By Peter W. O’Hearn, Robert D. Tennent
To build a compiler for a contemporary higher-level programming languagel one must constitution the interpretation to a machine-like intermediate language in a manner that displays the semantics of the language. little is related approximately such struc turing in compiler texts which are meant to hide a wide selection of application ming languages. extra is related within the Iiterature on semantics-directed compiler building  yet the following too the perspective is especially normal (though restricted to at least one languages with a finite variety of syntactic types). at the different handl there's a substantial physique of labor utilizing the continuation-passing transformation to constitution compilers for the categorical 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 according to the functor-category semantics devel oped by means of Reynolds  and Oles [51 6]. another procedure utilizing type conception to constitution compilers is the early paintings of F. L. Morris 1 which anticipates our therapy of boolean expressionsl yet doesn't take care of methods. 2 forms and Syntax An ALGOL-like language is a typed lambda calculus with an strange repertoire of primitive kinds. all through such a lot of this paper we think that the primi tive forms 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 kinds and closed less than the binary operation -.
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A second question is whether the approach will lend itself to a proof of compiler correctness. One would expect that the close connections between functor-category semantics and our approach to code generation would lead to simple proofs of the relationship between semantics and compilation. However, wehavenot yet pursued this topic beyond intuitive arguments. Acknowledgements This research was sponsored in part by National Science Foundation Grant CCR8922109 andin part by a fellowship from the Science and Engineering Research Council.
Essentially, these equations describe a compiler where the lambda-calculus aspects of the source language are completely reduced at compile-time, leaving target code that is purely imperative. This is in pleasant contrast with conventional approaches to compiling conventional languages, where inline implementation of procedures is notoriously hard to get right. 28 Chapter 12. Using Functor Categories to Generate Intermediate Code 12 Closed Subroutines Closed subroutines are necessary for the implementation of procedures, and other types of phrases, that are defined recursively.
Bn- intexp) .. ·). Thus a procedure of the first type can be implemented by a pair of subroutines corresponding to the second and third types. The general Situation is that a type is mapped into a sequence of simple types by the function r such that r compl = compl r intcompl = intcompl r comm = compl - compl r intexp = intcompl - compl r intacc = compl - intcompl r intvar = compl - intcompl, intcompl - compl r boolcompl = compl, compl r boolexp = compl - compl - compl , andif and r e' =