Hyland, John Martin Elliott
Overview
Works:  6 works in 26 publications in 2 languages and 421 library holdings 

Genres:  Conference papers and proceedings Periodicals 
Roles:  Editor, Author, Opponent, 956 
Classifications:  QA9.A1, 511.3 
Publication Timeline
.
Most widely held works by
John Martin Elliott Hyland
Logic Colloquium 76 : proceedings of a conference held in Oxford in July 1976 by
Logic Colloquium. [1976. Oxford.](
Book
)
20 editions published between 1976 and 1977 in 3 languages and held by 283 WorldCat member libraries worldwide
20 editions published between 1976 and 1977 in 3 languages and held by 283 WorldCat member libraries worldwide
Recursion theory on the countable functionals by
John Martin Elliott Hyland(
Book
)
2 editions published in 1975 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1975 in English and held by 2 WorldCat member libraries worldwide
On Forcing and Classical Realizability by
Lionel Rieg(
)
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
This thesis focuses on the computational interpretation of Cohen's forcing through the classical CurryHoward correspondence, using the tools of classical realizability. In a first part, we start by a general introduction to classical realizability in secondorder arithmetic (PA2). We cover the description of the Krivine Abstract Machine (KAM), the construction of the realizability models, the realizers for arithmetic and the main two computational topics: specification and witness extraction. To illustrate the flexibility of this approach, we show that it can be effortlessly adapted to several extensions such as new instructions in the KAM or primitive datatypes like natural, rational and real numbers. These various works are formalized in the Coq proof assistant.In the second part, we redesign this framework in a higherorder setting and compare it to PA2.This change is necessary to fully express the forcing transformation, but it also allows us to uniformize the theory and integrate all datatypes. We present forcing in classical realizability, initially due to Krivine, and extend it to generic filters whenever the forcing conditions form a datatype. We can then see forcing as a program transformation adding a memory cell with its access primitives. Our aim is to find more efficient realizers rather than independence results, which are the common use of forcing techniques. The methodology is illustrated on the example of Herbrand's theorem, the proof by forcing of which gives a much more efficient program than the usual proof. Furthermore, we can recover the natural algorithm that one can write to solve the underlying computational problem if we use a datatype as forcing poset
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
This thesis focuses on the computational interpretation of Cohen's forcing through the classical CurryHoward correspondence, using the tools of classical realizability. In a first part, we start by a general introduction to classical realizability in secondorder arithmetic (PA2). We cover the description of the Krivine Abstract Machine (KAM), the construction of the realizability models, the realizers for arithmetic and the main two computational topics: specification and witness extraction. To illustrate the flexibility of this approach, we show that it can be effortlessly adapted to several extensions such as new instructions in the KAM or primitive datatypes like natural, rational and real numbers. These various works are formalized in the Coq proof assistant.In the second part, we redesign this framework in a higherorder setting and compare it to PA2.This change is necessary to fully express the forcing transformation, but it also allows us to uniformize the theory and integrate all datatypes. We present forcing in classical realizability, initially due to Krivine, and extend it to generic filters whenever the forcing conditions form a datatype. We can then see forcing as a program transformation adding a memory cell with its access primitives. Our aim is to find more efficient realizers rather than independence results, which are the common use of forcing techniques. The methodology is illustrated on the example of Herbrand's theorem, the proof by forcing of which gives a much more efficient program than the usual proof. Furthermore, we can recover the natural algorithm that one can write to solve the underlying computational problem if we use a datatype as forcing poset
Provability, Computability and Reflection by
Lev Dmitrievich Beklemishev(
Book
)
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
Provability, Computability and Reflection
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
Provability, Computability and Reflection
Logic Colloquium 1976 : proceedings of a conference held in Oxford in July 1976(
Book
)
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
Studies in Logic and the Foundations of Mathematics, 87 Provability, Computability and Reflection. Symposium Proceedings by
R. O Gandy(
)
1 edition published in 1977 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 1977 in English and held by 0 WorldCat member libraries worldwide
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Gandy, R. O. Author Editor
 Mostowski, Andrzej (19131975)
 Association for Symbolic Logic
 Rieg, Lionel (1986....). Author
 Miquel, Alexandre Opponent Thesis advisor
 Hyland, M.
 University of Oxford
 Laboratoire de l'informatique du parallélisme (Lyon)
 École normale supérieure de Lyon Degree grantor
 Régnier, Laurent Opponent
Associated Subjects