David Pym. Proofs, Search and Computation in General Logic. PhD thesis, University of Edinburgh, 1990. Available as CST-69-90, also published as ECS-LFCS-90-125. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Logic Programming in the LF Logical Framework - Pfenning (1991) (138 citations) (Correct)
....style of Prolog, see [22, 24] It achieves this unification by giving types an operational interpretation, much the same way that Prolog gives certain formulas (Horn clauses) an operational interpretation. An alternative approach to logic programming in LF has been developed independently by Pym [28]. Here are some of the salient characteristics of our unified approach to logic definition and metaprogramming. First of all, the Elf search process automatically constructs terms that can represent object logic proofs, and thus a program need not construct them explicitly. This is in contrast to ....
.... This result notwithstanding, a complete pre unification algorithm for the simply typed calculus with generally good operational Logic Programming in the LF Logical Framework 8 behavior has been devised by Huet [15] Extensions to LF have been developed independently by Elliott [5, 7] and Pym [28]. Pre unification here refers to the fact that the algorithm will not enumerate unifiers, but simply reduce the original problem to a satisfiable set of constraints (so called flex flex pairs) whose unifiers are difficult to enumerate. While this unification algorithm has proven quite useful in ....
David Pym. Proofs, Search and Computation in General Logic. PhD thesis, University of Edinburgh, 1990. Available as CST-69-90, also published as ECS-LFCS-90-125.
Modularity in the LF Logical Framework - Harper, Pfenning (1991) (Correct)
....types and deductions as objects. The framework was intentionally kept weak (by excluding, for example, polymorphism and impredicative constructs) in order to better support mechanization and to allow a simple meta theory. This has proved auspicious: algorithms for unification have been developed [5, 21] and the type theory underlying LF has been amenable to an operational interpretation which is realized in the Elf programming language [18, 19] Furthermore, it also seems possible to express a wide range of meta theoretic properties of deductive systems within LF, though this line of research is ....
David Pym. Proofs, Search and Computation in General Logic. PhD thesis, University of Edinburgh, 1990. Available as CST-69-90, also published as ECS-LFCS-90-125.
Unification and Anti-Unification in the Calculus of Constructions - Pfenning (1991) (31 citations) (Correct)
.... environments have been constructed on the basis of such type theories (see, for example, 6, 18, 20] In order to give sophisticated assistance for proof development and management in these frameworks, preunification algorithms for LF have been developed independently by Elliott [7] and Pym [23]. The drawbacks of non determinism and undecidability were inherited by these algorithms from the simply typed case. A combination of the ideas of Miller and Elliott for a deterministic, though incomplete algorithm for the LF Logical Framework is presented by the author in [21] This forms the ....
David Pym. Proofs, Search and Computation in General Logic. PhD thesis, University of Edinburgh, 1990. Available as CST-69-90, also published as ECS-LFCS-90-125.
Implementing the Meta-Theory of Deductive Systems - Pfenning, Rohwedder (1992) (20 citations) (Correct)
....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. Proofs, Search and Computation in General Logic. PhD thesis, University of Edinburgh, 1990. Available as CST-69-90, also published as ECS-LFCS-90-125.
The Practice of Logical Frameworks - Frank Pfenning (1996) (15 citations) (Correct)
....postponed as constraints. Huet s algorithm has been used extensively in Prolog and Isabelle and generally seems to have good computational properties. It also generalizes smoothly from the simply typed to the dependently typed case, as discovered independently by Elliott [Ell89, Ell90] and Pym [Pym90, Pym92] The practical success of Huet s algorithm seems to be in part due to the fact that difficult, higher order unification problems rarely arise in practice. An analysis of this observation led Miller [Mil91] to discover higher order patterns, a sublanguage of the simply typed calculus with ....
David Pym. Proofs, Search and Computation in General Logic. PhD thesis, University of Edinburgh, 1990. Available as CST-69-90, also published as ECS-LFCS-90-125.
Unification and Anti-Unification in the Calculus of.. - Frank Pfenning School (1991) (31 citations) (Correct)
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David Pym. Proofs, Search and Computation in General Logic. PhD thesis, University of Edinburgh, 1990. Available as CST-69-90, also published as ECS-LFCS-90-125.
Compilation - The Model Of (Correct)
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David Pym. Proofs, Search and Computation in General Logic.PhD thesis, University of Edinburgh, 1990. Available as CST-69-90, also published as ECS-LFCS-90-125.
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