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ECC, an extended calculus of constructions

Z. Luo
[1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science  
We present a higher-order 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.  ...  It is shown that ECC is strongly normalizing and has other nice prooftheoretic properties. An !?  ...  e ort to consider models of hierarchy.  ... 
doi:10.1109/lics.1989.39193 dblp:conf/lics/Luo89 fatcat:n5lk5ii5uzadjoleevfveoi5yu

Page 2260 of Mathematical Reviews Vol. , Issue 94d [page]

1994 Mathematical Reviews  
The extended calculus of constructions, ECC; 2. Inductive types in a first-order calculus; 3. ECC with inductive types; 4. An w-Set model for ECC with inductive types: 4.1.  ...  Summary: “Luo’s extended calculus of constructions (ECC) is a higher-order functional calculus based on Coquand’s and Huet’s calculus of constructions, but has in addition strong sums and a 68 COMPUTER  ... 

A higher-order calculus and theory abstraction

Zhaohui Luo
1991 Information and Computation  
We present a higher-order calculus ECC which naturally combines Coquand-Huet's calculus of constructions and Martin-LX's type theory with universes.  ...  After a summary of the meta-theoretic properties of the calculus, an w-Set (realizability) model of ECC is described to show how its essential properties can be captured set-theoretically.  ...  In this paper, we present and study an extended cakulus of constructions, ECC, which can be seen as a natural combination of Coquand-Huet's calculus of constructions (Coquand and Huet, 1988) and Martin-Lof's  ... 
doi:10.1016/0890-5401(91)90062-7 fatcat:k63z6crl65fgdinttyhh3hopkm

The Extended Calculus of Constructions (ECC) with inductive types

Christian-Emil Ore
1992 Information and Computation  
THE EXTENDED CALCULUS OF CONSTRUCTIONS, ECC The extended calculus of constructions (ECC) is based in Coquand and Huet's theory of constructions, a higher order types functional calculus (Coquand, 1986a  ...  The theme for this paper is to extend ECC with inductive types on the predicative levels. Hence it is necessary to extend the calculus with an explicit disjoint sum operator.  ...  The lemma is proved by induction on the construction of dTvM,?. In the following L, denotes the required bound for an operator 4. 1.  ... 
doi:10.1016/0890-5401(92)90031-a fatcat:gtq4stqyxbhbjcutyc6admw6vm

A Calculus of Communicating Systems with Label Passing

Uffe Engberg, Mogens Nielsen
1986 DAIMI Report Series  
Milner's Calculus of Communicating Systems (CCS) is extended with a mechanism for label passing - as an attempt to remedy some of the shortcomings of CCS w.r.t. dynamic change of agent interconnections  ...  In the extended calculus, restriction is viewed formally as a binder, and the calculus allows dynamic change of scope (of label) in connection with communication.  ...  Acknowledgement We would like to thank Paola Quaglia, the editors, and two anonymous referees for valuable comments on various drafts of this note.  ... 
doi:10.7146/dpb.v15i208.7559 fatcat:ptzsoqiq2nh7bnmwjhgis3wbfi

Page 3954 of Mathematical Reviews Vol. , Issue 92g [page]

1992 Mathematical Reviews  
In fact, ECC extends the calculus of constructions to so-called Z-types (or, strong sum  ...  The author presents a higher-order calculus ECC which combines the ideas of T. Coquand and G.  ... 

The Rho Cube [chapter]

Horatiu Cirstea, Claude Kirchner, Luigi Liquori
2001 Lecture Notes in Computer Science  
As a consequence, this brings matching and rewriting as the first class concepts of the Rho-versions of the Logical Framework (LF) of Harper-Honsell-Plotkin, and of the Calculus of Constructions (CC) of  ...  Due to the matching capabilities of the calculus, the type systems use only one abstraction mechanism and therefore gives an original answer to the identification of the standard "λ" and "Π" abstractors  ...  We would also like to thank all the members of the ELAN group for their comments and interactions on the topics of the Rho Calculus.  ... 
doi:10.1007/3-540-45315-6_11 fatcat:6y7dqwly7fe6lg65rcw6hyrh7y

Construction and deduction methods for the formal development of software [chapter]

F. W. von Henke, A. Dold, H. Rueß, D. Schwier, M. Strecker
1995 Lecture Notes in Computer Science  
In this paper we present an approach towards a framework based on the type theory ECC (Extended Calculus of Constructions) in which speci cations, programs and operators for modular development by stepwise  ...  For formalizing transformations that require syntactic manipulation of objects, we introduce a two-level system combining a meta-level and an object level and show how to express and reason about transformations  ...  Our approach is based on a type theory, the Extended Calculus of Constructions (ECC) Luo90, Luo91a] , as the unifying logical foundation.  ... 
doi:10.1007/bfb0015465 fatcat:pp3j3vctxnazfiwagzermlxfq4

Computation and Reasoning

R. L. Crole
1994 Computer journal  
The author compares and contrasts the ECC with other well known type theories, in particular showing how the ECC extends the Calculus of Constructions and why the ECC may be considered as an extension  ...  The book Computation and Reasoning is a comprehensive account of (the meta-theory and application of) one particular type theory, the Extended Calculus of Constructions (ECC), developed by Chaohui Luo  ... 
doi:10.1093/comjnl/37.6.552-a fatcat:meirvrwy3jholjsuuduz6kk3ca

Information Retrieval in a Coq Proof Library Using Type Isomorphisms [chapter]

David Delahaye
2000 Lecture Notes in Computer Science  
We introduce a theory which is a generalization of the axiomatization for the simply typed λ-calculus (associated with Closed Cartesian Categories) to an Extended Calculus of Constructions with a more  ...  Thus, we see how we must adapt this theory for goq and we dene an approximation of the contextual part of this theory, which is implemented in a decision procedure.  ...  Reduction (→ ) and conversion ( ) are dened as usual from the following one-step rules: ECCE can be seen as an extension of the Extended Calculus of Constructions (ECC) [14] with unit and extensionality  ... 
doi:10.1007/3-540-44557-9_8 fatcat:fdnzk5waijfzhkkpqzpaf5drkm

An Intuitionistic Set-theoretical Model of the Extended Calculus of Constructions [article]

Masahiro Sato
2015 arXiv   pre-print
Werner's set-theoretical model is one of the most intuitive models of ECC. It combines a functional view of predicative universes with a collapsed view of the impredicative sort Prop.  ...  However this model of Prop is so coarse that the principle of excluded middle holds.  ...  ECC (the Extended Calculus of Constructions) extends CC with a hierarchy of predicative sorts Type i and strong sums Σx : A.B.  ... 
arXiv:1412.2235v3 fatcat:4wlrkk25hzdrdgxisx2u6euecu

A calculus of higher order communicating systems

B. Thomsen
1989 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '89  
The calculus is an extension of CCS [MilSO] in the sense that ail the constructions of CCS are included or may be derived from more fundamental constructs and most of the mathematical framework of CCS  ...  Milner in (MilSO], CCS has its limitations when one wants to describe unboundedly expanding systems as e.g. an unbounded number of procedure invocations in an imperative concurrent programming language  ...  Boudol and for making me aware of the fact that my first definition of procedures in the semantics of P described dynamic binding.  ... 
doi:10.1145/75277.75290 dblp:conf/popl/Thomsen89 fatcat:dg7zmllo5ffvzhlar3hl2cosiu

Page 1108 of Mathematical Reviews Vol. , Issue 96b [page]

1996 Mathematical Reviews  
The underlying theory of types is presented in two forms. In Chapters Two through Eight, it is presented directly as the ex- tended calculus of constructions (ECC).  ...  This work uses the well-known impredicative facilities of the calculus of constructions to construct an internal higher-order intuitionistic logic based on the principle of propositions-as-types (also  ... 

The Implicit Calculus of Constructions Extending Pure Type Systems with an Intersection Type Binder and Subtyping [chapter]

Alexandre Miquel
2001 Lecture Notes in Computer Science  
In this paper, we introduce a new type system, the Implicit Calculus of Constructions, which is a Curry-style variant of the Calculus of Constructions that we extend by adding an intersection type bindercalled  ...  We also illustrate the specificities of this calculus by revisitting the impredicative encodings of the Calculus of Constructions, and we show that their translation into the implicit calculus helps to  ...  the impredicative sorts, and (Type i ) i>0 the usual predicative universe hierarchy of the Extended Calculus of Constructions [9] .  ... 
doi:10.1007/3-540-45413-6_27 fatcat:2xpmxsobwnfkfepe4n6bwuzwfq

Deliverables: a categorical approach to program development in type theory [chapter]

James McKinna, Rod Burstall
1993 Lecture Notes in Computer Science  
This thesis considers the problem of program correctness within a rich theory of dependent types, the Extended Calculus of Constructions (ECC).  ...  In the presence of enough extra structure, the interpretation extends to the whole of ECC. The wheel turns full circle.  ...  Luo's Extended Calculus of Constructions, ECC [58, 59] , is sketched as the basic framework of types and terms.  ... 
doi:10.1007/3-540-57182-5_3 fatcat:hlgxycetmnft7emuo4534yfpr4
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