Publications (16)1.07 Total impact
- Theor. Comput. Sci. 01/1984; 28:45-81.
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ABSTRACT: This paper is concerned mainly with classes (categories) of ordered algebras which in some signature are axiomatizable by a set of inequations between terms (‘varieties’ of ordered algebras) and also classes which are axiomatizable by implications between inequations (‘quasi varieties’ of ordered algebras). For example, if the signature contains a binary operation symbol (for the monoid operation) and a constant symbol (for the identity) the class of ordered monoids M can be axiomatized by a set of inequations (i.e. expressions of the form t≤t'. However, if the signature contains only the binary operation symbol, the same class M cannot be so axiomatized (since it is not now closed under subalgebras). Thus, there is a need to find structural, signature independent conditions on a class of ordered algebras which are necessary and sufficient to guarantee the existence of a signature in which the class is axiomatizable by a set of inequations (between terms in this signature). In this paper such conditions are found by utilizing the notion of ‘P-categories’. A P-category C is a category such that each ‘Hom-set’ C(a,b) is equipped with a distiguished partial order which is preserved by composition. Aside from proving the characterization theorem, it is also the purpose of the paper to begin the investigation of P-categories.Journal of Pure and Applied Algebra 07/1983; 29(1):13–58. · 0.53 Impact Factor
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ABSTRACT: The purpose of this paper is two-fold: first to show how a natural mathematical formulation of the “solution” of a system of recursion equations is formally almost identical with well-known formulations of a solution of a system of “iteration equations.” The second aim is to present a construction which takes an algebraic theory T and yields another algebraic theory M(T) whose morphisms correspond to systems of recursion equations over T. This construction is highly uniform, i.e., the correspondence between T and M(T) is functorial.Journal of Computer and System Sciences. 01/1983;
Article: Finitary quasi-varieties[show abstract] [hide abstract]
ABSTRACT: A pair (,U) consisting of a category with coequalizers and a functor U: → Set is a weak quasi-variety if U has a left adjoint and U preserves and reflects regular epis. It is known that every weak quasi-variety is equivalent to a concrete quasi-variety, i.e. a category of Σ-algebras which has all free algebras and which is closed with respect to products and subalgebras. It is also known that if U preserves monic direct limits, is equivalent to a concrete quasi-variety of Σ-algebras in which Σ contains no function symbols of infinite rank; and if U preserves all direct limits, is equivalent to a concrete quasi-variety of Σ-algebras definable by a set of implications of the form where ti and si are Σ-terms and m is a nonnegative integer. This paper concerns several definitions of ‘finiteness’ in a category theoretic setting and some theorems on weak quasi-varieties. Two main theorems characterize those weak quasi-varieties (, U) such that U preserves all direct limits.Journal of Pure and Applied Algebra 08/1982; 25(2):121–154. · 0.53 Impact Factor
- ACM Trans. Program. Lang. Syst. 01/1982; 4:711-732.
Conference Proceeding: Parameter Passing in Algebraic Specification Languages.Program Specification, Proceedings of a Workshop, Aarhus, Denmark, August 1981; 01/1981
- Theor. Comput. Sci. 01/1981; 15:223-249.
- SIAM J. Comput. 01/1980; 9:25-45.
- SIAM J. Comput. 01/1980; 9:525-540.
Conference Proceeding: More on advice on structuring compilers and proving them correct.Semantics-Directed Compiler Generation, Proceedings of a Workshop, Aarhus, Denmark, January 14-18, 1980; 01/1980
Conference Proceeding: Parameterized Data Types in Algebraic Specification Languages (Short Version).Automata, Languages and Programming, 7th Colloquium, Noordweijkerhout, The Netherland, July 14-18, 1980, Proceedings; 01/1980
Conference Proceeding: Programming Languages as Mathematical Objects.Mathematical Foundations of Computer Science 1978, Proceedings, 7th Symposium, Zakopane, Poland, September 4-8, 1978; 01/1978
- J. ACM. 01/1977; 24:68-95.
Conference Proceeding: A Uniform Approach to Inductive Posets and Inductive Closure.Mathematical Foundations of Computer Science 1977, 6th Symposium, Tatranska Lomnica, Czechoslovakia, September 5-9, 1977, Proceedings; 01/1977
Conference Proceeding: Some Fundamentals of Order-Algebraic Semantics.Mathematical Foundations of Computer Science 1976, 5th Symposium, Gdansk, Poland, September 6-10, 1976, Proceedings; 01/1976
Conference Proceeding: Factorizations, Congruences, and the Decomposition of Automata and Systems.Mathematical Foundations of Computer Science, 3rd Symposium at Jadwisin near Warsaw, June 17-22, 1974, Proceedings; 01/1974
Armonk, NY, United States
- Thomas J. Watson Research Center