We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science --- LICS'96 (E. Clarke editor), pp. 264--275, New Brunswick, NJ, July 27--30 1996. mal basis for a conservative extension of the LF logical framework. LLF combines the expressive power of dependent types with linear logic to permit the natural and concise representation of a whole new class of deductive systems, namely those dealing with state. As an example we encode a version of Mini-ML with references including its type system, its operational semantics, and a proof of type preservation. Another example is the encoding of a sequent calculus for classical linear logic and its cut elimination theorem. LLF can also be given an operational interpretation as a logic programming language under which the representations above can be used for type inference, evaluation and cut-elimination. 1 Introduction A logical framework is a formal system desig...

Rewriting logic [72] is proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems. Using concepts from the theory of general logics [70], representations of an object logic L in a framework logic F are understood as mappings L ! F that translate one logic into the other in a conservative way. The ease with which such maps can be defined for a number of quite different logics of interest, including equational logic, Horn logic with equality, linear logic, logics with quantifiers, and any sequent calculus presentation of a logic for a very general notion of "sequent," is discussed in detail. Using the fact that rewriting logic is reflective, it is often possible to reify inside rewriting logic itself a representation map L ! RWLogic for the finitely presentable theories of L. Such a reification takes the form of a map between the abstract data types representing the finitary theories of...

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A formal methodology is presented for the systematic evolution of modular Standard ML programs from specifications by means of verified refinement steps, in the framework of the Extended ML specification language. Program development proceeds via a sequence of design (modular decomposition), coding and refinement steps. For each of these three kinds of steps, conditions are given which ensure the correctness of the result. These conditions seem to be as weak as possible under the constraint of being expressible as "local" interface matching requirements. Interfaces are only required to match up to behavioural equivalence, which is seen as vital to the use of data abstraction in program development. Copyright c fl 1989 by D. Sannella and A. Tarlecki. All rights reserved. An extended abstract of this paper will appear in Proc. Colloq. on Current Issues in Programming Languages, Joint Conf. on Theory and Practice of Software Development (TAPSOFT), Barcelona, Springer LNCS (1989)....

. In this paper an overview on proof systems for structured algebraic specifications is presented. As underlying language we choose an ASL-like kernel language which includes reachability and observability operators. Three different kinds of proof systems are studied. The first two approaches are non-compositional systems where the basic idea is to compute for any structured specification a flat unstructured set of axioms and rules which, combined with some standard proof systems for the underlying logic, may be used for deriving theorems of the specification. In the normal form approach of Bergstra, Hering and Klint, a flat set of axioms is constructed for each structured specification, whereas in the second approach not only individual axioms but also individual proof rules are taken into account. The drawback of the non-compositional proof systems is that they do not reflect the modular structure of specifications. Therefore we present also a structured proof system the derivations ...

We give a categorical account of Kripke-Beth-Joyal models of the - calculus. Kripke models. Emphasize semantics of (terms/representatives/realizers for) consequences. 1 Introduction This paper, \Functorial Kripke-Beth-Joyal models of the -calculus I: type theory and internal logic" (henceforth abbreviated to I), is rst of a sequence of three connected works. It is concerned with the basic model theory of the - calculus considered on the one hand as a system of rst-order dependent function types and on the other as presentation of the f8; g-fragment of minimal rstorder predicate logic with proof-objects. From the point of view of type theory, ... MITCHELL/MOGGI From the point of view of logic, the ... At the core of our denition of Kripke(-Beth-Joyal) models of lies our treatment of comprehension, context extension and (rst-order) dependent function spaces. The essential idea is similar that of earlier work [?, ?, ?]; however, our treatment has the following two advant...

In this paper a new language for Knowledge Engineering is presented. Its main characteristics are: modularity, incremental programming of KB's, partial evaluation and modular uncertainty treatment. The partial evaluation is presented as a good mechanism to provide richer communication patterns of the system and the final users. It allows to give more explanatory answers that the classical inference mechanisms employed in expert systems. A rough description of the language MILORD II is presented stressing its modularity structures that allow to define generic modules and incremental programming operations between the modules. Some examples obtained from the applications developed using this language are presented.

The Ergo Project at Carnegie Mellon University conducts a program of research into the foundations of formal program development. The overall goal of the project is to provide a framework for the development and maintenance of provably correct programs and demonstrate its utility through prototype implementations and examples. In this report we describe some selected aspects of our research towards this goal. 3