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Automatic reduction of cuch expression by means of the value method

  • Parte III Memorie Presentate Nelle Quindici Sessioni del Congresso (Dalla Lettera A Alla J)
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Abstract

The first part of this paper is an introduction to CUCH, a formal language created in 1962 by merging the A-formulae language (A. Church) and the combinators language (H. B. Curry). The second part deals with the automatic reduction of the CUCH formulae. In the years between 1960 and 1964 McCarthy and Landin, using the characteristics of Λ-conversion and introducing the semantic notion of «value of an expression» created some languages, which, even using completely different algorithms, utilize the notion of reduction to normal form as a mechanism of an abstract machine for computing recursive function (of list, the former, of integer, the latter).

The algorithm proposed here makes use, as those by McCarthy and Landin, of the method of the evaluation of expressions (in contraposition with the syntactic method used by Church); however this method is a simple syntactic instrument, that is it allows us to use absolutely free variables, it considers the notion of value only locally and therefore does not bind from outside the interpretation of formulae, leaving it absolutely available. The third part of the paper presents some examples of applications and a study of the possible expansions of the system.

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Bibliography

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Authors and Affiliations

  1. Istituto per le Applicazioni del Calcolo (IAC)-CNR, Roma

    G. Ausiello

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  1. G. Ausiello
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Work carried out at IAC in the frame of the Italian CNR Research Group No. 43.

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Ausiello, G. Automatic reduction of cuch expression by means of the value method. Calcolo 5 (Suppl 1), 174–184 (1968). https://doi.org/10.1007/BF02576064

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