By Peter W. O’Hearn, Robert D. Tennent
To build a compiler for a latest higher-level programming languagel one must constitution the interpretation to a machine-like intermediate language in a fashion that displays the semantics of the language. little is expounded approximately such struc turing in compiler texts which are meant to hide a wide selection of application ming languages. extra is expounded within the Iiterature on semantics-directed compiler building  yet right here too the perspective is especially basic (though restricted to one languages with a finite variety of syntactic types). at the different handl there's a enormous physique of labor utilizing the continuation-passing transformation to constitution compilers for the explicit case of call-by-value languages reminiscent of SCHEME and ML [21 3]. ln this paperl we are going to describe a style of structuring the interpretation of ALGOL-like languages that's in keeping with the functor-category semantics devel oped by means of Reynolds  and Oles [51 6]. another technique utilizing class thought to constitution compilers is the early paintings of F. L. Morris 1 which anticipates our therapy of boolean expressionsl yet doesn't care for tactics. 2 kinds and Syntax An ALGOL-like language is a typed lambda calculus with an strange repertoire of primitive varieties. all through such a lot of this paper we suppose that the primi tive kinds are comm(and) int(eger)exp(ression) int(eger)acc(eptor) int(eger)var(iable) I and that the set eight of varieties is the least set containing those primitive varieties and closed below the binary operation -.
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Extra resources for ALGOL-like Languages
49 Robert D. Tennent We now define the same constructions in categories of functors. For any (small) category X, let X '* D be the category of all functors from X to D, with all natural transformations as the morphisms, and similarly for X '* S. Let F and G be functors from X to D, x, y and z be X-objects, and f: x - y and g: y - z be X-morphisms. Then the four constructions needed are as follows: (i) Product: (F x G)(x) = F(x) x G(x) and (F x (ü) G)(f)((d,d') E F(x) x G(x)) = (F(f)(d), G(f)(d')).
Nivat and J. C. Reynolds. Cambridge University Press, Cambridge, England, 1985, pp. 543-573. See Chapter 11. [7) Morris, F. L. Correctness of Translations of Programming Languages-An Algebraic Approach, Ph. D. Dissertation. Stanford University, August 1972. [8) Reynolds, j. C. Conjunctive types and ALGOL-like languages (abstract of invited lecture). In Proceedings Symposium on Logic in Computer Science, Ithaca, New York, June 22-25. 1987, p. 119. [9) Reynolds, j. C. Preliminary Design of the Programming Language FoRSYTHE.
Specifically, the mapping from types to simple types does not apply to types containing intvar, boolcompl, or boolexp. The key to filling this lacuna is that the meanings of a type such as BI-(··· (On- intvar) · · ·) are isomorphic to pairs of meanings of the types BI-(· ..