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A New Framework for Declarative Programming
, 2001
"... We propose a new indexedcategory syntax and semantics of Weak Hereditarily Harrop logic programming with constraints, based on resolution over taucategories:finite product categories with canonical structure. ..."
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Cited by 6 (3 self)
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We propose a new indexedcategory syntax and semantics of Weak Hereditarily Harrop logic programming with constraints, based on resolution over taucategories:finite product categories with canonical structure.
A Fibrational Semantics for Logic Programs
 Proceedings of the Fifth International Workshop on Extensions of Logic Programming, volume 1050 of LNAI
, 1996
"... . We introduce a new semantics for logic programming languages. It generalises the traditional Herbrand universe semantics, and specialises the semantics of logical relations, as used in analysing parametricity in functional and imperative programming languages. We outline a typed logic programming ..."
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. We introduce a new semantics for logic programming languages. It generalises the traditional Herbrand universe semantics, and specialises the semantics of logical relations, as used in analysing parametricity in functional and imperative programming languages. We outline a typed logic programming language, give it this semantics, and show how it supports structured development of logic programs as advocated by Sterling et al. In particular, it gives semantics for some dynamic aspects of logic programs. 1 Introduction In 1989, Power and Sterling wrote "A notion of map between logic programs" [10], in which they began a stepwise structured development of logic programs (see [7],[12] for further developments). Although their work was generally expressed syntactically, there was a new semantics for logic programs implicit in their setting: each logic program was assigned a monoid, a semilattice (modulo some isomorphisms), and an action of the monoid on the semilattice. Then a map of l...
Some Notes on Logic Programming with a Relational Machine (Extended Abstract)
 Relational Methods in Computer Science, Technical Report Nr. 199803
, 1998
"... James Lipton Dept. of Mathematics Wesleyan University Emily Chapman Dept. of Mathematics Wesleyan University Abstract We study the use of relation calculi for compilation and execution of Horn Clause programs with an extended notion of input and output. We consider various other extensions to the Pr ..."
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James Lipton Dept. of Mathematics Wesleyan University Emily Chapman Dept. of Mathematics Wesleyan University Abstract We study the use of relation calculi for compilation and execution of Horn Clause programs with an extended notion of input and output. We consider various other extensions to the Prolog core.
Encapsulating data in Logic Programming via Categorical Constraints
 Meinke (Eds.), Principles ofDeclarative Programming, Lecture Notes in Computer Sciences
, 1998
"... We define a framework for writing executable declarative specifications which incorporate categorical constraints on data, Horn Clauses and datatype specification over finiteproduct categories. We construct a generic extension of a base syntactic category of constraints in which arrows correspond t ..."
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Cited by 2 (1 self)
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We define a framework for writing executable declarative specifications which incorporate categorical constraints on data, Horn Clauses and datatype specification over finiteproduct categories. We construct a generic extension of a base syntactic category of constraints in which arrows correspond to resolution proofs subject to the specified data constraints. 1 Introduction Much of the research in logic programming is aimed at expanding the expressive power and efficiency of declarative languages without compromising the logical transparency commitment: programs should (almost) read like specifications. One approach is to place more expressive power and more of the control components into the logic itself, possibly by expanding the scope of the underlying mathematical formalism. This has been the goal of constraint logic programming (CLP, Set constraints, Prolog III), and extensions to higherorder and linear logic, to name a few such efforts. This paper is a step in this direction. ...
Indexed Categories and BottomUp Semantics of Logic Programs
, 2001
"... We propose a categorical framework which formalizes and extends the syntax, operational semantics and declarative model theory of a broad range of logic programming languages. A program is interpreted in an indexed category in such a way that the base category contains all the possible states wh ..."
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We propose a categorical framework which formalizes and extends the syntax, operational semantics and declarative model theory of a broad range of logic programming languages. A program is interpreted in an indexed category in such a way that the base category contains all the possible states which can occur during the execution of the program (such as global constraints or type information), while each ber encodes the logic at each state.
An algebraic presentation of predicate logic (extended abstract)
"... Abstract. We present an algebraic theory for a fragment of predicate logic. The fragment has disjunction, existential quantification and equality. It is not an algebraic theory in the classical sense, but rather within a new framework that we call ‘parameterized algebraic theories’. We demonstrate t ..."
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Abstract. We present an algebraic theory for a fragment of predicate logic. The fragment has disjunction, existential quantification and equality. It is not an algebraic theory in the classical sense, but rather within a new framework that we call ‘parameterized algebraic theories’. We demonstrate the relevance of this algebraic presentation to computer science by identifying a programming language in which every type carries a model of the algebraic theory. The result is a simple functional logic programming language. We provide a syntaxfree representation theorem which places terms in bijection with sieves, a concept from category theory. We study presentationinvariance for general parameterized algebraic theories by providing a theory of clones. We show that parameterized algebraic theories characterize a class of enriched monads. 1