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Representing WP Semantics in Isabelle/ZF
 TPHOLs: The 12th International Conference on Theorem Proving in HigherOrder Logics, number 1690 in lncs
, 1999
"... . We present a shallow embedding of the weakest precondition semantics for a program renement language. We use the Isabelle/ZF theorem prover for untyped set theory, and statements in our renement language are represented as set transformers. Our representation is signi cant in making use of the ..."
Abstract

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. We present a shallow embedding of the weakest precondition semantics for a program renement language. We use the Isabelle/ZF theorem prover for untyped set theory, and statements in our renement language are represented as set transformers. Our representation is signi cant in making use of the expressiveness of Isabelle/ZF's set theory to represent states as dependentlytyped functions from variable names to their values. This lets us give a uniform treatment of statements such as variable assignment, framed specication statements, local blocks, and parameterisation. ZF set theory requires set comprehensions to be explicitly bounded. This requirement propagates to the denitions of statements in our renement language, which have operands for the state type. We reduce the syntactic burden of repeatedly writing the state type by using Isabelle's metalogic to dene a lifted set transformer language which implicitly passes the state type to statements. Weakest precondi...
Representation and Validation of Mechanically Generated Proofs Final Report
"... Introduction The goal of this project was to demonstrate the feasibility of the independent and trusted validation of the proofs generated by existing theorem provers. Our intention was to design, implement and formally verify a proof checking program for HOL [5] generated proofs. A proof checker ..."
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Introduction The goal of this project was to demonstrate the feasibility of the independent and trusted validation of the proofs generated by existing theorem provers. Our intention was to design, implement and formally verify a proof checking program for HOL [5] generated proofs. A proof checker can be much simpler than a full theorem prover such as HOL as it is only concerned with checking existing proofs rather than searching for or generating them. Our work has clearly demonstrated the feasibility of this approach. In particular, the main achievements of the project are as follows. ffl We have developed a computer representation suitable for communicating large, formal, machine generated proofs. ffl We have modified the HOL system to allow primitive inference proofs to be recorded in the above format. ffl We have formalised, within the HOL theorem proving system, theories of higherorder logic, Hilb
Checking Proofs from Linked Tools
"... We describe a Cambridge project (now completed) which demonstrated the feasibility of producing independent, veri ed proof checkers for the HOL theorem proving system 1. We then brie y overview a joint Cambridge University/Hong Kong Baptist University proof checking project which is about to commenc ..."
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We describe a Cambridge project (now completed) which demonstrated the feasibility of producing independent, veri ed proof checkers for the HOL theorem proving system 1. We then brie y overview a joint Cambridge University/Hong Kong Baptist University proof checking project which is about to commence. It aims to extend the HOL work to other logics and proof tools. We discuss how this relates to the formal linking of tools and theories. 1 Independent Proof Checking There is a growing interest in the use of formal methods in the validation of computer systems. Correctness proofs tend to be very long and shallow in the sense that they are not mathematically interesting. As such they can only realistically be carried out with any degree of con dence using machine assistance. A wide variety of di erent theorem proving systems incorporating various degrees of automation have been developed to this end, embodying various underlying logics. However, theorem provers are themselves just computer systems which can themselves contain errors. In many correctnesscritical applications (eg safety