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Abstract: In computer science we speak of implementing a logic; this is done in a programming language, such as Lisp, called here the implementation language. We also reason about the logic, as in understanding how to search for proofs; these arguments are expressed in the metalanguage and conducted in the metalogic of the object language being implemented. We also reason about the implementation itself, say to know it is correct; this is done in a programming logic. How do all these logics relate? ... (Update)
Context of citations to this paper: More
.... 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...
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BibTeX entry: (Update)
D. A. Basin and R. L. Constable. Metalogical frameworks. In G. Huet and G. Plotkin, editors, Logical Environments, pages 1--29. Cambridge University Press, 1993. http://citeseer.ist.psu.edu/basin92metalogical.html More
@incollection{ basin93metalogical,
author = "David A. Basin and Robert L. Constable",
title = "Metalogical Frameworks",
booktitle = "Logical Environments",
publisher = "Cambridge University Press",
editor = "G. Huet and G. Plotkin",
pages = "1--29",
year = "1993",
url = "citeseer.ist.psu.edu/basin92metalogical.html" }
Citations (may not include all citations):505 Implementing Mathematics with the Nuprl Proof Development Sy.. - Constable - 1986
359 Introduction to Higher Order Categorical Logic (context) - Lambek, Scott - 1986
311 Abstract types have existential type (context) - Mitchell, Plotkin - 1985
266 Information and Computation (context) - Coquand, Huet et al. - 1988
210 Logic programming in the lf logical framework - Pfenning - 1991
127 General Logics (context) - Meseguer - 1989
109 Putting theories together to make specifications (context) - Burstall, Goguen - 1977
98 Using dependent types to express modular structure - MacQueen - 1986
96 A survey of the project Automath (context) - de Bruijn - 1980
72 Logic for Computer Science (context) - Gallier - 1986
67 Specifications in an arbitrary institution (context) - Sannella, Tarlecki - 1988
60 Contraction-free sequent calculi for intuitionistic logic (context) - Dyckhoff - 1991
53 The semantics of reflected proof - Allen, Constable et al. - 1990
53 Toward formal development of ML programs: foundations and me.. - Sannella, Tarlecki - 1989
49 Model-Theoretic Logics (context) - Barwise, Feferman - 1985
46 A higher-order implementation of rewriting - Paulson - 1983
41 Computational metatheory in Nuprl (context) - Howe - 1988
39 Do-it-yourself type theory (context) - Backhouse, Chisholm et al. - 1989
35 Characterization of computable data types by means of a fini.. (context) - Bergstra, Tucker - 1980
33 Adjointness in foundations (context) - Lawvere - 1969
33 The Collected Papers of Gerhard Gentzen (context) - Gentzen - 1969
29 Finitary inductively presented logics - Feferman - 1988
26 Axioms for abstract model theory (context) - Barwise - 1974
25 truth and set (context) - Aczel, the et al. - 1980
21 Formalized metareasoning in type theory (context) - Knoblock, Constable - 1986
19 Implementing metamathematics as an approach to automatic the.. (context) - Constable, Howe - 1990
19 Automating Reasoning in an Implementation of Constructive Ty.. (context) - Howe - 1988
17 Institutions: Abstract Model Theory for Computer Science (context) - Goguen, Burstall - 1985
17 Representation independence and data abstraction (context) - Mitchell - 1986
16 Experience with FS 0 as a Framework Theory - Matthews, Smaill et al. - 1991
12 Prolegomena to a theory of formal reasoning (context) - Weyhrauch - 1980
11 Mitchell and Robert Harper (context) - John - 1988
8 Computer Assisted Proof for Mathematics: an Introduction Usi.. (context) - Burstall - 1991
6 Automating meta-theory creation and system extension - Basin, Giunchiglia et al. - 1991
5 Inductive definitions in the calculus of constructions (context) - Paulin-Mohring - 1989
4 Inductively presented systems and the formalization of meta-.. (context) - Feferman - 1980
3 Mathematical Intuitionism -- introduction to proof theory Tr.. (context) - Dragalin - 1988
3 Meta-Level and Reflexive Extension in Mechanical Theorem Pro.. (context) - Matthews - 1991
3 Equality of terms containing associative-commutative functio.. (context) - Basin - 1990
3 Burstall and Joseph (context) - Rod - 1980
2 Term Declaration Logic and Generalized Composita (context) - Aczel - 1991
1 Using Constructions as a MetaLanguage (context) - Taylor - 1988
1 A Decision Procedure for Intuitionistic Propositional Logic (context) - Hudelmaier - 1990
1 MacLogic -- a proof assistant for first-order logic (context) - Dyckhoff, Leslie et al. - 1989
1 Equality in lazy lambda calculi (context) - Howe - 1990
1 Technische Universitat Munchen (context) - Bauer, Wossner et al. - 1977
The graph only includes citing articles where the year of publication is known.
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A Recursion Planning Analysis of Inductive Completion - Barnett, Basin, Hesketh (1994) (Correct)
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