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ECC, an extended calculus of constructions

*
[1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science
*

We present a higher-order

doi:10.1109/lics.1989.39193
dblp:conf/lics/Luo89
fatcat:n5lk5ii5uzadjoleevfveoi5yu
*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. ...##
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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 ...##
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A higher-order calculus and theory abstraction

1991
*
Information and Computation
*

We present a higher-order

doi:10.1016/0890-5401(91)90062-7
fatcat:k63z6crl65fgdinttyhh3hopkm
*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 ...##
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The Extended Calculus of Constructions (ECC) with inductive types

1992
*
Information and Computation
*

THE

doi:10.1016/0890-5401(92)90031-a
fatcat:gtq4stqyxbhbjcutyc6admw6vm
*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. ...##
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A Calculus of Communicating Systems with Label Passing

1986
*
DAIMI Report Series
*

Milner's

doi:10.7146/dpb.v15i208.7559
fatcat:ptzsoqiq2nh7bnmwjhgis3wbfi
*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. ...##
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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. ...##
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The Rho Cube
[chapter]

2001
*
Lecture Notes in Computer Science
*

As a consequence, this brings matching and rewriting as the first class concepts

doi:10.1007/3-540-45315-6_11
fatcat:6y7dqwly7fe6lg65rcw6hyrh7y
*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*. ...##
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Construction and deduction methods for the formal development of software
[chapter]

1995
*
Lecture Notes in Computer Science
*

In this paper we present

doi:10.1007/bfb0015465
fatcat:pp3j3vctxnazfiwagzermlxfq4
*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. ...##
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Computation and Reasoning

1994
*
Computer journal
*

The author compares and contrasts the

doi:10.1093/comjnl/37.6.552-a
fatcat:meirvrwy3jholjsuuduz6kk3ca
*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 ...##
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Information Retrieval in a Coq Proof Library Using Type Isomorphisms
[chapter]

2000
*
Lecture Notes in Computer Science
*

We introduce a theory which is a generalization

doi:10.1007/3-540-44557-9_8
fatcat:fdnzk5waijfzhkkpqzpaf5drkm
*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 ...##
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An Intuitionistic Set-theoretical Model of the Extended Calculus of Constructions
[article]

2015
*
arXiv
*
pre-print

Werner's set-theoretical model is one

arXiv:1412.2235v3
fatcat:4wlrkk25hzdrdgxisx2u6euecu
*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. ...##
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A calculus of higher order communicating systems

1989
*
Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '89
*

The

doi:10.1145/75277.75290
dblp:conf/popl/Thomsen89
fatcat:dg7zmllo5ffvzhlar3hl2cosiu
*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. ...##
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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 ...##
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The Implicit Calculus of Constructions Extending Pure Type Systems with an Intersection Type Binder and Subtyping
[chapter]

2001
*
Lecture Notes in Computer Science
*

In this paper, we introduce a new type system, the Implicit

doi:10.1007/3-540-45413-6_27
fatcat:2xpmxsobwnfkfepe4n6bwuzwfq
*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] . ...##
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Deliverables: a categorical approach to program development in type theory
[chapter]

1993
*
Lecture Notes in Computer Science
*

This thesis considers the problem

doi:10.1007/3-540-57182-5_3
fatcat:hlgxycetmnft7emuo4534yfpr4
*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. ...
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