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:
“What he loved so much in the plant morphological structure of the tree was that given a fixed mathematical basis, the final evolution was so incalculable.”
—D.H. (David Herbert)
“His purity was too great, his aspiration too high for this poor, miserable world! His great soul is now only enjoying that for which it was worthy!”
—Victoria (1819–1901)