Amy Felty and Dale Miller. Encoding a dependent-type -calculus in a logic programming language. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, pages 221--235, Kaiserslautern, Germany, July 1990. Springer-Verlag LNCS 449.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....equal, we can hope to discover this without reducing both to normal form. These problems were side stepped in the original paper on the LF logical framework [HHP93] by restricting attention to # conversion for definitional equality. This is su#cient if we also restrict attention to # long forms [FM90, Cer96]. This restriction is somewhat unsatisfactory, especially in linear variants of LF [CP98] More recently, # expansion has been studied in its own right, using modification of standard techniques from rewriting theory to overcome the lack of strong normalization when expansion is not restricted ....

Amy Felty and Dale Miller. Encoding a dependent-type #-calculus in a logic programming language. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, pages 221--235, Kaiserslautern, Germany, July 1990. Springer-Verlag LNCS 449.

....to richer theories such as those including unit types or subtyping. These problems were sidestepped in the original paper on the LF logical framework [HHP93] by restricting attention to fi conversion for definitional equality, which is sufficient if we also restrict attention to j long forms [FM90, Cer96]. This restriction is somewhat unsatisfactory, especially in linear variants of LF [CP98] More recently, j expansion has been studied in its own right, using modification of standard techniques from rewriting theory to overcome the lack of strong normalization when expansion is not restricted ....

Amy Felty and Dale Miller. Encoding a dependent-type -calculus in a logic programming language. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, pages 221--235, Kaiserslautern, Germany, July 1990. Springer-Verlag LNCS 449.

....particularly good properties such as conservativity 1 . A number of logics, particularly higher order logics based on typed lambda calculi, have been proposed as logical frameworks, including the Edinburgh logical framework LF [35, 2, 27] generic theorem provers such as Isabelle [56] Prolog [54, 25], and Elf [57] and the work of Basin and Constable [4] on metalogical frameworks. Other approaches, such as Feferman s logical framework FS 0 [24] that has been used in the work of Matthews, Smaill, and Basin [46] earlier work by Smullyan [59] and the 2OBJ generic theorem prover of Goguen, ....

A. Felty and D. Miller. Encoding a dependent-type -calculus in a logic programming language. In M. Stickel, editor, Proc. 10th. Int. Conf. on Automated Deduction, Kaiserslautern, Germany, July

....good properties such as conservativity 1 . A number of logics, particularly higher order logics originating in constructive type theory, have been proposed as logical frameworks, including the Edinburgh logical framework LF [30, 2, 23] meta theorem provers such as Isabelle [47] Prolog [46, 21], and Elf [48] and the work of Basin and Constable [3] on metalogical frameworks. Other approaches, such as Feferman s logical framework FS 0 [20] that has been used in the work of Matthews, Smaill, and Basin [38] earlier work by Smullyan [50] and the the 2OBJ meta theorem prover of Goguen, ....

A. Felty and D. Miller. Encoding a dependent-type -calculus in a logic programming language. In M. Stickel, editor, Proc. 10th. Int. Conf. on Automated Deduction, Kaiserslautern, Germany, July 1990, volume 449 of LNCS, pages 221--235. Springer-Verlag, 1990.

....be sound and complete. Translations of Martin Lof s type theory to theories based on predicate logic have been considered earlier by Aczel [1] and Smith [21] but with purposes different from automated theorem proving. Our translation is also similar to the translation given by Felty and Miller [10] of the logical framework LF to the logic hh of hereditary Harrop formulas with quantification at all non predicate types. However, our work differs from theirs in that we consider translations of fragments of type theory into first order logic and that our main interest is in optimizing the ....

A. Felty and D. Miller. Encoding a Dependent-type -Calculus in a Logic Programming Language. In Proceedings of CADE-10. Lecture Notes in Artificial Intelligence 449, Springer Verlag, 1990.

....recognising that some representation already exists and reusing it. Folding amounts to recognising that two different representations represent the same thing and replacing one by the other. We assume a basic knowledge of Prolog and Prolog. 2 Introduction The logic programming language Prolog [28, 27, 29, 15, 13, 26, 14, 30] improves greatly on standard Prolog because it features very powerful operations on terms and programs while still giving them a logical semantics. A keyword common to all these features is scoping. terms introduce scoping at the term level, explicit quantifications (universal and existential) ....

A. Felty and D.A. Miller. Encoding a Dependent-Type -Calculus in a Logic Programming Language. Rapport de recherche 1259, Inria, 1990.

....other approaches can now be defined in an executable way within rewriting logic. Our proposal of using rewriting logic as a logical framework is related to other logical framework proposals such as the Edinburgh logical framework LF [69, 6, 51] meta theorem provers such as Isabelle [165] Prolog [160, 43], and Elf [167] the metalogical framework proposal of Basin and Constable [8] who advocate constructive type theory as the framework logic; and the work of Matthews, Smaill, and Basin [111] who use Feferman s FS 0 [42] a logic designed with the explicit purpose of being a metalogical ....

A. Felty and D. Miller. Encoding a dependent-type -calculus in a logic programming language. In M.E. Stickel, editor, Proc. 10th. Int. Conf. on Automated Deduction, Kaiserslautern, Germany, July 1990, volume 449 of LNCS, pages 221--235. Springer-Verlag, 1990.

....nouveaut es de Prolog comme les types, la fi r eduction et la suspension de l unification. Mots cl e : Impl ementation, Programmation logique, Prolog, Gestion de m emoire, Mali The Architecture of an Implementation of Prolog: Prolog Mali 3 1 Introduction The logic programming language Prolog [30, 29, 31, 17, 15, 28, 16, 32] improves on standard Prolog because it features more powerful operations on terms and programs while still giving them a logical semantics. A keyword common to all these features is scoping. Terms introduce scoping at the term level, explicit quantifications (universal and existential) introduce ....

A. Felty and D.A. Miller. Encoding a Dependent-Type -Calculus in a Logic Programming Language. Rapport de recherche 1259, Inria, 1990.

....scale to richer theories such as those including unit types or subtyping. These problems were side stepped in the original paper on the LF logical framework [HHP93] by restricting attention to fi conversion for definitional equality. This is sufficient if we also restrict attention to j long forms [FM90, Cer96]. This restriction is somewhat unsatisfactory, especially in linear variants of LF [CP98] More recently, j expansion has been studied in its own right, using modification of standard techniques from rewriting theory to overcome the lack of strong normalization when expansion is not restricted ....

Amy Felty and Dale Miller. Encoding a dependent-type -calculus in a logic programming language. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, pages 221--235, Kaiserslautern, Germany, July 1990. Springer-Verlag LNCS 449.

....scale to richer theories such as those including unit types or subtyping. These problems were side stepped in the original paper on the LF logical framework [HHP93] by restricting attention to fi conversion for definitional equality. This is sufficient if we also restrict attention to j long forms [FM90, Cer96]. This restriction is somewhat unsatisfactory, especially in linear variants of LF [CP98] More recently, j expansion has been studied in its own right, using modification of standard techniques from rewriting theory to overcome the lack of strong normalization when expansion is not restricted ....

Amy Felty and Dale Miller. Encoding a dependent-type -calculus in a logic programming language. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, pages 221--235, Kaiserslautern, Germany, July 1990. Springer-Verlag LNCS 449.

....to richer theories such as those including unit types or subtyping. These problems were side stepped in the original paper on the LF logical framework [HHP93] by restricting attention to fi conversion for definitional equality, which is sufficient if we also restrict attention to j long forms [FM90, Cer96]. This restriction is somewhat unsatisfactory, especially in linear variants of LF [CP98] More recently, j expansion has been studied in its own right, using modification of standard techniques from rewriting theory to overcome the lack of strong normalization when expansion is not restricted ....

Amy Felty and Dale Miller. Encoding a dependent-type -calculus in a logic programming language. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, pages 221--235, Kaiserslautern, Germany, July 1990. Springer-Verlag LNCS 449.

....scale to richer theories such as those including unit types or subtyping. These problems were sidestepped in the original paper on the LF logical framework [HHP93] by restricting attention to fi conversion for definitional equality, which is sufficient if we also restrict attention to j long forms [FM90, Cer96]. This restriction is somewhat unsatisfactory, especially in linear variants of LF [CP98] More recently, j expansion has been studied in its own right, using modification of standard techniques from rewriting theory to overcome the lack of strong normalization when expansion is not restricted ....

Amy Felty and Dale Miller. Encoding a dependent-type -calculus in a logic programming language. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, pages 221--235, Kaiserslautern, Germany, July 1990. Springer-Verlag LNCS 449.

....ESPRIT Basic Research Action 3245 Logical Frameworks: Design, Implementation and Experiment . A selection of papers presented in the first Workshop are collected in the book [25] Among the recent work most closely related to the topics presented here we mention Frank Pfenning [42] and Amy Felty [17, 18, 19]. This paper is organized as follows. In section 2 we introduce the LF specification language (or type theory) In section 3 we discuss the LF paradigm for specifying a logical system. The subsequent sections illustrate this paradigm. Section 4 deals with modal logics. Section 5 deals with various ....

Amy Felty., and Dale Miller. Encoding a dependent-type -calculus in a logic programming language. in Tenth International Conference on Automated Deduction. Kaiserslautern, Germany, July 1990.

....intuitionistic logic. Translations of Martin Lof s type theory to theories based on predicate logic have been considered earlier by Aczel [1] and Smith [19] but with purposes different from automated theorem proving. Our translation is also similar to the translation given by Felty and Miller [10] of the logical framework LF to the logic hh of hereditary Harrop formulas with quantification at all non predicate types. However, our work differs from theirs in that we consider translations of fragments of type theory into first order logic and that our main interest is in optimizing the ....

A. Felty and D. Miller. Encoding a Dependent-type -Calculus in a Logic Programming Language. In Proceedings of CADE-10. Lecture Notes in Artificial Intelligence 449, Springer Verlag, 1990.

....logic. Moreover one optimises such a translation for enhancing the efficiency of automated proof search for the initial problem. Such encoding has been developed from MLTT [161] but also from LF to the logic hh w of hereditary Harrop formulae with quantification at all non predicate types [48]. We can also consider an alternative and dual use of such encodings. As finding proofs corresponds to finding inhabitants of types one can in the case of implicational logics, specify the set of all the terms representing proofs in these logics. Therefore, new proof search algorithms have been ....

A. Felty and D. Miller. Encoding a dependent-type -calculus in a logic programming language. In 10th International Conference on Automated Deduction, LNAI 449, pages 221--235, Kaiserslautern, FRG, July 1990.

....it becomes possible to implement through it all the other object logics that can be adequately represented in the framework logic. Much work has already been done in this area, including the Edinburgh logical framework LF [41, 42, 28] and meta theorem provers such as Isabelle [91] Prolog [87, 26], and Elf [92] all of which adopt as framework logics different variants of higher order logics or type theories. There has also been important work on what Basin and Constable [9] call metalogical frameworks. These are frameworks supporting reasoning about the metalogical aspects of the logics ....

A. Felty and D. Miller, Encoding a dependent-type -calculus in a logic programming language, in: M. E. Stickel (ed.), Proc. 10th. Int. Conf. on Automated Deduction, Kaiserslautern, Germany, July 1990, LNCS (subseries LNAI) 449, Springer-Verlag, 1990, pages 221--235.

....correctness guarantees than functional meta languages without dependent types (such as ML, for example) The way dependent types can be used to impose constraints on logic variables is one of the attractive features of Elf. The feature is missing if one follows the proposal by Felty Miller [9] to interpret LF signatures in Hereditary Harrop logic. While their encoding is adequate on the declarative level, it is inadequate on the operational level, since typing constraints are expressed as predicates which are checked after the execution of a goal, thus potentially leading to much ....

Amy Felty and Dale Miller. Encoding a dependent-type -calculus in a logic programming language. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, Kaiserslautern, Germany, pages 221--235. Springer-Verlag LNCS 449, July 1990.

....was originally naive, partly inspired by SchroederHeister s [40] rules of higher level in natural deduction. The current version borrows ideas from type theoretic logical frameworks. It is essentially the higher order hereditary Harrop (hohh) formul# of Felty and Miller, who have exhibited [9] a translation between it and the Edinburgh Logical Framework. Prolog is a logic programming language based on higher order uni cation and hohh. Felty [8] has used it to implement theorem provers. This work is closely related to Isabelle. Elf [36] is an analogous language based on the Edinburgh ....

Amy Felty and Dale Miller. Encoding a dependent-type -calculus in a logic programming language. In Mark E. Stickel, editor, 10th International Conference on Automated Deduction, LNAI 449, pages 221235. Springer, 1990.

....search. Thus, besides answering the theoretical question about the precise relationship between these two meta languages, this translation also describes how LF specifications of object logics can be implemented within such systems. The translation we present here extends a translation given in [9]. As in that paper, we consider a form of LF such that all terms in derivable assertions are in canonical form, a notion which corresponds to fij long normal form in the simply typed calculus. In the translation given there, the form of proofs was also greatly limited. As we will illustrate, ....

Amy Felty and Dale Miller. Encoding a dependent-type -calculus in a logic programming language. In Tenth International Conference on Automated Deduction, Kaiserslautern, Germany, July 1990.

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Amy Felty and Dale Miller. Encoding a dependent-type -calculus in a logic programming language. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, pages 221--235, Kaiserslautern, Germany, July 1990. Springer-Verlag LNCS 449.

No context found.

Amy Felty and Dale Miller. Encoding a dependent-type -calculus in a logic programming language. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, pages 221--235, Kaiserslautern, Germany, July 1990. Springer-Verlag LNCS 449.

No context found.

Felty, A. and Miller, D. 1990. Encoding a dependent-type #-calculus in a logic programming language. In 10th International Conference on Automated Deduction, M. Stickel, Ed. SpringerVerlag LNCS 449, Kaiserslautern, Germany, 221--235.

No context found.

Amy Felty and Dale Miller. Encoding a dependent-type #-calculus in a logic programming language. In Mark E. Stickel, editor, 10th International Conference on Automated Deduction, LNAI 449, pages 221--235. Springer, 1990.

No context found.

A. Felty and D. Miller, Encoding a dependent-type -calculus in a logic programming language, in: M. E. Stickel, ed., Proc. 10th. Int. Conf. on Automated Deduction, Kaiserslautern, Germany (LNAI 449, Springer-Verlag, 1990) 221--235. 33

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