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Memoization in typedirected partial evaluation
 PROCEEDINGS OF THE 2002 ACM SIGPLAN/SIGSOFT CONFERENCE ON GENERATIVE PROGRAMMING AND COMPONENT ENGINEERING, NUMBER 2487 IN LECTURE NOTES IN COMPUTER SCIENCE
, 2002
"... We use a code generator—typedirected partial evaluation— to verify conversions between isomorphic types, or more precisely to verify that a composite function is the identity function at some complicated type. A typed functional language such as ML provides a natural support to express the function ..."
Abstract

Cited by 14 (6 self)
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We use a code generator—typedirected partial evaluation— to verify conversions between isomorphic types, or more precisely to verify that a composite function is the identity function at some complicated type. A typed functional language such as ML provides a natural support to express the functions and typedirected partial evaluation provides a convenient setting to obtain the normal form of their composition. However, offtheshelf typedirected partial evaluation turns out to yield gigantic normal forms. We identify that this gigantism is due to redundancies, and that these redundancies originate in the handling of sums, which uses delimited continuations. We successfully eliminate these redundancies by extending typedirected partial evaluation with memoization capabilities. The result only works for pure functional programs, but it provides an unexpected use of code generation and it yields ordersofmagnitude improvements both in time and in space for type isomorphisms.
Subtyping Recursive Types modulo Associative Commutative Products
 Seventh International Conference on Typed Lambda Calculi and Applications (TLCA ’05
, 2003
"... We study subtyping of recursive types in the presence of associative and commutative productsthat is, subtyping modulo a restricted form of type isomorphisms. We show that this relation, which we claim is useful in practice, is a composition of the usual subtyping relation with the recently propo ..."
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Cited by 8 (0 self)
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We study subtyping of recursive types in the presence of associative and commutative productsthat is, subtyping modulo a restricted form of type isomorphisms. We show that this relation, which we claim is useful in practice, is a composition of the usual subtyping relation with the recently proposed notion of equality up to associativity and commutativity of products, and we propose an efficient decision algorithm for it. We also provide an automatic way of constructing coercions between related types.
Keeping sums under control
, 2004
"... In a recent paper [31], I presented with Marcelo Fiore and Roberto Di Cosmo a new normalisation tool for the λcalculus with sum types, based on the technique of normalisation by evaluation, and more precisely on techniques developped by Olivier Danvy for partial evaluation, using control operators. ..."
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In a recent paper [31], I presented with Marcelo Fiore and Roberto Di Cosmo a new normalisation tool for the λcalculus with sum types, based on the technique of normalisation by evaluation, and more precisely on techniques developped by Olivier Danvy for partial evaluation, using control operators. The main characteristic of this tool is that it produces a result in a canonical form we introduced. That is to say: two βηequivalent terms will be normalised into (almost) identical terms. It was not the case with the traditional algorithm, which could even lead to an explosion of the size of code. This canonical form is an ηlong βnormal form with constraints, which capture the definition of ηlong normal form for the λcalculus without sums, and reduces drastically the ηconversion possibilities for sums. The present paper recall the definition of these normal forms and the normalisation algorithm, and shows how it is possible to use these tools to solve a problem of characterization of type isomorphisms. Indeed, the canonical form allowed to find the complicated counterexamples we exhibited in another work [6], that proves that type isomorphisms in the λcalculus with sums are not finitely axiomatisable. What’s more, when proving that these terms are isomorphisms, the new partial evaluation algorithm avoids an explosion of the size of the term that arises with the old one.
Algebraic MetaTheories and . . .
"... Fiore and Hur [18] recently introduced a novel methodology—henceforth referred to as Sol—for the Synthesis of equational and rewriting logics from mathematical models. In [18], Sol was successfully applied to rationally reconstruct the traditional equational logic for universal algebra of Birkhoff [ ..."
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Fiore and Hur [18] recently introduced a novel methodology—henceforth referred to as Sol—for the Synthesis of equational and rewriting logics from mathematical models. In [18], Sol was successfully applied to rationally reconstruct the traditional equational logic for universal algebra of Birkhoff [3] and its multisorted version [26], and also to synthesise a new version of the Nominal Algebra of Gabbay and Mathijssen [41] and the Nominal Equational Logic of Clouston and Pitts [8] for reasoning about languages with namebinding operators. Based on these case studies and further preliminary investigations, we contend that Sol can make an impact in the problem of engineering logics for modern computational languages. For example, our proposed research on secondorder equational logic will provide foundations for designing a secondorder extension of the Maude system [37], a firstorder semantic and logical framework used in formal software engineering for specification and programming. Our research strategy can be visualised as follows: (I)