Sort Inheritance for Order-Sorted Equational Presentations
نویسندگان
چکیده
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 speciications, needed for uniication in this context. A test and three speciic 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 speciications: at and linear, shallow and general terms t are studied.
منابع مشابه
Dynamically-Typed Computations for Order-Sorted Equational Presentations
Equational presentations with ordered sorts encompass partially deened functions and subtyping information in an algebraic framework. In this work we address the problem of computing in order-sorted 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...
متن کاملUni cation in Extensions of Shallow Equational Theories
We show that uni cation in certain extensions of shallow equational theories is decidable Our extensions generalize the known classes of shallow or standard equational theories In order to prove de cidability of uni cation in the extensions a class of Horn clause sets called sorted shallow equational theories is introduced This class is a natural extension of tree automata with equality constra...
متن کاملUniication in Extensions of Shallow Equational Theories
We show that uniication in certain extensions of shallow equational theories is decidable. Our extensions generalize the known classes of shallow or standard equational theories. In order to prove de-cidability of uniication in the extensions, a class of Horn clause sets called sorted shallow equational theories is introduced. This class is a natural extension of tree automata with equality con...
متن کاملCompletion of Rewrite Systems with Membership Constraints. Part I: Deduction Rules
We consider a constrained equational logic where the constraints are membership conditions t 2 s where s is interpreted as a regular tree language. Our logic includes a fragment of second order equational logic (without projections) where second order variables range over regular sets of contexts. The problem with constrained equational logics is the failure of the critical pair lemma. That is ...
متن کاملLogic Programming over Polymorphically Order-Sorted Types
This thesis presents the foundations for relational logic programming over polymorphically order-sorted data types. This type discipline combines the notion of parametric polymorphism, which has been developed for higher-order functional programming, with the notion of order-sorted typing, which has been developed for equational rst-order speci cation and programming. Polymorphically order-sort...
متن کامل