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Abstract: We present formalizations of constructive proofs of the Intuitionistic Ramsey Theorem and Higman's Lemma in Martin-Lof's Type Theory. We analyze the computational content of these proofs and we compare it with programs extracted out from some classical proofs. Contents 1 Introduction 2 2 The proofs 4 2.1 An inductive formulation of almost-fullness (AF ID ) : : : : : : : : : : 5 2.1.1 Intuitionistic Ramsey Theorem (IRT ID ) : : : : : : : : : : : : 7 2.1.2 Higman's Lemma (HL ID ) : : : : : : :... (Update)
Context of citations to this paper: More
.... s function is not primitive recursive [38] functional completeness of combinatorial logic [16] Tait s normalization proof for G#del s T [17] the fundamental theorem of arithmetic [40] a constructive version of Ramsey s theorem [15], and a semantical analysis of...
...S, K and I. ffl Daniel Fridlender presented formal proofs of Higman s lemma and of an intuitionistic version of Ramsey s theorem. [8]. ffl Peter Dybjer and Thierry Coquand formalized a normalization proof for intuitionistic propositional logic using glueing. 1 See [10]...
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Type Theory and Programming - Coquand, Nordström, Smith, von Sydow (1994) (Correct)
Higman's Lemma in Type Theory - Fridlender (1997) (Correct)
A user's guide to ALF - Altenkirch, Gaspes, Nordström, von.. (1994) (Correct)
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0.1: An intuitionistic proof of Kruskal's Theorem - Veldman (2000) (Correct)
0.1: Refined Program Extraction from Classical Proofs - Berger, Buchholz.. (2000) (Correct)
0.1: A proof of Higman's lemma by structural induction - Coquand, Fridlender (1993) (Correct)
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4: American Mathematical Monthly (context) - Erdos, Rado et al. - 1952
4: Formal Aspects of Computing (context) - Dybjer - 1994
4: Pattern matching with dependent types (context) - Coquand - 1992
BibTeX entry: (Update)
Daniel Fridlender. Ramsey's theorem in type theory. Licentiate Thesis, Chalmers University of Technology and University of G#teborg, Sweden, October 1993. http://citeseer.ist.psu.edu/fridlender93ramseys.html More
@mastersthesis{ fridlender93ramseys,
author = "Daniel Fridlender",
title = "Ramsey's Theorem in Type Theory",
address = "Sweden",
year = "1993",
url = "citeseer.ist.psu.edu/fridlender93ramseys.html" }
Citations (may not include all citations):79 Pattern-matching with dependent types (context) - Coquand - 1992
46 Oxford University Press (context) - Dummett, Intuitionism - 1977
41 Notes on Constructive Mathematics (context) - Martin-Lof - 1968
29 A short description of Another Logical Framework (context) - Augustsson, Coquand et al. - 1990
23 The new Implementation of ALF (context) - Magnusson - 1992
21 A semantics of evidence for classical arithmetic (context) - Coquand - 1991 ACM DBLP
21 Programming in MartinL of's Type Theory (context) - Nordstrom, Petersson et al. - 1990
7 Well Quasi-Ordered Sets (context) - Richman, Stolzenberg - 1993
7 Ramsey's theorem and the pigeonhole principle in intuitionis.. (context) - Veldman, Bezem - 1992
1 Effectivit'e de calculs polynomiaux (context) - Lejeune-Jalabert - 1985
1 Fifth annual IEEE symposium on Logic in Computer Science (context) - Murthy, Russell et al. - 1990
1 Programming Methodology Group's report (context) - Nordstrom, Recursion - 1988
1 From ALF to LML (context) - von Sydow - 1993
Documents on the same site (http://www.cs.chalmers.se/~frito/): More
A proof of Higman's lemma by structural induction - Coquand, Fridlender (1993) (Correct)
Higman's Lemma in Type Theory - Fridlender (1997) (Correct)
A lambda calculus model of Martin-Löf's theory of types with.. - Fridlender (1997) (Correct)
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