Switch Statement - History

History

In his 1952 text Introduction to Metamathematics, Stephen Kleene formally proved that the CASE function (the IF-THEN-ELSE function being its simplest form) is a primitive recursive function, where he defines the notion definition by cases in the following manner:

"#F. The function φ defined thus
φ(x1, ..., xn ) =
  • φ1(x1, ..., xn ) if Q1(x1, ..., xn ),
  • . . . . . . . . . . . .
  • φm(x1, ..., xn ) if Qm(x1, ..., xn ),
  • φm+1(x1, ..., xn ) otherwise,
where Q1, ..., Qm are mutually exclusive predicates (or φ(x1, ..., xn) shall have the value given by the first clause which applies) is primitive recursive in φ1, ..., φm+1, Q1, ..., Qm+1.

Kleene provides a proof of this in terms of the Boolean-like recursive functions "sign-of" sg( ) and "not sign of" ~sg( ) (Kleene 1952:222-223); the first returns 1 if its input is positive and −1 if its input is negative.

Boolos-Burgess-Jeffrey make the additional observation that "definition by cases" must be both mutually exclusive and collectively exhaustive. They too offer a proof of the primitive recursiveness of this function (Boolos-Burgess-Jeffrey 2002:74-75).

The IF-THEN-ELSE is the basis of the McCarthy formalism: its usage replaces both primitive recursion and the mu-operator.

Read more about this topic:  Switch Statement

Famous quotes containing the word history:

    “There is a constant in the average American imagination and taste, for which the past must be preserved and celebrated in full-scale authentic copy; a philosophy of immortality as duplication. It dominates the relation with the self, with the past, not infrequently with the present, always with History and, even, with the European tradition.”
    —Umberto Eco (b. 1932)

    “English history is all about men liking their fathers, and American history is all about men hating their fathers and trying to burn down everything they ever did.”
    —Malcolm Bradbury (b. 1932)

    “I saw the Arab map.
    It resembled a mare shuffling on,
    dragging its history like saddlebags,
    nearing its tomb and the pitch of hell.”
    —Adonis [Ali Ahmed Said] (b. 1930)