Joy (programming language): Difference between revisions

Revision as of 17:11, 12 October 2021

Revision as of 03:29, 23 January 2022

Line 71:

== 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]] rather than 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 *").

Joy 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://www.latrobe.edu.au/phimvt/joy/j02maf.html |url-status=dead |archive-url=https://web.archive.org/web/20111007025556/http://www.latrobe.edu.au/phimvt/joy/j02maf.html |archive-date=October 7, 2011 }}</ref>