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The Theory of LEGO  A Proof Checker for the Extended Calculus of Constructions
, 1994
"... LEGO is a computer program for interactive typechecking in the Extended Calculus of Constructions and two of its subsystems. LEGO also supports the extension of these three systems with inductive types. These type systems can be viewed as logics, and as meta languages for expressing logics, and LEGO ..."
Abstract

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LEGO is a computer program for interactive typechecking in the Extended Calculus of Constructions and two of its subsystems. LEGO also supports the extension of these three systems with inductive types. These type systems can be viewed as logics, and as meta languages for expressing logics, and LEGO is intended to be used for interactively constructing proofs in mathematical theories presented in these logics. I have developed LEGO over six years, starting from an implementation of the Calculus of Constructions by G erard Huet. LEGO has been used for problems at the limits of our abilities to do formal mathematics. In this thesis I explain some aspects of the metatheory of LEGO's type systems leading to a machinechecked proof that typechecking is decidable for all three type theories supported by LEGO, and to a verified algorithm for deciding their typing judgements, assuming only that they are normalizing. In order to do this, the theory of Pure Type Systems (PTS) is extended and f...
Z and HOL
, 1994
"... A simple `shallow' semantic embedding of the Z notation into the HOL logic is described. The Z notation is based on set theory and first order predicate logic and is typically used for humanreadable formal specification. The HOL theorem proving system supports higher order logic and is used fo ..."
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A simple `shallow' semantic embedding of the Z notation into the HOL logic is described. The Z notation is based on set theory and first order predicate logic and is typically used for humanreadable formal specification. The HOL theorem proving system supports higher order logic and is used for machinechecked verification. A wellknown case study is used as a running example. The presentation is intended to show people with some knowledge of Z how a tool such as HOL can be used to provide mechanical support for the notation, including mechanization of proofs. No specialized knowledge of HOL is assumed.
Z and HOL
, 1994
"... A simple `shallow' semantic embedding of the Z notation into the HOL logic is described. The Z notation is based on set theory and first order predicate logic. The HOL theorem proving system supports higher order logic. A wellknown case study is used as a running example. The presentation is i ..."
Abstract
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A simple `shallow' semantic embedding of the Z notation into the HOL logic is described. The Z notation is based on set theory and first order predicate logic. The HOL theorem proving system supports higher order logic. A wellknown case study is used as a running example. The presentation is intended to show people with some knowledge of Z how a tool such as HOL can be used to provide mechanical support for the notation, including mechanization of proofs. No specialized knowledge of HOL is assumed.