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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

Cited by 68 (10 self)
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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...
Towards a Structure Preserving Encoding of Z in HOL
, 1986
"... We present a semantic representation of the core concepts of the specification language Z in higherorder logic. Although it is a "shallow embedding" like the one presented by Bowen and Gordon, our representation preserves the structure of a Z specification and avoids expanding Z schemas. The repres ..."
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We present a semantic representation of the core concepts of the specification language Z in higherorder logic. Although it is a "shallow embedding" like the one presented by Bowen and Gordon, our representation preserves the structure of a Z specification and avoids expanding Z schemas. The representation is implemented in the higherorder logic instance of the generic theorem prover Isabelle. Its powerful parsing and prettyprinting mechanisms can convert the concrete syntax of Z schemas into their semantic representation behind the scenes. Our representation essentially conforms with the latest draft of the Z standard and may give both a clearer understanding of Z schemas and inspire the development of proof calculi for Z. 1 Introduction Implementations of proof support for Z [Spi92b, Nic95] can roughly be divided into two categories. In direct implementations, the rules of the logic are directly represented by functions of the prover's implementation language. These implementat...
Z and HOL
"... 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 ..."
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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