scholarly journals Proof-term synthesis on dependent-type systems via explicit substitutions

2001 ◽  
Vol 266 (1-2) ◽  
pp. 407-440 ◽  
Author(s):  
César Muñoz
2004 ◽  
Vol 14 (1) ◽  
pp. 1-2
Author(s):  
GILLES BARTHE ◽  
PETER DYBJEN ◽  
PETER THIEMANN

Modern programming languages rely on advanced type systems that detect errors at compile-time. While the benefits of type systems have long been recognized, there are some areas where the standard systems in programming languages are not expressive enough. Language designers usually trade expressiveness for decidability of the type system. Some interesting programs will always be rejected (despite their semantical soundness) or be assigned uninformative types.


Author(s):  
DANIEL FRIDLENDER ◽  
MIGUEL PAGANO

AbstractWe introduce a new formulation of pure type systems (PTSs) with explicit substitution and de Bruijn indices and formally prove some of its meta-theory. Using techniques based on Normalisation by Evaluation, we prove that untyped conversion can be typed for predicative PTSs. Although this equivalence was settled by Siles and Herbelin for the conventional presentation of PTSs, we strongly conjecture that our proof method can also be applied to PTSs with η.


2020 ◽  
Vol 4 (POPL) ◽  
pp. 1-29 ◽  
Author(s):  
Stephen Chang ◽  
Michael Ballantyne ◽  
Milo Turner ◽  
William J. Bowman
Keyword(s):  

2001 ◽  
Vol 11 (4) ◽  
pp. 437-437
Author(s):  
Gilles Barthe ◽  
Peter Dybjer ◽  
Peter Thiemann

Modern programming languages rely on advanced type systems that detect errors at compile-time. While the benefits of type systems have long been recognized, there are some areas where the standard systems in programming languages are not expressive enough. Language designers usually trade expressiveness for decidability of the type system. Some interesting programs will always be rejected (despite their semantical soundness) or be assigned uninformative types.There are several remedies to this situation. Dependent type systems, which allow the formation of types that explicitly depend on other types or values, are one of the most promising approaches. These systems are well-investigated from a theoretical point of view by logicians and type theorists. For example, dependent types are used in proof assistants to implement various logics and there are sophisticated proof editors for developing programs in a dependently typed language.To the present day, the impact of these developments on practical programming has been small, partially because of the level of sophistication of these systems and of their type checkers. Only recently, there have been efforts to integrate dependent systems into intermediate languages in compilers and programming languages. Additional uses have been identified in high-profile applications such as mobile code security, where terms of a dependently typed lambda calculus to encode safety proofs.A special issue of the Journal of Functional Programming will be devoted to the interplay between dependent type theory and programming practice. We welcome technical contributions in the field, as well as position papers that:[bull ] make researchers in programming languages aware of new developments and research directions on the theory side;[bull ] point out to theorists practical uses of advanced type systems and urge them to address theoretical problems arising in emerging applications.Authors who are concerned about the appropriateness of a topic are welcome to contact the guest editors. Manuscripts should be unpublished works and not submitted elsewhere. Revised and enhanced versions of papers published in conference proceedings that have not appeared in archival journals are eligible for submission. All submissions will be reviewed according to the usual standards of scholarship and originality.Submissions should be sent to Gilles Barthe ([email protected]), with a copy to Nasreen Ahmad ([email protected]). Submitted articles should be sent in postscript format, preferably gzipped and uuencoded. In addition, please send, as plain text, title, abstract and contact information.The submission deadline is December 1st, 2001.


2001 ◽  
Vol 11 (1) ◽  
pp. 91-129 ◽  
Author(s):  
CÉSAR MUÑOZ

We present a dependent-type system for a λ-calculus with explicit substitutions. In this system, meta-variables, as well as substitutions, are first-class objects. We show that the system enjoys properties like type uniqueness, subject reduction, soundness, confluence, and weak normalization.


2012 ◽  
Vol 76 ◽  
pp. 112-162 ◽  
Author(s):  
Vilhelm Sjöberg ◽  
Chris Casinghino ◽  
Ki Yung Ahn ◽  
Nathan Collins ◽  
Harley D. Eades III ◽  
...  
Keyword(s):  

2003 ◽  
Vol 13 (2) ◽  
pp. 261-293 ◽  
Author(s):  
GILLES BARTHE ◽  
VENANZIO CAPRETTA ◽  
OLIVIER PONS

Formalising mathematics in dependent type theory often requires to represent sets as setoids, i.e. types with an explicit equality relation. This paper surveys some possible definitions of setoids and assesses their suitability as a basis for developing mathematics. According to whether the equality relation is required to be reflexive or not we have total or partial setoid, respectively. There is only one definition of total setoid, but four different definitions of partial setoid, depending on four different notions of setoid function. We prove that one approach to partial setoids in unsuitable, and that the other approaches can be divided in two classes of equivalence. One class contains definitions of partial setoids that are equivalent to total setoids; the other class contains an inherently different definition, that has been useful in the modeling of type systems. We also provide some elements of discussion on the merits of each approach from the viewpoint of formalizing mathematics. In particular, we exhibit a difficulty with the common definition of subsetoids in the partial setoid approach.


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