G. Barthe and P.-A. Mellies. On the subject reduction property for algebraic type systems. In Proc. of the 10th Int. Work. on Computer Science Logic, LNCS 1258, 1996. Home/Search Document Details and Download
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A Generic Normalisation Proof for Pure Type Systems - Melliès, Werner (1996) (Correct)
....of Pure Type Systems: the terms will carry more type information than usual in the cases of abstraction and application. This approach can be seen as related to the labeled terms used in [4] However, here, we will use these labels to restrict the usual formulation of fi reduction, see [1, 3]. In section 7, we will verify that, provided the strong normalization property holds, our definition of PTS s is equivalent to the usual ones, and hence strong normalization itself is inherited by the unlabeled PTS. Definition 1 A term is described by M : x j s j app x:M:M (M; M) j x:M:M ....
G. Barthe, P.-A. Melli`es. On the Subject Reduction property for algebraic type systems. In Proceedings CSL'96, LNCS 1258, Springer Verlag, 1996.
Termination of Algebraic Type Systems: The Syntactic Approach - Barthe, van Raamsdonk (1997) (2 citations) Self-citation (Barthe) (Correct)
....based on saturated sets so it re does the termination proof for the corresponding pure type system. Unfortunately, the criterion requires the algebraic type system to have the subject reduction property, a severe restriction in the current state of knowledge. The problem is partially overcome in [9] where Barthe and Melli es use a labelled syntax to prove termination and subject reduction of algebraic type systems. However, the approach is complicated and requires to redo the proof of termination of the underlying pure type system. Using a completely different approach, van de Pol shows in ....
.... 1 : S S 0 2 : F F 0 such that for every f : s 1 Theta : Theta s n s in (S; F ) we have 2 (f) 1 (s 1 ) Theta : Theta 1 (s n ) 1 (s) in (S 0 ; R 0 ) 2. 3 Algebraic Type Systems The definition we present in this subsection is equivalent to the one given in [9] and inspired from [4, 7] An algebraic type system is a combination of a pure type system and a typed term rewriting system. In order to define the combination, we need to specify how sorts are embedded into universes. This is the purpose of the embedding axioms EA below. Definition 9. An ....
[Article contains additional citation context not shown here]
G. Barthe and P.-A. Melli`es. On the subject reduction property for algebraic type systems. Proceedings of CSL'96. To appear as LNCS, 1996.
Termination of Algebraic Type Systems: The Syntactic Approach - Barthe, van Raamsdonk (1997) (2 citations) Self-citation (Barthe) (Correct)
....saturated sets so it re does the strong normalisation proof for the corresponding pure type system. Unfortunately, the criterion requires the algebraic type system to have the subject reduction property, a severe restriction in the current state of knowledge. The problem is partially overcome in [11] where Barthe and Melli es use a labelled syntax to prove strong normalisation and subject reduction of algebraic type systems. However, the approach is complicated and requires to redo the proof of strong normalisation of the underlying pure type system. Using a completely different approach, van ....
....S 0 2 : F F 0 such that the following holds: if f : s 1 Theta : Theta s 1 s in (S; F ) then 2 (f) 1 (s 1 ) Theta : Theta 1 (s 2 ) 1 (s) in (S 0 ; R 0 ) 2. 3 Algebraic Type Systems The definition we present in this subsection is equivalent to the one given in [11] and inspired from [5, 9] An algebraic type system is a combination of a pure type system and a typed term rewriting system. In order to define the combination, we need to specify how sorts are embedded into universes. This is the purpose of embedding axioms EA below. Definition 9 An algebraic ....
[Article contains additional citation context not shown here]
G. Barthe and P-A. Melli`es. On the subject reduction property for algebraic type systems. Proceedings of CSL'96. To appear as LNCS, 1996.
An Induction Principle for Pure Type Systems - Barthe, Hatcliff, Sørensen (1998) (1 citation) Self-citation (Barthe) (Correct)
....notion of affiliated term. As mentioned in the introduction, affiliated terms provide an appealing alternative to labels. It remains to be seen whether affiliated terms may be applied advantageously to other situations where labels have been used, e.g. subject reduction of algebraic type systems [7]. ....
G. Barthe and P.-A. Melli`es. On the subject reduction property for algebraic type systems. In D. van Dalen and M. Bezem, editors, Proceedings of CSL'96, volume 1258 of Lecture Notes in Computer Science, pages 34--57. Springer-Verlag, 1997.
Type Theory and Rewriting - BLANQUI (2001) (1 citation) (Correct)
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G. Barthe and P.-A. Mellies. On the subject reduction property for algebraic type systems. In Proc. of the 10th Int. Work. on Computer Science Logic, LNCS 1258, 1996.
Definitions by rewriting in the Calculus of Constructions - Blanqui (2003) (2 citations) (Correct)
No context found.
G. Barthe and P.-A. Mellis. On the subject reduction property for algebraic type systems. In Proc. of the 10th Int. Work. on Computer Science Logic, LNCS 1258, 1996.
A Generic Normalisation Proof for Pure Type Systems.. - Paulm Dcs Ed (Correct)
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G. Barthe, P.-A. Melli`es. On the Subject Reduction property for algebraic type systems. In Proceedings CSL'96, LNCS 1258, Springer Verlag, 1996.
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