R. Pollack. Typechecking in pure type systems. In B. Nordstrom, editor, Informal proceedings of Logical Frameworks'92, pages 271--288, 1992. Home/Search Document Details and Download
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The Semi-Full Closure of Pure Type Systems - Barthe (1998) (Correct)
....the second premise of the abstraction rule, which makes it difficult to prove completeness by induction on the structure of derivations. Nevertheless several authors have proposed type checking algorithms that are sound and complete for some specific classes of PTSs. In the early 90s, R. Pollack [7, 8] introduced the class of semi full PTSs informally a PTS is semi full if it has enough rules and gave a sound and complete type checking algorithm for PTSs in that class. Unfortunately, many PTSs of interest are not semi full. Later L.S. van Benthem Jutting, J. McKinna and R. Pollack [3, 8] ....
R. Pollack. Typechecking in pure type systems. In B. Nordstrom, editor, Informal proceedings of Logical Frameworks'92, pages 271--288, 1992.
Constructions, Inductive Types and Strong Normalization - Altenkirch (1993) (Correct)
....Church terms. This is already quite close to a PTS presentation. However, there are still some differences, in particular the presentation of the rule, but the PTS presentation of the rule seems questionable anyway. 10 10 It seems that the problem with the expansion postponement property in [Pol92] are mainly caused by the way the rule is presented for PTSes. Chapter 3 Semantics and strong normalization for the core calculus We will now analyze the system semantically and establish consistency and strong normalization. For this purpose we will introduce the notion of a CC structure ....
Randy Pollack. Typechecking in pure type systems. In Workshop on Types for Proofs and Programs, Bastad, Sweden, 1992. Preliminary Proceedings.
Type-checking injective Pure Type Systems - Barthe (1998) (3 citations) (Correct)
....rule which may be applied at any moment. In order to achieve syntax directedness while maintaining essentially the same set of derivable judgements, one may want to distribute the (conversion) rule over the remaining rules of Pure Type Systems. The algorithm below, which is due to R. Pollack [15, 16], is the result of performing such a distribution there is a certain irony in coining the next definition as Pollack s algorithm, since the algorithm is called worse in [16] Definition 13 (Pollack s algorithm) ffl Weak head reduction wh is the smallest relation such that for every x 2 V and ....
.... Gamma nat M : A is given by the rules of Figure 2. A simple induction on the structure of derivations establishes soundness, i.e. nat . The problem of completeness is defined as follows. Open Problem 14 Gamma M : A ) 9A 0 2 T : Gamma nat M : A 0 A = fi A 0 As observed in [15], we have to restrict ourselves to functional Pure Type Systems, otherwise nat is not complete with respect to . The main problem in proving the completeness of nat is the second premise in the (abstraction) rule. When trying to prove the above implications by (axiom) hi nat s 1 : s 2 if ....
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R. Pollack. Typechecking in pure type systems. In B. Nordstrom, editor, Informal proceedings of Logical Frameworks'92, pages 271--288, 1992.
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