Introduction Deductive systems, given via axioms and rules of inference, are a common conceptual tool in mathematical logic and computer science. They are used to specify many varieties of logics and logical theories as well as aspects of programming languages such as type systems or operational semantics. A logical framework is a meta-language for the specification of deductive systems. Research on logical frameworks is still in its infancy. Nonetheless, different frameworks have been proposed, implemented, and applied to a variety of problems. In addition, some general reasoning systems have been used to study deductions as mathematical objects, without specific support for the domain of deductive systems. This short survey cannot be complete, but we will try to highlight the major themes, concepts, and design choices for logical frameworks and provide some pointers to the literature. We concentrate on systems designed specifically as frameworks and among th
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544
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A framework for defining logics
– Harper, Honsell, et al.
- 1993
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469
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Linear logic
– Girard
- 1987
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446
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Introduction to HOL: A Theorem Proving Environment for Higher Order Logic
– Gordon, Melham
- 1993
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431
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Lambda Calculi with Types
– Barendregt
- 1992
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394
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Untersuchungen über das Logische Schliessen
– Gentzen
- 1935
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383
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Institutions: abstract model theory for specification and programming
– Goguen, Burstall
- 1992
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358
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Isabelle: A Generic Theorem Prover
– Paulson
- 1994
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353
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The formulas-as-types notion of construction
– Howard
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299
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Uniform proofs as a foundation for logic programming
– Miller, Nadathur, et al.
- 1991
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252
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Natural semantics
– Kahn
- 1987
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245
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A Logic Programming Language with Lambda Abstraction, Function Variables, and Simple Unification
– Miller
- 1986
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230
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Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser Theorem
– Bruijn
- 1972
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220
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Logic Programming with Focusing Proofs in Linear Logic
– Andreoli
- 1992
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214
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C.: Higher-order abstract syntax
– Pfenning, Elliott
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208
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Programming in Martin-Lof 's Type Theory: An Introduction
– Nordstrom, Petersson, et al.
- 1990
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204
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Constructive Mathematics and Computer Programming
– Martin-Löf
- 1983
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174
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An overview of Prolog
– Nadathur, Miller
- 1988
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168
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A uni algorithm for typed -calculus
– Huet
- 1975
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168
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Logic programming in the LF logical framework
– Pfenning
- 1991
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131
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Proving and applying program transformations expressed with second-order patterns
– Huet, Lang
- 1978
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127
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Rewriting logic as a logical and semantic framework
– Marti-Oliet, Meseguer
- 1993
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111
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The undecidability of the second-order unification problem
– Goldfarb
- 1981
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108
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Higher-order critical pairs
– Nipkow
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106
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Primitive recursion for higher-order abstract syntax
– Despeyroux, Pfenning, et al.
- 1997
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103
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Introduction to Higher-Order Categorical Logic
– Lambek, Scott
- 1986
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99
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An algorithm for testing conversion in type theory
– Coquand
- 1991
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97
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On the meanings of the logical constants and the justifications of the logical laws
– Martin-Löf
- 1996
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94
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The ALF proof editor and its proof engine
– Magnusson, Nordström
- 1994
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87
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A survey of the project AUTOMATH
– Bruijn
- 1980
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85
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An overview of ELAN
– Borovansk´y, Kirchner, et al.
- 1998
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84
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A multiple-conclusion meta-logic
– Miller
- 1994
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76
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A unification algorithm for typed λ-calculus
– Huet
- 1975
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74
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Using typed lambda calculus to implement formal systems on a machine
– Avron, Honsell, et al.
- 1992
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72
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The Semantics of Reflected Proof
– Allen, Constable, et al.
- 1990
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70
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Partial polymorphic type inference and higher-order unification
– Pfenning
- 1988
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67
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On equivalence and canonical forms in the lf type theory
– Harper, Pfenning
- 2000
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66
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Elf: A language for logic definition and verified metaprogramming
– Pfenning
- 1989
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64
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The Theory of LEGO: A Proof Checker for the Extended Calculus of Constructions
– Pollack
- 1994
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62
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Implementing tactics and tacticals in a higher-order logic programming language
– Felty
- 1993
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59
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The Mathematical Language AUTOMATH, its usage and some of its extensions
– Bruijn
- 1968
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55
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Specifying Theorem Provers in a Higher-Order Logic Programming Language
– Felty, Miller
- 1988
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52
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Metalogical frameworks
– Basin, Constable
- 1993
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52
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Unification and anti-unification in the calculus of constructions
– Pfenning
- 1991
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50
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Some properties of conversion
– Church, Rosser
- 1936
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48
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Structural cut elimination
– Pfenning
- 1995
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43
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The Coq proof assistant user’s guide. Rapport Techniques 154
– Dowek, Felty, et al.
- 1993
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42
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Natural deduction as higher-order resolution
– Paulson
- 1986
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41
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Specifying and Implementing Theorem Provers in a Higher-Order Logic Programming Language
– Felty
- 1989
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41
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Grundlagen der Mathematik
– Hilbert, Bernays
- 1934
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40
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Natural semantics and some of its meta-theory in Elf
– Michaylov, Pfenning
- 1991
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