Julian Richardson

System Description: Proof Planning in Higher-Order Logic with Lambda-Clam

This system description outlines the λClam system for proof planning in higher-order logic. The usefulness and feasibility of applying higher-order proof planning to a number of types of problem is outlined, in particular the synthesis and verification of software and hardware systems. The use of a higher-order metatheory overcomes problems encountered in Clam because of its inability to reason properly about higher-order objects. λClam is written in λProlog.

Symbolic Verification with Gap-Order Constraints

Finite state automata with counters are useful for modelling systems with discrete parameters. The calculation of state invariants is an important tool in the analysis of such systems. Previous authors have presented techniques for the calculation of state invariants based on their approximation by convex polyhedra or periodic sets.

Deductive Synthesis of Recursive Plans in Linear Logic

Linear logic has previously been shown to be suitable for describing and deductively solving planning problems involving conjunction and disjunction. We introduce a recursively defined datatype and a corresponding induction rule, thereby allowing recursive plans to be synthesised. In order to make explicit the relationship between proofs and plans, we enhance the linear logic deduction rules to handle plans as a form of proof term.

Applying adversarial planning techniques to go

Approaches to computer game playing based on alpha-beta search of the tree of possible move sequences combined with a position evaluation function have been successful for many games, notably Chess. Such approaches are less successful for games with large search spaces and complex positions, such as Go, and we are led to seek alternatives. One such alternative is to model the goals of the players, and their strategies for achieving these goals. This approach means searching the space of possible goal expansions, typically much smaller than the space of move sequences. Previous attempts to apply these techniques to Go have been unable to provide results for anything other than a high strategic level or very open game positions. In this paper we describe how adversarial hierarchical task network planning can provide a framework for goal-directed game playing in Go which is also applicable both strategic and tactical problems.

Development of Correct Transformation Schemata for Prolog Programs

Schema-based program transformation [8] has been proposed as an effective technique for the optimisation of logic programs. Schemata are applied to a logic program, mapping inefficient constructs to more efficient ones. One challenging aspect of the technique is that of proving that the schemata are correct.

Automating changes of data type in functional programs

I present an automatic technique for transforming a program by changing the data types in that program to ones which are more appropriate for the task. Programs are synthesised by proving modified synthesis theorems in the proofs-as-programs paradigm. The transformation can be verified in the logic of type theory. Transformations are motivated by the presence of subexpressions in the synthesised program. A library of data type changes is maintained, indexed by the motivating subexpressions. These transformations are extended from the motivating expressions to cover as much of the program as possible. I describe the general pattern of the revised synthesis proof, and show how such a proof can be guided by difference matching followed by rippling.

An Adversarial Planning Approach to Go

Approaches to computer game playing based on (typically α-β) search of the tree of possible move sequences combined with an evaluation function have been successful for many games, notably Chess. For games with large search spaces and complex positions, such as Go, these approaches are less successful and we are led to seek alternative approaches. One such alternative is to model the goals of the players, and their strategies for achieving these goals. This approach means searching the space of possible goal expansions, typically much smaller than the space of move sequences. In this paper we describe how adversarial hierarchical task network planning can provide a framework for goal-directed game playing, and its application to the game of Go.

Computers and Games

Approaches to computer game playing based on (typically α-β) search of the tree of possible move sequences combined with an evaluation function have been successful for many games, notably Chess. For games with large search spaces and complex positions, such as Go, these approaches are less successful and we are led to seek alternative approaches. One such alternative is to model the goals of the players, and their strategies for achieving these goals. This approach means searching the space of possible goal expansions, typically much smaller than the space of move sequences. In this paper we describe how adversarial hierarchical task network planning can provide a framework for goal-directed game playing, and its application to the game of Go.

Abstract: Proof Planning with Program Schemas

Schema-based program synthesis and transformation techniques tend to be either pragmatic, designed for carrying out real program transformation or synthesis operations but lacking the logical basis to ensure correctness of the programs they synthesise/transform, or rigorous, with strong theoretical foundations, but generating proof obligations which are difficult to satisfy.