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Abstract not found

Introducing types into a logic programming language leads to the need for typed unification within the computation model. In the presence of polymorphism and higher-order features, this aspect forces analysis of types at run-time. We propose extensions to the Warren Abstract Machine (WAM) that permit such analysis to be done with reasonable efficiency. Much information about the structures of types is present at compile-time, and we show that this information can be used to considerably reduce the work during execution. We illustrate our ideas in the context of a typed version of Prolog. We describe a modified representation for terms, new instructions and additional data areas that in conjunction with existing WAM structures suffice to implement this language. The nature of compiled code is illustrated through examples, and the kind of run-time overheads that are incurred for processing types is analyzed, especially in those cases where others have shown that type checking can be eliminated during execution. The ideas

Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Defining data types : : : : : : : : : : : : : : : : : : : : : 6 2.4 Describing processes : : : : : : : : : : : : : : : : : : : : : 8 2.5 Expressing convergence using second order validity : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.6 Truth definitions: the analytical hierarchy : : : : : : : : 10 2.7 Inductive definitions : : : : : : : : : : : : : : : : : : : : : 13 3 Canonical semantics of higher order logic : : : : : : : : : : : : 15 3.1 Tarskian semantics of second order logic : : : : : : : : : 15 3.2 Function and re

We present a compiled implementation of Prolog that uses the abstract memory MALI for representing the execution state. Prolog is a logic programming language allowing a more general clause form than Standard Prolog 's (namely hereditary Harrop formulas instead of Horn formulas) and using simply typed -terms as a term domain instead of first order terms. The augmented clause form causes the program (a set of clauses) and the signature (a set of constants) to be changeable in a very disciplined way. The new term domain has a semi-decidable and infinitary unification theory, and it introduces the need for a fi-reduction operation at run-time. MALI is an abstract memory that is suitable for storing the search-state of depth-first search processes. Its main feature is its efficient memory management. We have used an original Prolog-to-C translation along which predicates are transformed into functions operating on continuations for handling failure and success in unifications, and change...

This paper develops a method to infer a polymorphic well-typing for a logic program. One of the main motivations is to contribute to a better automation of termination analysis in logic programs, by deriving types from which norms can automatically be constructed. Previous work on type-based termination analysis used either types declared by the user, or automatically generated monomorphic types describing the success set of predicates. Declared types are typically more precise and result in stronger termination conditions than those obtained with inferred types. Our type inference procedure involves solving set constraints generated from the program and derives a well-typing in contrast to a success-set approximation. Experiments show that our automatically inferred well-typings are close to the declared types and thus result in termination conditions that are as good as those obtained with declared types for all our experiments to date. We describe the method, its implementation and experiments with termination analysis based on the inferred types.

Abstract. A long standing problem in logic programming is how to impose directionality on programs in a safe fashion. The benefits of directionality include freedom from explicit sequential control, the ability to reason about algorithmic properties of programs (such as termination, complexity and deadlock-freedom) and controlling concurrency. By using Girard’s linear logic, we are able to devise a type system that combines types and modes into a unified framework, and enables one to express directionality declaratively. The rich power of the type system allows outputs to be embedded in inputs and vice versa. Type checking guarantees that values have unique producers, but multiple consumers are still possible. From a theoretical point of view, this work provides a “logic programming interpretation ” of (the proofs of) linear logic, adding to the concurrency and functional programming interpretations that are already known. It also brings logic programming into the broader world of typed languages and types-as-propositions paradigm, enriching it with static scoping and higher-order features.

We analyze basic shortcomings of existing proposals for type checking and type inferencing in logic programming languages. A new type system is presented using simple and declarative type annotations. It includes parametric polymorphism and subtyping. Static type checking and inferencing within the new type system is able to detect more programming errors than in other comparable systems. Our approach is independent of a specific resolution calculus and therefore applicable to a wide range of logic languages. A type inferencing algorithm is presented for reconstructing variable typings. As a concrete instance, the results were applied to unrestricted standard Prolog with type annotations, for which a type checking and type inferencing tool is available. This report is part of the documentation for a type checking tool available at !URL:http://www.fernuni-hagen.de/pi8/typical/?. It is complemented by a report "On the Use of Types in Logic Programming" [Mey96]. Research supported by ...

. In this paper, we describe a binding-time analysis (BTA) for a statically typed and strongly moded pure logic programming language, in casu Mercury. Binding-time analysis is the key concept in achieving o-line program specialisation: the analysis starts from a description of the program's input available for specialisation, and propagates this information throughout the program, deriving directives for when and how to perform specialisation. 1

We consider a general prescriptive type system with parametric polymorphism and subtyping for logic programs. The property of subject reduction expresses the consistency of the type system w.r.t. the execution model: if a program is well-typed, then all derivations starting in a well-typed goal are again well-typed. It is well-established that without subtyping, this property is readily obtained for logic programs w.r.t. their standard (untyped) execution model. Here we give syntactic conditions that ensure subject reduction also in the presence of general subtyping relations between type constructors. The idea is to consider logic programs with a xed dataow, given by modes.