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Proving Properties of Programs by Structural Induction
 Computer Journal
, 1969
"... This paper discusses the technique of structural induction for proving theorems about programs. This technique is closely related to recursion induction but makes use of the inductive definition of the data structures handled by the programs. It treats programs with recursion but without assignments ..."
Abstract

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This paper discusses the technique of structural induction for proving theorems about programs. This technique is closely related to recursion induction but makes use of the inductive definition of the data structures handled by the programs. It treats programs with recursion but without assignments or jumps. Some syntactic extensions to Landin's functional programming language ISWIM are suggested which make it easier to program the manipulation of data structures and to develop proofs about such programs. Two sample proofs are given to demonstrate the technique, one for a tree sorting algorithm and one for a simple compiler for expressions. (First received April 1968 and in revised form August 1968) Since the problem of proving that computer programs really do what their inventors allege them to do was discussed by McCarthy (1963), there has been considerable progress and proofs have been produced for nontrivial programs such as a simple compiler (Painter, 1967;