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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 ..."
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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...
Checking Proofs from Linked Tools
, 1996
"... We describe a Cambridge project (now completed) which demonstrated the feasibility of producing independent, verified proof checkers for the HOL theorem proving system. We then briefly 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, verified proof checkers for the HOL theorem proving system. We then briefly 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.