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:
“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)
“Man flows at once to God when the channel of purity is open. By turns our purity inspires and our impurity casts us down.”
—Henry David Thoreau (1817–1862)