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Abstract: The Calculus of Constructions (CC) ([Coquand 1985]) is a typed lambda calculus for higher order intuitionistic logic: proofs of the higher order logic are interpreted as lambda terms and formulas as types. It is also the union of Girard's system F! ([Girard 1972]), a higher order typed lambda calculus, and a first order dependent typed lambda calculus in the style of de Bruijn's Automath ([de Bruijn 1980]) or Martin-Lof's intuitionistic theory of types ([Martin-Lof 1984]). Using the... (Update)
Context of citations to this paper: More
...way that P2 corresponds to PRED2) it is known that the formulas as types embedding is not conservative. See e.g. Berardi 1990] or [Geuvers 1995]. However, for P , that corresponds to constructive minimal first order order predicate logic, the formulas as types embedding...
.... of logics, have been studied as formal systems for theorem proving ( Coquand and Huet 1985, Nordstrom et al. 1990, Barendregt 1992, Geuvers 1995] and have also been implemented as automated theorem provers ( NUPRL 1986, COQ 1995, LEGO 1992, ALF 1994] These implementations...
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3: A framework for defining logics - Harper, Honsell et al. - 1987
2: Information and Computation (context) - Coquand, Huet - 1988
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BibTeX entry: (Update)
J.H. Geuvers, The Calculus of Constructions and Higher Order Logic, in The Curry-Howard isomorphism, ed. Ph. de Groote, Volume 8 of the "Cahiers du Centre de logique" (Universit'e catholique de Louvain), Academia, Louvain-la-Neuve (Belgium), pp. 139-191. http://citeseer.ist.psu.edu/geuvers92calculus.html More
@misc{ geuvers-calculus,
author = "J. Geuvers",
title = "The Calculus of Constructions and Higher Order Logic",
text = "J.H. Geuvers, The Calculus of Constructions and Higher Order Logic, in
The Curry-Howard isomorphism, ed. Ph. de Groote, Volume 8 of the Cahiers
du Centre de logique (Universit'e catholique de Louvain), Academia, Louvain-la-Neuve
(Belgium), pp. 139-191.",
url = "citeseer.ist.psu.edu/geuvers92calculus.html" }
Citations (may not include all citations):729 The lambda calculus: its syntax and semantics (context) - Barendregt - 1984
359 Introduction to higher order Categorical Logic (context) - Lambek, Scott - 1986
266 Information and Computation (context) - Coquand, Huet et al. - 1988
236 Intuitionistic Type Theory (context) - Martin-Lof - 1984
132 Interpr'etation fonctionelle et 'elimination des coupures da.. (context) - Girard - 1972
96 A survey of the project Automath (context) - de Bruijn - 1980
72 North-Holland (context) - Takeuti, Theory et al. - 1975
64 Metamathematical investigations of a calculus of constructio.. (context) - Coquand - 1990
56 The formulas-as-types notion of construction (context) - Howard - 1980
53 Automatic synthesis of typed-programs on term algebras Theor (context) - Bohm, Berarducci - 1985
45 Strong normalization in a typed lambda calculus with lambda .. (context) - Nederpelt - 1973
44 An analysis of Girard's paradox - Coquand - 1986
31 Inductive types and type constraints in second-order lambda .. (context) - Mendler - 1987
29 Correctness and completeness of a categorical semantics of t.. (context) - Streicher - 1988
25 A modular proof of strong normalisation for the calculus of .. (context) - Geuvers, Nederhof - 1991
24 Recursive programming with proofs (context) - Parigot - 1992
20 Tracts in Theoretical Computer Science (context) - Girard, Lafont et al. - 1989
18 Towards a mathematical analysis of the Coquand-Huet calculus.. (context) - Berardi - 1988
17 ECC: An extended Calculus of Constructions - Luo - 1989
14 Typed lambda calculi (context) - Barendregt
13 fifteen years later (context) - Girard, system et al. - 1986
12 Algorithm development in the calculus of constructions (context) - Mohring - 1986
11 Infinitely long terms of transfinite type (context) - Tait - 1965
10 ese de troisi`eme cycle, Universit (context) - Coquand, des et al. - 1985
8 The Church-Rosser property for fij-reduction (context) - Salvesen
7 Independence of the induction principle and the axiom of cho.. (context) - Streicher - 1991
6 A theory of types (context) - Martin-Lof - 1971
6 INRIA Rocquencourt - CNRS ENS Lyon (context) - Dowek, Felty et al. - 1991
6 Type checking with universes - Harper, Pollack - 1991
5 Encoding of data types in Pure Construction Calculus: a sema.. (context) - Berardi - 1991
5 Definite descriptions and excluded middle in the theory of c.. (context) - Pottinger - 1989
5 The Church-Rosser property for fij-reduction in typed lambda.. (context) - Geuvers - 1992
4 Jumelage meeting on typed lambda calculus (context) - Pollack, at - 1989
4 Jumelage meeting on typed lambda calculus (context) - Berardi, at - 1989
4 Grundlehren der mathematischen Wissenschaften (context) - Schutte, Theory - 1977
4 Jumelage meeting on typed lambda calculus (context) - Geuvers, at - 1989
3 To appear in Information and Computation (context) - Jutting, Pure et al.
3 Paulin-Mohring Inductively defined types (context) - Coquand - 1990
3 ese, Universit (context) - Paulin-Mohring, programmes et al. - 1989
2 Excluded middle without definite descriptions in the theory .. - Seldin - 1990
2 documentation and users guide (context) - of - 1989
2 Candidats de Reductibilit'e (context) - Girard's - 1990
1 The cube of typed lambda calculi (context) - Barendregt - 1992
1 A formulation of the simple theory of types J (context) - Church - 1940
1 Examples of formalised proofs in LEGO (context) - Pollack
1 vol 121 and volume (context) - Troelstra, van Dalen et al. - 1988
Documents on the same site (http://www.win.tue.nl/cs/fm/Herman.Geuvers/): More
Explicit Substitution: on the Edge of Strong Normalization - Bloo, Geuvers (1997) (Correct)
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Use and Meaning of Open Terms in Interactive Formal Problem.. - Nederpelt, al. (Correct)
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