Finkelstein, S., Freyd, P. and Lipton, J., "A New Framework for Declarative Programming", to appear in Theoretical Computer Science, Elsevier. Home/Search Document Details and Download
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Some Notes on Logic Programming with a Relational Machine.. - Lipton, Chapman (1998) (3 citations) (Correct)
....satisfy the axioms R Sigma. We call these Rel Sigma interpretations. In addition to the semantics just given, natural categorical models exist: tabular distributive allegories [FreySce] provide a semantics for a considerably more general notion of logic program, over a finite product category [FFL, NFDP, PowKin, CorMont]. We will not have need of this generality to describe relational complilation of conventional Horn Clause programs, although, in the presence of types and other programming features, there are interesting applications of such structures to logic programming, abstract interpretation and ....
....technique to extensions of the logic and to constraints, as well as to a denotational treatment based on relations, which we are currently exploring. Categorical treatments of logic programming provide alternative ways of algebraicizing the subject, which are, in a sense, variable free (see e.g. [AspMart, Diac, PowKin, FFL, NFDP, Pym]) Corradini and Montanari [CorMont] have given a categorical analysis of logic program execution in terms of transition systems. None of these approaches have as yet been applied to compilation or the definition of an abstract machine for logic programs, although this might be an interesting ....
Finkelstein, S., Freyd, P. and Lipton, J., "A New Framework for Declarative Programming", to appear in Theoretical Computer Science, Elsevier.
Encapsulating data in Logic Programming via Categorical.. - Lipton, McGrail (1998) (1 citation) Self-citation (Lipton) (Correct)
.... to analyze or generalize different facets of declarative programming has been carried out by Corradini, Asperti and Montanari [1, 5, 4] Panangaden, Scott, Seely, Saraswat, 19] Power and Kinoshita [21] Diaconescu [8] Pym [22] Orejas, Ehrig and Pino [18] and Finkelstein, Freyd and Lipton [9, 10]. 2 Logic Programming Categories In the remainder of this paper, we build on the basic categorical framework defined in [9] based on standard approaches to categorical logic, e.g. 16, 11] It is briefly sketched here. Categorical Logic: In a nutshell, the categorical representation of the ....
....when they exist. Note that separating the domains of terms u and v is what standardizes them apart 2 . In extensions of Horn logic, such as prolog, queries and programs may share variables, which requires explicit sharing of domains. Unification then reduces to equalizing the arrows (see [10]) For basic concepts of category theory, we refer the reader to [11] and for the elements of indexed category theory, see [6] We note that compositions of arrows are written in diagrammatic order: A f B composed with B g C is A fg C. 2 If the ambient category is the Herbrand ....
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Stacy E. Finkelstein, Peter Freyd, and James Lipton. A new framework for declarative programming. Theoretical Computer Science, To appear. Technical report available as www.cs.wesleyan.edu/~lipton/jftp/dist96-nfdp.ps.
Some Notes on Logic Programming with a Relational Machine.. - Lipton, Chapman (1998) (3 citations) Self-citation (Lipton) (Correct)
....satisfy the axioms R Sigma. We call these Rel Sigma interpretations. In addition to the semantics just given, natural categorical models exist: tabular distributive allegories [FreySce] provide a semantics for a considerably more general notion of logic program, over a finite product category [FFL, NFDP, PowKin, CorMont]. We will not have need of this generality to describe relational complilation of conventional Horn Clause programs, although, in the presence of types and other programming features, there are interesting applications of such structures to logic programming, abstract interpretation and ....
....technique to extensions of the logic and to constraints, as well as to a denotational treatment based on relations, which we are currently exploring. Categorical treatments of logic programming provide alternative ways of algebraicizing the subject, which are, in a sense, variable free (see e.g. [AspMart, Diac, PowKin, FFL, NFDP, Pym]) Corradini and Montanari [CorMont] have given a categorical analysis of logic program execution in terms of transition systems. None of these approaches have as yet been applied to compilation or the definition of an abstract machine for logic programs, although this might be an interesting ....
Finkelstein, S., Freyd, P. and Lipton, J., "A New Framework for Declarative Programming ", to appear in Theoretical Computer Science, Elsevier.
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