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A Certified Compiler for an Imperative Language
, 1998
"... This paper describes the process of mechanically certifying a compiler with respect to the semantic specification of the source and target languages. The proofs are performed in type theory using the Coq system. These proofs introduce specific theoretical tools: fragmentation theorems and general in ..."
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Cited by 9 (2 self)
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This paper describes the process of mechanically certifying a compiler with respect to the semantic specification of the source and target languages. The proofs are performed in type theory using the Coq system. These proofs introduce specific theoretical tools: fragmentation theorems and general induction principles.
The HahnBanach Theorem in Type Theory
, 1997
"... We give the basic deønitions for pointfree functional analysis and present constructive proofs of the Alaoglu and HahnBanach theorems in the setting of formal topology. 1 Introduction We present the basic concepts and deønitions needed in a pointfree approach to functional analysis via formal topol ..."
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Cited by 7 (0 self)
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We give the basic deønitions for pointfree functional analysis and present constructive proofs of the Alaoglu and HahnBanach theorems in the setting of formal topology. 1 Introduction We present the basic concepts and deønitions needed in a pointfree approach to functional analysis via formal topology. Our main results are the constructive proofs of localic formulations of the Alaoglu and HellyHahnBanach 1 theorems. Earlier pointfree formulations of the HahnBanach theorem, in a topostheoretic setting, were presented by Mulvey and Pelletier (1987,1991) and by Vermeulen (1986). A constructive proof based on points was given by Bishop (1967). In the formulation of his proof, the norm of the linear functional is preserved to an arbitrary degree by the extension and a counterexample shows that the norm, in general, is not preserved exactly. As usual in pointfree topology, our guideline is to deøne the objects under analysis as formal points of a suitable formal space. After this has...
A realizability interpretation of MartinLöf's type theory
"... In this paper we present a simple argument for normalization of the fragment of MartinLöf's type theory that contains the natural numbers, dependent function types and the first universe. We do this by building a realizability model of this theory which directly reflects that terms and types are ge ..."
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Cited by 7 (1 self)
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In this paper we present a simple argument for normalization of the fragment of MartinLöf's type theory that contains the natural numbers, dependent function types and the first universe. We do this by building a realizability model of this theory which directly reflects that terms and types are generated simultaneously.
A normalization proof for MartinLöf's type theory
, 1996
"... The theory we will be concerned with in this paper is MartinLöf's polymorphic type theory with intensional equality and the universe of small sets. We will give a different proof of normalization for this theory. ..."
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The theory we will be concerned with in this paper is MartinLöf's polymorphic type theory with intensional equality and the universe of small sets. We will give a different proof of normalization for this theory.