McCarthy formalism is a formalism for defining functions recursively, first introduced in classic paper Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I (1960).
From Wikipedia:
In his 1967 Computation: Finite and Infinite Machines, Marvin Minsky in his § 10.6 Conditional Expressions: The McCarthy Formalism describes the "formalism" as follows:
"Practical computer languages do not lend themselves to formal mathematical treatment--they are not designed to make it easy to prove theorems about the procedures they describe. In a paper by McCarthy [1963] we find a formalism that enhances the practical aspect of the recursive-function concept, while preserving and improving its mathematical clarity.
McCarthy introduces "conditional expressions" of the form
f = (if p1 then e1 else e2)where theeiare expressions andp1is a statement (or equation) that may be true or false. This expression means: See ifp1is true; if so the value offis given bye1. IFp1is false, the value offis given bye2. [...]The McCarthy formalism is like the general recursive (Kleene) system, in being based on some basic functions, composition, and equality, but with the conditional expression alone replacing both the primitive-recursive scheme and the minimization operator." (Minsky 1967:192-193)
I'm interested in chronology. Was there any other formalism regarding recursive function before McCarthy Formalism (in computer science)?
