Raymond McDowell and Dale Miller. A logic for reasoning with higher-order abstract syntax: An extended abstract. In Glynn Winskel, editor, Proceedings of the Twelfth Annual Symposium on Logic in Computer Science, pages 434-- 445, Warsaw, Poland, June 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....original form at least, is that one looses the ability to de ne functions on syntax by structural recursion and to prove properties by structural induction absolutely essential tools, especially for applications to operational semantics. There are recent proposals to overcome this shortcoming [McM97, DPS97]. They result in systems that are technically very interesting but force the designer of algorithms and proofs modulo conversion to use forms of expression that are rather far from familiar informal practice. Indeed, the whole HOAS approach by its very nature disallows a feature that we regard ....

McDowell, R. and Miller, D: A logic for reasoning with higher-order abstract syntax. In 12th Annual Symposium on Logic in Computer Science. IEEE Computer Society Press, Washington, DC, 1997, , pp. 434-445.

....binding signatures of is a direct consequence of the work in [2, 4] on untyped binding signatures and in [3] for the specific case of simply typed # calculus. Metalogical systems for reasoning on datatypes with variables and binders, following many di#erent approaches, have been presented in [8, 15, 19, 20], among others. In our opinion, the development we carried out in this paper tries to close the gap between [2,4] which are oriented towards an algebraic point of view) and [1, 7] which, on the other hand, are inspired by a logical perspective) Indeed, as we have seen in 3.4 we can also ....

R. McDowell and D. Miller. A logic for reasoning with higher-order abstract syntax. In Proc. 12 th LICS. IEEE, 1997.

....as possible worlds (see the completion construction in [9] for N Prolog and [4] for Hypothetical Datalog) 3. By embracing the idea of partiality in inductive de nitions and using the rule of de nitional re ection to incorporate a proof theoretical notion of closure analogous to the completion [22, 14]. None of those approaches are satisfactory for our purposes: most of the predicates we want to negate are open ended; similarly, de nitional re ection is not well behaved, since the version of the latter rule does not t well with the operational semantics required by that very class of ....

R. McDowell and D. Miller. A logic for reasoning with higher-order abstract syntax: An extended abstract. In G. Winskel, editor, Proceedings of the Twelfth Annual Symposium on Logic in Computer Science, pages 434-445, Warsaw, Poland, June 1997.

....nitions [Hal87] and de nitional re ection [SH93] are purely logical systems. Even when interpreted functionally, their proofs require all arguments to be closed and recursion must not traverse binders. Figure 1 can also be encoded in a logical framework implemented in the meta logic FO IN [MM97] FO IN , however, is a sequent calculus, and does not support functions to range over those encodings. Miller [Mil90] suggests to extend ML datatypes by a parameter mechanism to support higher order abstract syntax. New parameters can be dynamically generated and (recursive) function ....

Raymond McDowell and Dale Miller. A logic for reasoning with higher-order abstract syntax: An extended abstract. In Glynn Winskel, editor, Proceedings of the Twelfth Annual Symposium on Logic in Computer Science, pages 434-445, Warsaw, Poland, June 1997.

....aspects of term replacement required in implementing and reasoning about term rewriting systems. This is especially true when the object level This paper appears in Theorem Proving in Higher Order Logics, 11th International Conference Springer Verlag LNCS Vol. 1479. September 1998. 2 See [17, 4, 10, 5] for background and sample work on higher order abstract syntax. rewriting system is itself higher order. Higher order rewriting requires substitution to be regarded in the broadest sense, one in which the scopes of bound variables are not necessarily respected. We are required to consider x as, ....

R. McDowell and D. Miller. A logic for reasoning with higher-order abstract syntax. In Symposium on Logic in Computer Science. IEEE, 1997.

....for debugging. To attack this problem, in our opinion there are at least two interesting directions to investigate. The rst one is the use of a meta logic to reason about speci cations in languages like hhf and Forum. Embedding the logic speci cation within a meta logic like the one described in [MM97] could give in fact a further tool in order to study intensional properties (i.e. that do not require an explicit state exploration [CJM98] of security protocols. The other direction concerns alternative execution models for (linear logic and or intuitionistic based) speci cations that do not ....

R. McDowell, D. Miller. A Logic for Reasoning with Higher-Order Abstract Syntax. LICS '97, pages 434-445, 1997.

....possibility of reasoning on the properties which are delegated on the metalanguage, e.g. substitution and # equivalence themselves. Various approaches have been proposed to overcome these problems based on di#erent techniques such as modal types, functor categories, permutation models of ZF, etc. [3, 4, 8, 6, 5, 13]. The purpose of this paper is to present in broad generality yet another logical framework for reasoning on systems presented in HOAS, called # , based on an axiomatic syntactic standpoint. This system stems from the technique originally used by the authors in [10] for formally deriving in Coq ....

....verify the adequacy of these translations, and to compare the advantages of using FM versus the Theory of Contexts in, possibly mechanized, proof search. Programming in # . Currently there is a great deal of research on programming languages featuring contexts and binding structures as datatypes [18,13,5]. The term language of # could be extended naturally to a functional programming language to this end, possibly adding a fixed point operator. However, in view of Remark 4 this would not be a very expressive language. A much better alternative would be to define separately a programming language ....

R. McDowell and D. Miller. A logic for reasoning with higher-order abstract syntax. In Proc. 12 th LICS. IEEE, 1997.

....logical frameworks supporting subtyping and linearity. We believe that this is a worthwhile endeavor because it permits reasoning about resource oriented logics and programming languages with state, and we are convinced that it is feasible because of the pioneering work by McDowell and Miller [MM97] who successfully encoded fragments of second order linear logic into their meta logic FO IN . Acknowledgment: I want to thank my advisor Frank Pfenning for all his contributions to this work. 15 8. CONCLUSION ....

Raymond McDowell and Dale Miller. A logic for reasoning with higher-order abstract syntax: An extended abstract. In Glynn Winskel, editor, Proceedings of the Twelfth Annual Symposium on Logic in Computer Science, pages 434-445, Warsaw, Poland, June 1997.

....as the one provided by almost all the current systems providing induction. Consequently, we are not able to use the technique of higher order abstract syntax to describe the higher order calculus today. However, there are already propositions for various meta logics in the literature [DPS97,DL98,MM97,Hof99] which could be used as a basis for the implementation of the system we need. Concerning future work, our main goal is to provide the basis for a machine checked study of languages based on the calculus. Particularly relevant here are proofs of properties such as the preservation of types ....

Raymond McDowell and Dale Miller. A logic for reasoning with higher-order abstract syntax: An extended abstract. In Glynn Winskel, editor, Proceedings of the Twelfth Annual Symposium on Logic in Computer Science, Warsaw, Poland, June 1997. To appear.

....point and the fact that we have adapted well known proof methods, our metatheoretic proofs are much more compact and easier to read. As a consequence, Recursion over Objects of Functional Type 15 our system seems to be a better candidate for further extensions than the previous proposition. Raymond McDowell and Dale Miller have proposed (MM97) a meta logic to reason about object logics coded using higher order abstract syntax. Their approach is quite different from ours, less ambitious in a sense. They do not provide a type system supporting the judgments as types principle. Instead, they propose two logics: one ....

Raymond McDowell and Dale Miller. A logic for reasoning with higher-order abstract syntax: An extended abstract. In Glynn Winskel, editor, Proceedings of the Twelfth Annual Symposium on Logic in Computer Science, Warsaw, Poland, June 1997. To appear.

....debugging. To attack this problem, in our opinion there are at least two interesting directions to investigate. The rst one is the use of a meta logic to reason about speci cations in languages like hhf and Forum. Embedding the logic speci cation within a meta logic like the one described in [MM97] could give in fact a further tool in order to study intensional properties (i.e. that do not require an explicit state exploration [CJM98] of security protocols. The other direction concerns alternative execution models for (linear logic and or intuitionistic based) speci cations that do not ....

R. McDowell, D. Miller. A Logic for Reasoning with Higher-Order Abstract Syntax. In Proc. LICS '97, 1997.

....the framework logic. Alternatively, in the calculus of constructions, given an inductive de nition, induction principles are simply added, soundly, to the metalogic. Current research in this area focuses on appropriate induction principles for logics that support higher order abstract syntax [16, 26, 35]. 3 Organization The remainder of our paper is organized as follows. In Section 2 we present the idea of a re ective metalogical framework and abstractly formalize our requirements for such a metalogic. In Section 3 we present background material on rewriting logic, membership equational logic, ....

R. McDowell and D. Miller. A logic for reasoning with higher-order abstract syntax. In Twelfth Annual IEEE Symposium on Logic in Computer Science, June 1997.

....its original form at least, is that one looses the ability to de ne functions on syntax by structural recursion and to prove properties by structural induction absolutely essential tools, especially for applications to operational semantics. There are recent proposals to overcome this shortcoming [MM97, DPS97]. They result in systems that are technically very interesting but force the designer of algorithms and proofs modulo conversion to use forms of expression that are rather far from familiar informal practice. Indeed, the whole HOAS approach by its very nature disallows a feature that we regard ....

R. McDowell and D. Miller. A logic for reasoning with higher-order abstract syntax. In 12th Annual Symposium on Logic in Computer Science, pages 434{ 445. IEEE Computer Society Press, Washington, 1997.

No context found.

Raymond McDowell and Dale Miller. A logic for reasoning with higher-order abstract syntax. In Glynn Winskel, editor, Proceedings, Twelfth Annual IEEE Symposium on Logic in Computer Science, pages 434--445, Warsaw, Poland, July 1997. IEEE Computer Society Press. 102

No context found.

Raymond McDowell and Dale Miller. A logic for reasoning with higher-order abstract syntax. In Glynn Winskel, editor, Proceedings, Twelfth Annual IEEE Symposium on Logic in Computer Science, pages 434--445, Warsaw, Poland, July 1997. IEEE Computer Society Press.

No context found.

Raymond McDowell and Dale Miller. A logic for reasoning with higher-order abstract syntax. In Glynn Winskel, editor, Proceedings, Twelfth Annual IEEE Symposium on Logic in Computer Science, pages 434--445, Warsaw, Poland, July 1997. IEEE Computer Society Press.

....a nat assumption. In [McD97, MM00] an intuitionistic logic incorporating definitions and inductions, was presented and cut elimination was shown. Although FO does not have the subformula property, the cut elimination theorem still provides a strong basis for reasoning about proofs in FO [McD97, MM97, MM00]. In fact, the formulation of the natL rule and the failure of the subformula property reflect the fact that in actual mathematical practice, finding the proper induction hypothesis requires insight and creativity; they are not simply rearrangements of the subformulas of the conclusion. As a ....

Raymond McDowell and Dale Miller. A logic for reasoning with higher-order abstract syntax. In Glynn Winskel, editor, Proceedings, Twelfth Annual IEEE Symposium on Logic in Computer Science, pages 434--445, Warsaw, Poland, July 1997. IEEE Computer Society Press.

....sequent inference rules that introduce logical connective will not directly help here. One natural extension of the sequent calculus is then to add left and right introduction rules for atoms. Hallnas and Schroeder Heister [HSH91,SH93] Girard [Gir92] and more recently, McDowell and Miller [MM97,MM00] have all considered just such introduction rules for non logical constants, using a notion of definition. 2 A proof theoretic notion of definitions A definition is a finite collection of definition clauses of the form = B] where H is an atomic formula (the one being defined) every free ....

Raymond McDowell and Dale Miller. A logic for reasoning with higherorder abstract syntax. In Glynn Winskel, editor, Proceedings, Twelfth Annual IEEE Symposium on Logic in Computer Science, pages 434--445, Warsaw, Poland, July 1997. IEEE Computer Society Press. 14

No context found.

Raymond McDowell and Dale Miller. A logic for reasoning with higher-order abstract syntax: An extended abstract. In Glynn Winskel, editor, Proceedings of the Twelfth Annual Symposium on Logic in Computer Science, pages 434-- 445, Warsaw, Poland, June 1997.

No context found.

Raymond McDowell and Dale Miller. A logic for reasoning with higher-order abstract syntax: An extended abstract. In Glynn Winskel, editor, Proceedings of the Twelfth Annual Symposium on Logic in Computer Science, pages 434-- 445, Warsaw, Poland, June 1997.

No context found.

McDowell, R. and Miller, D. (1997). A logic for reasoning with higher-order abstract syntax: An extended abstract. In Proc. of LICS'97.

No context found.

Raymond McDowell and Dale Miller. A logic for reasoning with higher-order abstract syntax. In Proceedings of LICS'97, pages 434445, Warsaw, 1997.

No context found.

Raymond McDowell and Dale Miller. A logic for reasoning with higherorder abstract syntax: An extended abstract. In Glynn Winskel, editor, Proceedings of the Twelfth Annual Symposium on Logic in Computer Science, pages 434--445, Warsaw, Poland, June 1997.

No context found.

R. McDowell and D. Miller. A logic for reasoning with higher-order abstract syntax. In Proc. 12 th LICS. IEEE, 1997.

No context found.

R. McDowell and D. Miller. A logic for reasoning with higher-order abstract syntax. In Proc. 12 th LICS. IEEE, 1997.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC