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Higherorder Unification via Explicit Substitutions (Extended Abstract)
 Proceedings of LICS'95
, 1995
"... Higherorder unification is equational unification for βηconversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the λσcal ..."
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Cited by 103 (13 self)
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Higherorder unification is equational unification for βηconversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the λσcalculus of explicit substitutions.
A Total Approach to Partial Algebraic Specification
, 2002
"... Partiality is a fact of life, but at present explicitly partial algebraic specifications lack tools and have limited proof methods. We propose a sound and complete way to support execution and formal reasoning of explicitly partial algebraic specifications within the total framework of membership eq ..."
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Cited by 8 (2 self)
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Partiality is a fact of life, but at present explicitly partial algebraic specifications lack tools and have limited proof methods. We propose a sound and complete way to support execution and formal reasoning of explicitly partial algebraic specifications within the total framework of membership equational logic (MEL) which has a highperformance interpeter (Maude) and proving tools. This is accomplished by a sound and complete mapping PMEL ! MEL of partial membership equational (PMEL) theories into total ones.
Constraint Solving by Narrowing in Combined Algebraic Domains
 Proc. 11th International Conference on Logic Programming
, 1994
"... Narrowing is a way to integrate function evaluation and equality definition into logic programming. Here we show how this can be combined with the constraint paradigm. We propose a solver for goals with constraints in theories defined by unconstrained equalities and rewrite rules with constraints ex ..."
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Cited by 5 (4 self)
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Narrowing is a way to integrate function evaluation and equality definition into logic programming. Here we show how this can be combined with the constraint paradigm. We propose a solver for goals with constraints in theories defined by unconstrained equalities and rewrite rules with constraints expressed in an algebraic builtin structure. The narrowing method reduces the goal solving problem in the whole theory to rewriting and constraint solving in an adequate combined theory. The combined solver is obtained through the combination of a solver in the builtin structure and a solver for the unconstrained equalities. Sufficient syntactic conditions are proposed to get a process that enumerates a complete set of solutions. 1 Introduction Narrowing provides integration of function evaluation and equality definition into logic programming [6, 12, 8, 18, 10]. In this work, we show how this can be connected with the constraint paradigm to get a constraint solver on combined algebraic dom...
Sort Inheritance for OrderSorted Equational Presentations
 In Recent Trends in Data Types Specification
, 1995
"... In an algebraic framework, where equational, membership and existence formulas can be expressed, decorated terms and rewriting provide operational semantics and decision procedures for these formulas. We focus in this work on testing sort inheritance, an undecidable property of specifications, neede ..."
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Cited by 5 (4 self)
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In an algebraic framework, where equational, membership and existence formulas can be expressed, decorated terms and rewriting provide operational semantics and decision procedures for these formulas. We focus in this work on testing sort inheritance, an undecidable property of specifications, needed for unification in this context. A test and three specific processes, based on completion of a set of rewrite rules, are proposed to check sort inheritance. They depend on the kinds of membership formulas (t : A) allowed in the specifications: flat and linear, shallow and general terms t are studied.
G²Algebras
"... n them. Example 1. Consider the following specification in pseudoOBJ syntax, where we distinguish between capital and small letters: obj NATS kind Nats sorts zero : ? Nats succ : Nats ? Nats sortvar X :: Nats ops 0 : ? zero s : X ? succ(X). In the initial algebra of this specification, ..."
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n them. Example 1. Consider the following specification in pseudoOBJ syntax, where we distinguish between capital and small letters: obj NATS kind Nats sorts zero : ? Nats succ : Nats ? Nats sortvar X :: Nats ops 0 : ? zero s : X ? succ(X). In the initial algebra of this specification, which is unique up to isomorphism, succ n (zero) is interpreted as singleton fs n (0)g and Nats is the set of all such singletons. Now intervals on natural numbers can be specified as follows: obj INATS kind INats import NATS sorts leq : Nats ? INats geq : Nats ? INats between :Nats Nats ? INats sortvar X,Y :: Nats subsorts X ! leq(X) ! leq(succ(X)) X ! geq(X) ? geq(succ(X)) X ! between(X,X) between(succ(X), Y) ! betwe
Algebraic System Specification and Development: Survey and Annotated Bibliography  Second Edition 
, 1997
"... Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5.4 Special Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 Semantics of Programming Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.1 Semantics of Ada . . . ..."
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Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5.4 Special Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 Semantics of Programming Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.1 Semantics of Ada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.2 Action Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.7 Specification Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7.1 Early Algebraic Specification Languages . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7.2 Recent Algebraic Specification Languages . . . . . . . . . . . . . . . . . . . . . . . 55 4.7.3 The Common Framework Initiative. . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5 Methodology 57 5.1 Development Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1.1 Applica...
R^n and G^nLogics
 HigherOrder Algebra, Logic, and Term Rewriting, volume 1074 of Lecture Notes in Computer Science
, 1996
"... This paper proposes a simple, settheoretic framework providing expressive typing, higherorder functions and initial models at the same time. Building upon Russell's ramified theory of types, we develop the theory of R logics, which are axiomatisable by an ordersorted equational Horn logic ..."
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This paper proposes a simple, settheoretic framework providing expressive typing, higherorder functions and initial models at the same time. Building upon Russell's ramified theory of types, we develop the theory of R logics, which are axiomatisable by an ordersorted equational Horn logic with a membership predicate, and of G logics, that provide in addition partial functions. The latter are therefore more adapted to the use in the program specification domain, while sharing interesting properties, like existence of an initial model, with R logics. Operational semantics of R logics presentations is obtained through ordersorted conditional rewriting.
R nandG nLogics
"... is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS ..."
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is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS