G. Barthe, J. Hatclioe, and M.H. S#rensen. An induction principle for Pure Type Systems. Submitted for publication, March 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....hand, the Con property is easy to prove in the n system. An interesting consequence of the property n is that it allows to obtain a direct proof of Con in the system since this is hereditary. Such proof can see in [13] Recently EP has been solved for a reduced class of normalizing PTS in [4]. The above approach can be extended to normalizing PTS since the used inductive relation is an extension of a similar one used in [14] So, in [13] we extend the method proposed in [4] in order to obtain a relation that we conjecture inductive. ....

....is hereditary. Such proof can see in [13] Recently EP has been solved for a reduced class of normalizing PTS in [4] The above approach can be extended to normalizing PTS since the used inductive relation is an extension of a similar one used in [14] So, in [13] we extend the method proposed in [4] in order to obtain a relation that we conjecture inductive. ....

G. Barthe, J. Hatcli, and M.H. Srensen. An induction principle for pure type systems. Theoretical Computer Science, 2000. Accepted for publication.

....intermediate languages. In this section, we therefore embark on dening CPS translations for traditional pure type systems. Two methods are considered: ffl the direct method which relies on a non standard induction principle, inspired from earlier work by Dowek, Huet and Werner [20] see also [9]. ffl the indirect method which relies on the close correspondence between domainfree and traditional pure type systems, see [12] This section is organized as follows. In the rst subsection, we brieAEy outline the main denitions for domain full pure type systems. In the second subsection, we ....

....induction over pairs ( Gamma; M) where Gamma is a pseudo context and M is a pseudo term, preserves typing and applies to most Pure Type Systems that appear in the literature. For the sake of conciseness, we gloss over technical details, including the denition of the order OE (to be found in [9]) and limit ourselves to an informal description of the order. Firstly, OE contains the subterm relation, dened on pairs ( Gamma; M) in the obvious way. However, this is not enough because the CPS translation cannot proceed by induction on the structure of pairs ( Gamma; M) where Gamma is a ....

[Article contains additional citation context not shown here]

G. Barthe, J. Hatclioe, and M.H. S#rensen. An induction principle for Pure Type Systems. Submitted for publication, March 1998.

....N 0 : M and A 2 W . By generation, A = fij M . We also have M = fij ( Gamma M) and hence A = fij ( Gamma M ) In addition, there exists s 0 2 S such that Gamma A : s 0 . By uniqueness of fi e j e normal forms, A = Gamma M) and hence ( Gamma M) Gamma N ) Elsewhere [5], J. Hatcliff, M.H.B. S rensen and the author strengthen this induction principle to define CPS translations and to prove Expansion Postponement for Pure Type Systems. 7 Conclusion Building up on previous work in the area, we have derived new results on the Existence and Uniqueness of Normal ....

G. Barthe, J. Hatcliff, and M.H.B. Sørensen. An induction principle for Pure Type Systems. Manuscript, 1998.

....M : s ) sort( GammajM ) s Then we use elmt( j: and sort( j: to eliminate the problematic clause in the (abstraction) rule of Pure Type Systems and obtain a sound and complete algorithm for type checking. Besides, we show that the same idea also applies to the problem of Expansion Postponement [4, 14, 16]. Contents The remaining of the paper is organized as follows: in Section 2, we provide a brief overview of Pure Type Systems. In Section 3, we present two motivating open problems, namely the completeness of Pollack s type checking algorithm and Expansion Postponement. In Section 4, we present a ....

....of nat , i.e. for the second premise in the (abstraction) rule [14, 16] In 1995, E. Poll [14] solved the r variant of the problem for normalising Pure Type Systems, i.e. for Pure Type Systems such that Gamma M : A ) M is weakly fi normalizing In 1998, J. Hatcliff, M.H.B. S rensen [4] and the author solved the R variant of the problem for a large class Pure Type Systems. In the next section, we define a new set of rules which, in the case of injective specifications, has the same derivable judgements as and has the Expansion Postponement property for its r variant. ....

G. Barthe, J. Hatcliff, and M.H.B. Sørensen. An induction principle for Pure Type Systems. Manuscript, 1998.

....intermediate languages. In this section, we therefore embark on defining CPS translations for traditional pure type systems. Two methods are considered: ffl the direct method which relies on a non standard induction principle, inspired from earlier work by Dowek, Huet and Werner [20] see also [9]. ffl the indirect method which relies on the close correspondence between domain free and traditional pure type systems, see [12] This section is organized as follows. In the first subsection, we briefly outline the main definitions for domain full pure type systems. In the second subsection, ....

....induction over pairs ( Gamma; M ) where Gamma is a pseudo context and M is a pseudo term, preserves typing and applies to most Pure Type Systems that appear in the literature. For the sake of conciseness, we gloss over technical details, including the definition of the order OE (to be found in [9]) and limit ourselves to an informal description of the order. Firstly, OE contains the subterm relation, defined on pairs ( Gamma; M) in the obvious way. However, this is not enough because the CPS translation cannot proceed by induction on the structure of pairs ( Gamma; M ) where Gamma is a ....

[Article contains additional citation context not shown here]

G. Barthe, J. Hatcliff, and M.H. Sørensen. An induction principle for Pure Type Systems. Submitted for publication, March 1998.

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