Imperative LF Meta-Programming

AbstractLogical frameworks have enjoyed wide adoption as meta-languages for describing deductive systems. While the techniques for representing object languages in logical frameworks are relatively well understood, languages and techniques for meta-programming with them are much less so. This paper presents work in progress on a programming language called Rogue-Sigma-Pi (RSP), in which general programs can be written for soundly manipulating objects represented in the Edinburgh Logical Framework (LF). The manipulation is sound in the sense that, in the absence of runtime errors, any putative LF object produced by a well-typed RSP program is guaranteed to type check in LF. An important contribution is an approach for soundly combining imperative features with higher-order abstract syntax. The focus of the paper is on demonstrating RSP through representative LF meta-programs

Initial Algebra Semantics for Cyclic Sharing Tree Structures

Terms are a concise representation of tree structures. Since they can be naturally defined by an inductive type, they offer data structures in functional programming and mechanised reasoning with useful principles such as structural induction and structural recursion. However, for graphs or "tree-like" structures - trees involving cycles and sharing - it remains unclear what kind of inductive structures exists and how we can faithfully assign a term representation of them. In this paper we propose a simple term syntax for cyclic sharing structures that admits structural induction and recursion principles. We show that the obtained syntax is directly usable in the functional language Haskell and the proof assistant Agda, as well as ordinary data structures such as lists and trees. To achieve this goal, we use a categorical approach to initial algebra semantics in a presheaf category. That approach follows the line of Fiore, Plotkin and Turi's models of abstract syntax with variable binding

Nominal Logic Programming

Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates logic programming based on nominal logic. We describe some typical nominal logic programs, and develop the model-theoretic, proof-theoretic, and operational semantics of such programs. Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we illustrate via examples.Comment: 46 pages; 19 page appendix; 13 figures. Revised journal submission as of July 23, 200

Theorem proving support in programming language semantics

We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational semantics, axiomatic semantics, and abstract interpretation. Descriptions as recursive functions are also provided whenever suitable, thus yielding a a verification condition generator and a static analyser that can be run inside the theorem prover for use in reflective proofs. Extraction of an interpreter from the denotational semantics is also described. All different aspects are formally proved sound with respect to the natural semantics specification.Comment: Propos\'e pour publication dans l'ouvrage \`a la m\'emoire de Gilles Kah