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:

    “Social history might be defined negatively as the history of a people with the politics left out.”
    —G.M. (George Macaulay)

    “The disadvantage of men not knowing the past is that they do not know the present. History is a hill or high point of vantage, from which alone men see the town in which they live or the age in which they are living.”
    —Gilbert Keith Chesterton (1874–1936)

    “If you look at the 150 years of modern China’s history since the Opium Wars, then you can’t avoid the conclusion that the last 15 years are the best 15 years in China’s modern history.”
    —J. Stapleton Roy (b. 1935)