Abstract not found

Introduction Architectural specifications are a mechanism to support formal program devel-opment [2, 11]. They have been introduced in the

Abstract. In informal mathematical usage we often reason using languages with binding. We usually find ourselves placing capture-avoidance constraints on where variables can and cannot occur free. We describe a logical derivation system which allows a direct formalisation of such assertions, along with a direct formalisation of their constraints. We base our logic on equality, probably the simplest available judgement form. In spite of this, we can axiomatise systems of logic and computation such as first-order logic or the lambda-calculus in a very direct and natural way. We investigate the theory of derivations, prove a suitable semantics sound and complete, and discuss existing and future research. 1

We propose a new style of writing graph algorithms in functional languages which is based on an alternative view of graphs as inductively defined data types. We show how this graph model can be implemented efficiently, and then we demonstrate how graph algorithms can be succinctly given by recursive function definitions based on the inductive graph view. We also regard this as a contribution to the teaching of algorithms and data structures in functional languages since we can use the functional-style graph algorithms instead of the imperative algorithms that are dominant today. Keywords: Graphs in Functional Languages, Recursive Graph Algorithms, Teaching Graph Algorithms in Functional Languages

More than being just a tool for expressing algorithms, a well-designed programming language allows the user to express her ideas efficiently. The design choices however effect the efficiency of the algorithms written in the languages. It is therefore of importance to understand how such choices effect the expressibility of programming languages. The paper pursues the very low complexity programs by presenting a first-order function algebra BC # that captures exactly LF, the functions computable in logarithmic space. This gives insights into the expressiveness of recursion. Moreover, it can be useful for the automatic analysis of programs' resource usage and the separation of complexity classes. The important technical features of BC # are (1) a separation of variables into safe and normal variables where recursion can only be done over the latter; (2) linearity of the recursive call; and (3) recursion with a variable step length (course-of-value recursion). Unlike formulations LF via Turin Machines, BC # makes no references to outside resource measures, e.g., the size of the memory used. This appears to be the first such characterization of LF-computable functions (not just predicates). The proof that all BC #-programs can be evaluated in LF is of separate interest to programmers: it trades space for time and evaluates recursion with at most one recursive call without a call stack.

In this paper, we take an engineering approach to atomic transaction verification. We discuss the design and implementation of a verification tool that can reason about the semantics of atomic database operations. To bridge the gap between language design and automated reasoning, we make use of a simple model of objects that imitates the type-tagged memory structure of an implementation. This simple model is sufficient to describe the operational semantics of the typical features of an object-oriented database programming language, such as bounded iteration, heterogeneity, object creation, and nil values. The same model lends itself to automated reasoning with a theorem prover system. We are thus able to apply theorem prover technology to verification problems that address transaction semantics. The work has applications in the areas of transaction safety, semantics-based concurrency control, and cooperative work. The approach is illustrated by a graph editing example, with heterogeneous node structures.

We present a semantics for architectural specifications in Casl, including an extended static analysis compatible with model-theoretic requirements. The main obstacle here is the lack of amalgamation for Casl models. To circumvent this problem, we extend the Casl logic by introducing enriched signatures, where subsort embeddings form a category rather than just a preorder. The extended model functor satisfies the amalgamation property as well as its converse, which makes it possible to express the amalgamability conditions in the semantic rules in static terms. Using these concepts, we develop the semantics at various levels in an institutionindependent fashion. Moreover, amalgamation for enriched Casl means that a variety of results for institutions with amalgamation, such as computation of normal forms and theorem proving for structured specifications, can now be used for Casl.

Cyclic data structures can be tricky to create and manipulate in declarative programming languages. In a declarative setting, a natural way to view cyclic structures is as denoting regular trees, those trees which may be infinite but have only a finite number of distinct subtrees. This paper shows how to implement the unfold (anamorphism) operator in both eager and lazy languages so as to create cyclic structures when the result is a regular tree as opposed to merely infinite lazy structures. The usual fold (catamorphism) operator when used with a strict combining function on any infinite tree yields an undefined result. As an alternative, this paper defines and show how to implement a cycfold operator with more useful semantics when used with a strict function on cyclic structures representing regular trees. This paper also introduces an abstract data type (cycamores) to simplify the use of cyclic structures representing regular trees in both eager and lazy languages. Implementions of cycamores in both SML and Haskell are presented.