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ECC, an Extended Calculus of Constructions
, 1989
"... We present a higherorder calculus ECC which can be seen as an extension of the calculus of constructions [CH88] by adding strong sum types and a fully cumulative type hierarchy. ECC turns out to be rather expressive so that mathematical theories can be abstractly described and abstract mathematics ..."
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Cited by 84 (4 self)
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We present a higherorder calculus ECC which can be seen as an extension of the calculus of constructions [CH88] by adding strong sum types and a fully cumulative type hierarchy. ECC turns out to be rather expressive so that mathematical theories can be abstractly described and abstract mathematics may be adequately formalized. It is shown that ECC is strongly normalizing and has other nice prooftheoretic properties. An !\GammaSet (realizability) model is described to show how the essential properties of the calculus can be captured settheoretically.
A Higherorder Calculus and Theory Abstraction
, 1988
"... ion Zhaohui Luo Department of Computer Science University of Edinburgh The King's Buildings Edinburgh EH9 3JZ, U.K. Abstract We present a higherorder calculus ECC which naturally combines CoquandHuet's calculus of constructions and MartinLof's type theory with universes. ECC is very expressive, b ..."
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Cited by 24 (9 self)
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ion Zhaohui Luo Department of Computer Science University of Edinburgh The King's Buildings Edinburgh EH9 3JZ, U.K. Abstract We present a higherorder calculus ECC which naturally combines CoquandHuet's calculus of constructions and MartinLof's type theory with universes. ECC is very expressive, both for structured abstract reasoning and for program specification and construction. In particular, the strong sum types together with the type universes provide a useful module mechanism for abstract description of mathematical theories and adequate formalization of abstract mathematics. This allows comprehensive structuring of interactive development of specifications, programs and proofs. After a summary of the metatheoretic properties of the calculus, an !\GammaSet (realizability) model of ECC is described to show how its essential properties can be captured settheoretically. The model construction entails the logical consistency of the calculus and gives some hints on how to adeq...
Understanding Inductive Types in Constructions
, 1993
"... In this paper we extend the Calculus of Constructions with generalized inductive types. The extension is justified by showing that the usual set theoretical model can be effectivized. It is also pointed out that the model given in a published paper for a collection of inductive types in a different ..."
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Cited by 2 (1 self)
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In this paper we extend the Calculus of Constructions with generalized inductive types. The extension is justified by showing that the usual set theoretical model can be effectivized. It is also pointed out that the model given in a published paper for a collection of inductive types in a different style is wrong. Copyright c fl1993. All rights reserved. Reproduction of all or part of this work is permitted for educational or research purposes on condition that (1) this copyright notice is included, (2) proper attribution to the author or authors is made and (3) no commercial gain is involved. Technical Reports issued by the Department of Computer Science, Manchester University, are available by anonymous ftp from m1.cs.man.ac.uk (130.88.13.4) in the directory /pub/TR. The files are stored as PostScript, in compressed form, with the report number as filename. Alternatively, reports are available by post from The Computer Library, Department of Computer Science, The University, Oxford R...