Joy (programming language): Difference between revisions

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== Mathematical purity ==

In Joy, the [[eval|meaning function]] is a [[homomorphism]] from the [[syntax|syntactic]] [[monoid]] onto the [[semantics|semantic]] [[monoid]]. That is, the syntactic relation of [[concatenation]] of [[symbol]]s maps directly onto the semantic relation of [[Function composition|composition]] of [[function (mathematics)|functions]]. It is a [[homomorphism]] insteadrather ofthan an [[isomorphism]], because it is [[onto]] but not [[bijection|one-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 *") but no symbol has more than one meaning.

In other words, it is a [[concatenative programming language]]: "The concatenation of two programs denotes the composition of the functions denoted by the two programs".<ref>{{cite web|title=Mathematical Foundations of Joy|url=http://web.archive.org/web/20111007025556/http://www.latrobe.edu.au/phimvt/joy/j02maf.html}}</ref>