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Abstract: We describe an implementation of a pointfree proof of the Alaoglu and the HahnBanach theorems in Type Theory. The proofs described here are formalisations of the proofs presented in "The Hahn-Banach Theorem in Type Theory" [4]. The implementation was partially developed simultaneously with [4] and it was a help in the development of the informal proofs. 1 Introduction We present a machine assisted formalisation of pointfree topology in Martin-Lof's type theory. The continuum and the basic... (Update)
Context of citations to this paper: More
.... theorem in an implementation of the intensional version of Type Theory with one universe and nitary inductive de nitions (see Cederquist 1997). 2 Preliminaries We recall here the de nition of formal topology introduced by Per Martin L#f and Giovanni Sambin (see Sambin...
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BibTeX entry: (Update)
Cederquist, J. (1997). A Machine Assisted Proof of the Hahn-Banach Theorem, submitted for publication. http://citeseer.ist.psu.edu/cederquist97machine.html More
@misc{ cederquist97machine,
author = "J. Cederquist",
title = "A Machine Assisted Proof of the Hahn-Banach Theorem",
text = "Cederquist, J. (1997). A Machine Assisted Proof of the Hahn-Banach Theorem,
submitted for publication.",
year = "1997",
url = "citeseer.ist.psu.edu/cederquist97machine.html" }
Citations (may not include all citations):191 Functional analysis (context) - Rudin - 1991
113 Computer Science Laboratory (context) - Owre, Shankar et al. - 1993
109 Programming in Martin-Lof's Type Theory (context) - Nordstrom, Petersson et al. - 1990
99 Foundations of Constructive Analysis (context) - Bishop - 1967
65 The Implementation of ALF - a Proof Editor based on Martin-L.. - Magnusson - 1995
35 Stone Spaces (context) - Johnstone - 1982
23 An algorithm for type-checking dependent types - Coquand - 1996
14 Intuitionistic formal spaces -- a first communication (context) - Sambin - 1987
13 A globalization of the Hahn-Banach theorem (context) - Mulvey, Pelletier - 1991
10 Sheaves in Geometry and Logic : A First Introduction to Topo.. (context) - MacLane, Moerdijk - 1992
8 Formal Spaces (context) - Fourman, Grayson - 1982
5 The Hahn-Banach Theorem in Type Theory - Cederquist, Coquand et al. - 1997
5 A plea for weaker frameworks (context) - de Bruijn - 1991
4 A constructive proof of the Heine-Borel covering theorem for.. - Cederquist, Negri - 1996
4 Constructive Techniques in Functional Analysis (context) - Vermeulen - 1986
3 The continuum as a formal space (context) - Negri, Soravia - 1996
3 A model of intensional Martin-Lof type theory in which unici.. (context) - Hofmann - 1993
2 A memorandum on the constructive axioms of linear order (context) - von Plato - 1995
2 Lamda calculi with types (context) - Barendregt - 1992
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