Abstract. We present the natural confluence of higher-order hereditary Harrop formulas (HH formulas) as developed concretely in λProlog, Constraint Logic Programming (CLP, [JL87]), and Concurrent Constraint Programming (CCP, [Sar93]) as a fragment of (intuitionistic, higher-order) logic. The combination is motivated by the need for a simple executable, logical presentation for static and dynamic semantics of modern programming languages. The power of HH formulas is needed for higher-order abstract syntax, and the power of constraints is needed to naturally abstract the underlying domain of computation. Underpinning this combination is a sound and complete operational interpretation of a two-sided sequent presentation of (a large fragment of) intuitionistic logic in terms of behavioral testing of concurrent systems. Formulas on the left hand side of a sequent style presentation are viewed as a system of concurrent agents, and formulas on the right hand side as tests against this evolving system. The language permits recursive definitions of agents and tests, allows tests to augment the system being tested and allows agents to be contingent on the success of a test. We present a condition on proofs, operational derivability (OD), and show that the operational semantics generates only operationally derivable proofs. We show that a sequent in this logic has a proof iff it has an operationally derivable proof. 1

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.

We define a framework for writing executable declarative specifications which incorporate categorical constraints on data, Horn Clauses and datatype specification over finite-product 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 higher-order and linear logic, to name a few such efforts. This paper is a step in this direction. ...

The paper introduces a semantics for logic programs based on first order hereditary Harrop formulas which are expressed in terms of intuitionistic derivations. The derivations are constructed by means of an intuitionistic proof procedure that constitutes the resolution mechanism of the language. The semantics of a program is a goal independent denotation which can be equivalently specified by a denotational and an operational semantics. The denotational semantics is defined using a set of primitive semantic operators that act on derivations and are directly related to the properties of the derivations. Keywords: Logic Programming, Abstract Interpretation, Harrop Formulas 1 Introduction The aim of this work is to introduce a semantics for logic programs based on first order hereditary Harrop (fohh) formulas expressed in terms of intuitionistic proofs, in order to study the various properties of such programs. The proof procedure presented by Nadathur in [10] constitutes the basis of t...

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.