Showing papers by "Lawrence C. Paulson published in 1994"
Book•
28 Jul 1994
TL;DR: This book discusses theories, terms and types, tactics, and theorems of Isabelle Theories as well as its application to proof management.
Abstract: Foundations.- Getting started with Isabelle.- Advanced methods.- Basic use of Isabelle.- Proof management: The subgoal module.- Tactics.- Tacticals.- Theorems and forward proof.- Theories, terms and types.- Defining logics.- Syntax transformations.- Substitution tactics.- Simplification.- The classical reasoner.- Basic concepts.- First-order logic.- Zermelo-Fraenkel set theory.- Higher-order logic.- First-order sequent calculus.- Constructive Type Theory.- Syntax of Isabelle Theories.
1,200 citations
26 Jun 1994
TL;DR: This paper presents a fixedpoint approach to inductive definitions: instead of using a syntactic test such as ‘strictly positive,’ the approach lets definitions involve any operators that have been proved monotone.
Abstract: This paper presents a fixedpoint approach to inductive definitions. Instead of using a syntactic test such as ‘strictly positive,’ the approach lets definitions involve any operators that have been proved monotone. It is conceptually simple, which has allowed the easy implementation of mutual recursion and other conveniences. It also handles coinductive definitions: simply replace the least fixedpoint by a greatest fixedpoint. This represents the first automated support for coinductive definitions.
58 citations
06 Jun 1994
TL;DR: In this article, a special final coalgebra theorem, in the style of Aczel's, is proved within standard Zermelo-Fraenkel set theory, which is intended for machine implementation and is already implemented using the theorem prover Isabelle.
Abstract: A special final coalgebra theorem, in the style of Aczel's [2], is proved within standard Zermelo-Fraenkel set theory. Aczel's Anti-Foundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions. Variant ordered pairs and tuples, of possibly infinite length, are special cases of variant functions. Analogues of Aczel's Solution and Substitution Lemmas are proved in the style of Rutten and Turi [12]. The approach is less general than Aczel's, but the treatment of non-well-founded objects is simple and concrete. The final coalgebra of a functor is its greatest fixedpoint. The theory is intended for machine implementation and a simple case of it is already implemented using the theorem prover Isabelle [10].
20 citations
01 Jan 1994
TL;DR: These notes focus only on non-dependent type theory, which will be the topic of the rst few lectures of the planned lectures, and include sections on Deduction and the untyped lambda calculus.
Abstract: Preface These notes do not give a fully accurate representation of the planned lectures. Nevertheless they should provide useful background material which I hope will supplement the bibliography. The notes focus only on non-dependent type theory, which will be the topic of the rst few lectures. The remaining lectures will extend the material to encompass constructive type theory with dependent types. The rst part of these notes looks at aspects of the non-dependent part of constructive type theory from the foundational point of view, starting with a quote from Godel's Dialectica paper. The second part of these notes consists of material prepared for an MSc course at Manchester University on the simply typed lambda calculus. It includes sections on Deduction and the untyped lambda calculus. Unfortunately I have not had time to adjust the presentation to properly serve the purposes of the Summer School. Nevertheless I hope that it may prove useful as a metatheoretical counterpart to the foundational rst part.
5 citations