference between revisions

Revision as of 15:10, 30 July 2005

Revision as of 19:09, 15 August 2005

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== 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]]. TheThat 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 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]].