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DynamicallyTyped Computations for OrderSorted Equational Presentations (Extended Abstract)
 Proc. 21st International Colloquium on Automata, Languages, and Programming, volume 820 of Lecture Notes in Computer Science
, 1994
"... Equational presentations with ordered sorts encompass partially defined functions and subtyping information in an algebraic framework. In this work we address the problem of computing in ordersorted algebras, with very few restrictions on the allowed presentations. We adopt an algebraic framework w ..."
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Cited by 10 (8 self)
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Equational presentations with ordered sorts encompass partially defined functions and subtyping information in an algebraic framework. In this work we address the problem of computing in ordersorted algebras, with very few restrictions on the allowed presentations. We adopt an algebraic framework where equational, membership and existence formulas can be expressed. A complete deduction calculus is provided to incorporate the interaction between all these formulas. The notion of decorated terms is proposed to memorize local sort information, dynamically changed by a rewriting process. A completion procedure for equational presentations with ordered sorts computes a set of rewrite rules with which not only equational theorems of the form (t = t 0 ), but also typing theorems of the for...
Sorted Unification And The Solution Of SemiLinear Membership Constraints
, 1992
"... This thesis describes a new representation for sortal constraints and a unification algorithm for the corresponding constrained terms. Variables range over sets of terms described by systems of set constraints , which can express limited intervariable dependencies. These sets of terms are more gene ..."
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Cited by 1 (1 self)
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This thesis describes a new representation for sortal constraints and a unification algorithm for the corresponding constrained terms. Variables range over sets of terms described by systems of set constraints , which can express limited intervariable dependencies. These sets of terms are more general than regular tree languages, but are still closed under intersection. The new unification algorithm shows sorted unification to be decidable for a broad class of sorted signatures, which we call semilinear , and, more generally, for sort theories with a least Herbrand model that can be represented using the new constraints. Even though the unification problem in question is NPhard, the generality of the algorithm may allow for particular efficient implementations for more restricted theories. This unification algorithm can be integrated into any of a variety of deductive systems, resulting in a hybrid substitutional reasoner. As an example, the soundness and completeness of a resolutio...
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...