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Abstract: : From a general perspective, a substitution is a transformation from one space to another, an equation is a pair of such substitutions, and a solution to an equation is a substitution that yields the same value when composed with (i.e., when substituted into) the substitutions that constitute the given equation. In some special cases, solutions are called unifiers. Other examples include Scott domain equations, unification grammars, type inference, and differential equations. The intuition... (Update)
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BibTeX entry: (Update)
@incollection{ goguen89what,
author = "Joseph Goguen",
title = "What is Unification? {A} Categorical View of Substitution, Equation and Solution",
booktitle = "Resolution of Equations in Algebraic Structures, Volume 1: Algebraic Techniques",
publisher = "Academic",
editor = "Maurice Nivat and Hassan A{\"i}t-Kaci",
pages = "217--261",
year = "1989",
url = "citeseer.ist.psu.edu/166243.html" }
Citations (may not include all citations):809 A theory of type polymorphism in programming (context) - Milner - 1978
562 Categories for the Working Mathematician (context) - Lane - 1971
243 An Introduction to Unification-Based Approaches to Grammar (context) - Shieber - 1986
133 Foundations of Logic Programming (context) - Lloyd - 1984
114 Building-in equational theories (context) - Plotkin - 1972
113 Functorial semantics of algebraic theories (context) - Lawvere - 1963
95 Hope: an experimental applicative language - Burstall, MacQueen et al. - 1980
72 Prolog and infinite trees (context) - Colmerauer - 1982
62 A unification algorithm for associative-commutative function.. (context) - Stickel - 1981
61 Logic and Data Bases (context) - Gallaire, Minker - 1978
57 Some fundamental algebraic tools for the semantics of comput.. - Goguen, Burstall - 1984
51 Recherches sur la th'eorie de la d'emonstration (context) - Herbrand - 1930
45 Jean-Pierre Jouannaud (context) - Futatsugi, Goguen - 1985
45 Operational semantics of order-sorted algebra (context) - Goguen, Jouannaud et al. - 1985
35 An algebraic semantics approach to the effective resolution .. (context) - it-Kaci - 1986
35 Logic Programming: Functions (context) - DeGroot, Lindstrom - 1986
30 Categorical foundations for general systems theory (context) - Goguen - 1973
28 Formal Philosophy: Selected Papers of Richard Montague (context) - Montague - 1974
27 Computational Category Theory (context) - Rydeheard, Burstall - 1988
20 A machine-oriented logic based on the resolution principle (context) - Robinson - 1965
20 Semantics and Theory of Computation Series (context) - Goguen, algebra et al. - 1978
19 Mathematical representation of hierarchically organized syst.. (context) - Goguen - 1971
19 the Categorial Analysis of Logic (context) - Goldblatt - 1979
16 Graduate Texts in Mathematics (context) - Manes, Springer - 1976
14 data types and semantics (context) - Scott - 1972
12 eneKirchner, and Jos (context) - Kirchner - 1988
10 Structures alg'ebriques dans les cat'egories (context) - Benabou - 1968
8 Parameterized programming in OBJ (context) - Futatsugi, Goguen et al. - 1987
4 A classification of many-sorted unification theories (context) - Walther - 1986
3 Unification over complex indeterminates in Prolog (context) - Mukai - 1985
3 eneKirchner, Aristide M (context) - Goguen, Kirchner - 1988
3 and Kimbal Marriott (context) - Lassez, Maher - 1988
3 eme Prolog. Technical report, Groupe d (context) - Colmerauer, Kanoui et al. - 1979
2 the recursive specification of data types (context) - Wand - 1975
2 Unification in many-sorted equational theories (context) - Schmidt-Schauss - 1986
1 Theoretical Computer Science (context) - Ehrich, Lipeck et al. - 1983
1 The impact of frege's principle of compositionality for the .. (context) - Boas, Janssen - 1979
1 Given as lecture at U (context) - Goguen, for et al. - 1991
1 Unification in categories (context) - Adachi - 1984
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