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Abstract: We present an algorithm for unification in the simply typed lambda calculus which enumerates complete sets of unifiers using a finitely branching search space. In fact, the types of terms may contain type-variables, so that a solution may involve typesubstitution as well as term-substitution. the problem is first translated into the problem of unification with respect to extensional equality in combinatory logic, and the algorithm is defined in terms of transformations on systems of... (Update)
Context of citations to this paper: More
...term rewriting system is known for this induced equality. This difficulty is solved here generalizing the techniques of [Dou93] by defining a certain notion of reduction on systems of CL terms. When E has a convergent presentation, this reduction captures the...
...also leads naturally to the study of linear systems. Explicit substitution leads to a cleaner treatment of unification [8] and Dougherty [7] has used combinators as the basis for higher order unification. We believe that our calculus could be used in a similar way. Combined...
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4: ACM Transactions on Programming Languages and Systems (context) - Martelli, Montanari et al. - 1982
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4: A formulation of the simple theory of types (context) - Church - 1940
BibTeX entry: (Update)
D. J. Dougherty. Higher-order Unification via Combinators. Theoretical Computer Science 114, pp. 273 -- 298, 1993. http://citeseer.ist.psu.edu/255654.html More
@article{ dougherty93higherorder,
author = "Daniel J. Dougherty",
title = "Higher-order unification via combinators",
journal = "Theoretical Computer Science",
volume = "114",
number = "2",
pages = "273--298",
year = "1993",
url = "citeseer.ist.psu.edu/255654.html" }
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259 Combinatory Logic (context) - Curry, Feys - 1958
259 Combinatory Logic (context) - Curry, Hindley et al. - 1972
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145 Isabelle: The Next 700 Theorem Provers (context) - Paulson - 1990
143 A new implementation technique for applicative languages (context) - Turner - 1979
137 Introduction to Combinators and -Calculus (context) - Hindley, Seldin - 1986
97 The undecidability of the second-order unification problem (context) - Goldfarb - 1981
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56 Higher-order unification revisited: complete sets of transfo.. (context) - Gallier, Snyder - 1989
55 Combining algebra and higher-order types (context) - Breazu-Tannen - 1988
54 First order unification in an equational theory (context) - Fay - 1979
54 Polymorphic rewriting conserves algebraic strong normalizati.. (context) - Breazu-Tannen, Gallier - 1989
51 The implementation of functional languages using custom hard.. (context) - Stoye - 1985
46 Complete sets of transformations for general E- unification (context) - Gallier, Snyder - 1989
31 A higher-order logic as the basis for logic programming - Nadathur - 1987
29 of programming laguages. Dissertation, Programming Research .. - Hughes, implementation - 1984
20 order type theory through unification (context) - Jensen, Pietrzykowski - 1973
19 The undecidability of unification in third-order logic (context) - Huet - 1973
15 Improving basic narrowing techniques (context) - R'ety - 1987
12 Higher-order unification with dependent function types - Elliott - 1989
11 Higher-order E-unification (context) - Snyder - 1990
9 A complete mechanization of second order logic (context) - Pietrzykowski - 1971
9 Super-Combinators (context) - Hughes - 1982
8 Norma: a graph reduction processor (context) - Scheevel - 1986
8 Adding algebraic rewriting to the Calculus of Constructions:.. (context) - Barbanera - 1990
7 An improved general E-unification method - Dougherty, Johann - 1990
4 On translating lambda terms into combinators: the basis prob.. (context) - Statman - 1986
3 Complete Sets of Transformations for Unification Problems (context) - Johann - 1991
2 R'esolution d'equations dans les langages d'ordre (context) - Huet - 1976
2 Strong reduction and normal form in combinatory logic (context) - Lercher - 1967
2 Adding algebra to the untyped lambda calculus (context) - Dougherty - 1991
1 Workshop on Conditional and Typed Rewriting Systems (context) - Nipkow, polymorphism et al. - 1990
1 A short proof of Curry's normal form theorem (context) - Hindley, Lercher
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.wesleyan.edu/~ddougherty/): More
A Combinatory Logic Approach to Higher-order E-unification - Dougherty, Johann (1992) (Correct)
Some Independence Results for Equational Unification - Otto, Narendran, Dougherty (1995) (Correct)
Adding Algebraic Rewriting to the Untyped Lambda Calculus - Dougherty (Correct)
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