Mathematical Purity
In Joy, the meaning function is a homomorphism from the syntactic monoid onto the semantic monoid. That is, the syntactic relation of concatenation of symbols maps directly onto the semantic relation of composition of 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.
In other words, "The concatenation of two programs denotes the composition of the functions denoted by the two programs".
Its library routines mirror those of ISO C, though the current implementation is not easily extensible with functions written in C.
Read more about this topic: Joy (programming Language)
Famous quotes containing the words mathematical and/or purity:
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“All sensuality is one, though it takes many forms; all purity is one. It is the same whether a man eat, or drink, or cohabit, or sleep sensually. They are but one appetite, and we only need to see a person do any one of these things to know how great a sensualist he is. The impure can neither stand nor sit with purity.”
—Henry David Thoreau (1817–1862)