G. Barthe. The relevance of proof-irrelevance. In Proc. of the 25th Int. Colloq. on Automata, Languages and Programming, LNCS 1443, 1998. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Monadic Type Systems: Pure Type Systems for Impure Settings - Barthe, Hatcliff, Thiemann (1998) (1 citation) Self-citation (Barthe) (Correct)
....(iii) S is cubic if (a) S = S [ S , b) v ; c 2 S , c) for every (s 1 ; s 2 ; s 3 ) 2 R, s 2 2 S , s 3 2 S . Our method to prove strong normalization is to define a reduction preserving translation from cubic MTSs to the Calculus of Constructions with Fixpoints C fix [1, 5]. The translation could be generalized to specifications that do not comply with requirement (a) of the above definition; in that case the target language would be a Logical Pure Type System with Fixpoints at the level. However, we would need to prove such systems to be strongly normalizing in ....
....specifications that do not comply with requirement (a) of the above definition; in that case the target language would be a Logical Pure Type System with Fixpoints at the level. However, we would need to prove such systems to be strongly normalizing in order to conclude a method is suggested in [5] but is still in need to be carried out in detail. Following standard practice, we write S j= SN(fi ) iff every legal term in S is fi strongly normalizing. Theorem 13 If S is a cubic specification, then S j= SN(fi ) Proof For the sake of simplicity, we consider a slightly modified syntax ....
G. Barthe. The relevance of proof-irrelevance. Manuscript, 1997.
Expanding the Cube - Barthe (1999) (1 citation) Self-citation (Barthe) (Correct)
....reduction if its underlying term rewriting system is strongly normalizing. In the second part of this paper, we solve their conjecture partially, under the extra assumption that the underlying term rewriting system is non duplicating. The proof is obtained by using ideas from [7] and modifying the model construction of the first part of the paper. Related work Much work has been devoted to extensionality in type systems so we shall only focus on systems of dependent types. 1 Throughout the paper, we shall be concerned with the extensional versions of the cube, in ....
.... cube and show that strong normalization is a modular property of the algebraic cube, provided the underlying term rewriting system is non duplicating. 4.1 The algebraic cube The algebraic cube is obtained from the cube by aggregating many sorted rewriting systems to the type systems. As in [7, 8, 10], we shall only consider first order term rewriting systems. Note however that there are other presentations of the algebraic cube based on higher order rewriting systems, see e.g. 3] Definition 15. A signature Sigma consists of a pair ( Fw;s ) w2List( s2 ) where is a set of universes ....
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G. Barthe. The relevance of proof-irrelevance. In K.G. Larsen, S. Skyum, and G. Winskel, editors, Proceedings of ICALP'98, volume 1443 of Lecture Notes in Computer Science, pages 755--768. Springer-Verlag, 1998.
Type Theory and Rewriting - BLANQUI (2001) (1 citation) (Correct)
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G. Barthe. The relevance of proof-irrelevance. In Proc. of the 25th Int. Colloq. on Automata, Languages and Programming, LNCS 1443, 1998.
Definitions by rewriting in the Calculus of Constructions - Blanqui (2003) (2 citations) (Correct)
No context found.
G. Barthe. The relevance of proof-irrelevance. In Proc. of the 25th Int. Colloq. on Automata, Languages and Programming, LNCS 1443, 1998.
Proof Irrelevance and Strict Definitions in a Logical Framework - Reed (2002) (2 citations) (Correct)
No context found.
G. Barthe. The relevance of proof-irrelevance. In S. Skyum K. Larsen and G. Winskel, editors, Proceedings of ICALP'98, LNCS, 1998.
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