David Pym and Lincoln Wallen. Investigations into proof-search in a system of first-order dependent function types. In M.E. Stickel, editor, Proceedings of the 10th International Conference on Automated Deduction, pages 236--250, Kaiserslautern, Germany, July 1990. SpringerVerlag LNCS 449.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....calculus would be to take annotations as primitive. Then we could define set theoretic (as opposed to pertheoretic) specifications as (x:#)P = let x : # in (x P ) 6.5 Search Calculi The thesis of Pym [Pym90] presents a theory of proof search. One idea developed there (and also in [PW90] is to give a hierarchy of calculi each of which can be regarded as the metatheory of the next and in which the search space for proofs is increasingly constrained. This idea could be applied to the present work on refinement. Refinement is traditionally formulated as a generalised equality ....

....than equational) refinement calculus. Then t is seen as a solution to the search for a program to satisfy #. In Section 5.5 we defined a number of auxiliary relations. The relationship between # # and is interesting because it mirrors the di#erence between refinement and search. Following [PW90] we could consider a hierarchy of subsystems of the full equational refinement theory. For example: 203 #,x : # # # # # 1 # # # # # # # # # # #,y : # # # # # # # # #,x : #,y : # # # # #,z : # # # # # #,x : # # # # #,y : # # # # ,z : # # # Figure 6.5: Type ....

David Pym and Lincoln Wallen. Investigations into proof-search in a system of first-order dependent function types. In Proceedings of the 10th International Conference on Automated Deduction, volume 449 of Lecture Notes in Artificial Intelligence, pages 236--250. SpringerVerlag, 1990. Also University of Edinburgh LFCS Report ECS-LFCS90 -111. 215

....classes known for intuitionistic logic. For decades, most of the research in automated theorem proving has been concentrated on classical logic. Relatively few papers are devoted on proof search in intuitionistic logic. The following is an incomplete list of such papers: 22] 7] 3] 11] 23] [15], 17] 18] 5] 13] Despite the fact that several intuitionistic theorem provers have been implemented (see [5] 18] 3] only very few published papers describe the actual implementation of an automated theorem prover and bring the results of running the prover on some benchmarks: 22] ....

Pym, D.J., Wallen, L.A. Investigations into proof-search in a system of first-order dependent function types. In CADE-10, pages 236--250, Springer Verlag 1990.

....properties about LF, but to Logic Programming in the LF Logical Framework 5 describe the operational behavior of Elf. This meta logic was called state logic in [26] since it is used to describe the states of an abstract interpreter for Elf. An alternative approach was taken by Pym Wallen [29] who give a sequent presentation for LF which allows free meta variables to appear in the sequents. We begin with the discussion of unification which will be extended to a logic strong enough to describe the complete state of the interpreter in Section 4. One important property of the unification ....

David Pym and Lincoln Wallen. Investigations into proof-search in a system of first-order dependent function types. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, Kaiserslautern, Germany, pages 236--250. Springer-Verlag LNCS 449, July 1990.

....unification to ensure that the introduction rules for S4 modalities are respected. While Wallen s method is an ingenious and effective one, the translation into S4, whether implicit or explicit, complicates the intuitive reading of the given intuitionistic formula and its proof. Pym and Wallen [PW90] present an approach to proof search in an intuitionistic type theory that is similar to our approach but they do not exploit Herbrand functions to encode impermutabilities during the proof search. 3 The technique of introducing Herbrand functions in this manner is fairly well known in automated ....

D. J. Pym and L. A. Wallen. Investigations into proof-search in a system of first-order dependent function types. In M. E. Stickel, editor, 10th International Conference on Automated Deduction, pages 236--250. Springer-Verlag, 1990.

....the representing object. Since type checking in the LF type theory is decidable, purported deductions can be checked automatically for validity. However, LF is a powerful basis for much more comprehensive tasks than mere proof checking. Unification and proof search algorithms have been developed [7, 27, 28, 24] and it has been amenable to an operational interpretation which is realized in the Elf programming language [21, 23] A wide range of deductive systems have been specified in LF and implemented in Elf [1, 15, 19, 20] In this paper we investigate the use of Elf to implement the meta theory of ....

David Pym and Lincoln Wallen. Investigations into proof-search in a system of firstorder dependent function types. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, Kaiserslautern, Germany, pages 236--250. Springer-Verlag LNCS 449, July 1990.

....seems that logic programming is often superior to implement specific algorithms such as for type inference, evaluation, or compilation, while tactics and tacticals work well for general reasoning and search within a specified logic. Methods for general proof search for LF have been investigated [PW90] but a general and practically efficient theorem proving procedure for a logical framework remains an important area for further research. Generality, as found in a logical framework, often comes at the price of efficiency. For example, compare the undecidability of higher order unification with ....

David Pym and Lincoln Wallen. Investigations into proof-search in a system of first-order dependent function types. In M.E. Stickel, editor, Proceedings of the 10th International Conference on Automated Deduction, pages 236-- 250, Kaiserslautern, Germany, July 1990. Springer-Verlag LNCS 449.

No context found.

David Pym and Lincoln Wallen. Investigations into proof-search in a system of first-order dependent function types. In M.E. Stickel, editor, Proceedings of the 10th International Conference on Automated Deduction, pages 236--250, Kaiserslautern, Germany, July 1990. SpringerVerlag LNCS 449.

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