John Hughes. Abstract interpretations of first order polymorphic functions. In Cordelia Hall, John Hughes, and John O'Donnell, editors, Proceedings of the 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....or outermost, or call byname) semantics. But because raw lazy evaluation is slow, lazy evaluation enthusiasts have built clever compilers that figure out when an eager (i.e. bottom up or call by value) evaluation can be used with exactly the same result; this is called strictness analysis [123, 95]. OBJ3 is more flexible, because each operator can have its own evaluation strategy. Moreover, the OBJ3 programmer gets this flexibility with minimum effort, because OBJ3 determines a default strategy if none is explicitly given. This default strategy is computed very quickly, because only a very ....

John Hughes. Abstract interpretations of first order polymorphic functions. In Cordelia Hall, John Hughes, and John O'Donnell, editors, Proceedings of the 1988.

....Abramsky s proof of the polymorphic invariance result is very syntactic and rather heavy going. By contrast, the same result is proved much more elegantly in [AJ91] using a categorical semantics for Hindley Milner style polymorphism based on a relational analogue to functors (this work builds on [Hug88] a precursor of [HL91] see below) In future we hope to be able to adapt this technique to the analyses we describe in later chapters. Unfortunately, polymorphic invariance does not give us all that we need. The B interpretation of a term can carry more information than just whether a function ....

John Hughes. Abstract interpretation of first-order polymorphic functions. In Glasgow Workshop on Functional Programming, University of Glasgow, Department of Computing Science, August 1988. Research Report 89/R4.

....[1] extended the strictness analysis for monomorphic languages to polymorphic languages based on the notion of polymorphic invariance. This implies that the strictness property derived from one monomorphic instance of a polymorphic function applies to all possible monomorphic instances. Hughes [47] proposed a method for extending abstract interpretation to first order polymorphic functions by calculating approximations to abstract functions of all instances from the abstract function of the simplest monomorphic instance. Abramsky and Jensen [3] showed a proof of the polymorphic invariance ....

R.J.M. Hughes. Abstract interpretation of first-order polymorphic functions. In Glascow Workshop on Functional Programming, University of Glasgow, Department of Computing Science, August, 1988.

....over . Monomorphic functional programs are morphisms of ; polymorphic programs are natural transformations. e.g. append : 8t: t Theta t t append : Delta) Theta ( Delta) Delta) where ( Delta) is the list construction functor. These ideas are used in [10] to develop a general framework for abstract interpretation of first order, polymorphic functions. We extend the basic approach of [10] to cover higher order functions and show that with this extension, the short cut techniques for computing function abstractions given in [10] can no longer work; ....

.... Theta t t append : Delta) Theta ( Delta) Delta) where ( Delta) is the list construction functor. These ideas are used in [10] to develop a general framework for abstract interpretation of first order, polymorphic functions. We extend the basic approach of [10] to cover higher order functions and show that with this extension, the short cut techniques for computing function abstractions given in [10] can no longer work; thus our main emphasis is on re establishing the polymorphic invariance results of [1] in this framework. The obvious problem in ....

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R.J.M. Hughes. Abstract interpretation of first--order polymorphic functions. In Glasgow Workshop on Functional Programming, University of Glasgow, Department of Computing Science, August 1988. Research Report 89/R4.

....backward analysis. There is yet another dimension along which strictness analysis techniques may be characterised: monomorphic vs. polymorphic. This paper considers only techniques for the analysis of monomorphic languages. Techniques for polymorphic languages are described in [Abr85] [Hug88], and [Hug89b] The rest of this paper is organised as follows. Section 2 defines the languages to be analysed. Section 3 describes first order and higher order low fidelity forward analysis. Section 4 introduces projections and projection transformers, and recounts the essential properties of ....

Hughes, R.J.M. "Abstract Interpretation of First-Order Polymorphic Functions." Proceedings of the 1988 Glasgow Workshop on Functional Programming. August 2-5, 1988, Rothesay, Isle of Bute, Scotland. Department of Computing Science, University of Glasgow, Glasgow, Scotland.

.... works for higher order functions [21] However backwards analysis has really only been applied to first order functions, though a possible extension is given in [59] polymorphism: there has been some progress on both abstract interpretation and backwards analysis of polymorphic functions [3, 60, 61]; however there are still some remaining problems. data structures: forwards analysis cannot analyse all the patterns of data structure strictness that backwards analysis can. 1 Strictness analysis can also be used to improve the efficiency of sequential programs. 2 Except in degenerate ....

R J M Hughes. Abstract interpretation of first-order polymorphic functions. In Proc. Workshop on Implementation of Lazy Functional Languages, Aspenas. Programming Methodology Group, Chalmers University, Sweden, 1988.

....over terms. Hughes used the semantic characterisation of first order polymorphic functions as natural transformations to strengthen Abramsky s result in the first order case, showing that an approximation to the abstract function of any instance can be calculated from that of the simplest [20]. Abramsky and Jensen have shown that higher order functions are lax natural transformations in a more complex category, and thereby proved a stronger version of Abramsky s original result [2] In addition, Abramsky and Jensen have shown that our Theorem 9 does not hold for higher order functions: ....

....proved a stronger version of Abramsky s original result [2] In addition, Abramsky and Jensen have shown that our Theorem 9 does not hold for higher order functions: polymorphic higher order functions are not characterised by any finite instance. In the future, we hope to generalise the result of [20] to the abstract interpretation of higher order functions. This is difficult because the function space type former is not a covariant functor. Possible approaches are to use dinatural transformations [12] or to make the function type covariant by working in a more complex category as both 24 ....

J. Hughes, Abstract Interpretation of First-order Polymorphic Functions, Proc. Aspenas Workshop on Graph Reduction, University of Gothenburg, 1988.

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