Konrad Slind

The PROSPER Toolkit

The PROSPER (Proof andS pecification Assisted Design Environments) project advocates the use of toolkits which allow existing verification tools to be adapted to a more flexible format so that they may be treated as components. A system incorporating such tools becomes another component that can be embedded in an application. n nThis paper describes the PROSPER Toolkit which enables this. The nature of communication between components is specifiedin a language-independent way. It is implemented in several common programming languages to allow a wide variety of tools to have access to the toolkit.

An Interface between Clam and HOL

This paper describes an interface between the CLAM proof planner and the HOL interactive theorem prover. The interface sends HOL goals to CLAM for planning, and translates plans back into HOL tactics that solve the initial goals. The combined system is able to automatically prove a number of theorems involving recursively defined functions.

Derivation and Use of Induction Schemes in Higher-Order Logic

We discuss how to formally derive induction schemes for recursively defined functions in higher order logic. The functions are able to be defined using ML-style pattern-matching, and the induction schemes are also phrased in terms of these patterns. As part of the TFL system, this facility is portable: it has been incorporated into both the HOL and Isabelle systems.

Another Look at Nested Recursion

Functions specified by nested recursions are difficult to define and reason about. We present several ameliorative techniques that use deduction in a classical higher-order logic. First, we discuss how an apparent circular dependency between the proof of nested termination conditions and the definition of the specified function can be avoided. Second, we propose a method that allows the specified function to be defined in the absence of a termination relation. Finally, we show how our techniques extend to nested program schemes, where a termination relation cannot be found until schematic parameters have been filled in. In each of these techniques, suitable induction theorems are automatically derived.

Automatic Derivation and Application of Induction Schemes for Mutually Recursive Functions

This paper advocates and explores the use of multipredicate induction schemes for proofs about mutually recursive functions. The interactive application of multi-predicate schemes stemming from datatype definitions is already well-established practice; this paper describes an automated proof procedure based on multi-predicate schemes. Multipredicate schemes may be formally derived from (mutually recursive) function definitions; such schemes are often helpful in proving properties of mutually recursive functions where the recursion pattern does not follow that of the underlying datatypes. These ideas have been implemented using the HOL theorem prover and the Clam proof planner.

Wellfounded Schematic Definitions

A program scheme looks like a recursive function definition, except that it has free variables ‘on the right hand side’. As is well-known, equalities between schemes can capture powerful program transformations, e.g., translation to tail-recursive form. In this paper, we present a simple and general way to define program schemes, based on a particular form of the wellfounded recursion theorem. Each program scheme specifies a schematic induction theorem, which is automatically derived by formal proof from the wellfounded induction theorem. We present a few examples of how formal program transformations are expressed and proved in our approach. The mechanization reported here has been incorporated into both the HOL and Isabelle/HOL systems.

System Description: An Interface Between CLAM and HOL

The CLAM proof planner has been interfaced to the HOL interactive theorem prover to provide the power of proof planning to people using HOL for formal verification, etc. The interface sends HOL goals to CLAM for planning and translates plans back into HOL tactics that solve the initial goals. The project homepage can be found at http://www.cl.cam.ac.uk/Research/HVG/Clam.HOL/intro.html.