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Page 8491 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
coalgebras (8-21); Thorsten Altenkirch and Thierry Coquand, A finitary subsystem of the polymorphic A-calculus (22-28); Martin Berger, Kohei Honda and Nobuko Yoshida, Sequentiality and the z-calculus (  ...  types, and explicit substitutions (121 135); Gilles Dowek, The stratified foundations as a theory modulo (136-150); Andrzej Filinski, Normalization by evaluation for the computational lambda-calculus  ... 

Sequence Types for the π-calculus

Sergio Maffeis
2005 Electronical Notes in Theoretical Computer Science  
We introduce channel sequence types to study finitary polymorphism in the context of mobile processes modelled in the π-calculus.  ...  We study finitary polymorphism for the π-calculus [13], a fundamental formalism to reason about concurrent and mobile processes.  ...  This work was inspired by a discussion with Steffen van Bakel on polyadic-synchronisation types for the e π-calculus. I am grateful to the anonymous referees for helpful comments and suggestions.  ... 
doi:10.1016/j.entcs.2005.06.012 fatcat:2ttzaqstljhabbjqelbf6bwehi

Parameter-free polymorphic types

Klaus Aehlig
2008 Annals of Pure and Applied Logic  
Consider the following restriction of the polymorphically typed lambda calculus ("System F"). All quantifications are parameter free.  ...  This fragment can be locally proven terminating in a system of intuitionistic second-order arithmetic known to have strength of finitely iterated inductive definitions.  ...  Altenkirch and Coquand proposed a "finitary subsystem of the polymorphic lambda calculus" [2] that characterises precisely the functions provably recursive in Peano Arithmetic.  ... 
doi:10.1016/j.apal.2008.06.002 fatcat:6urbuzeq4nednpa65hv2hxelga

Inheritance as implicit coercion

Val Breazu-Tannen, Thierry Coquand, Carl A. Gunter, Andre Scedrov
1991 Information and Computation  
Many of the results of this paper were obtained during Coquand's visit to the University of Pennsylvania, partially sponsored by Scedrov's funds from the Natural Sciences Association.  ...  Scedrov's research was partially supported by NSF Grant CCR-87-05596, by ONR Grant N00014-88-K-0635, and by the 1987 Young Faculty Award from the Natural Sciences Association of the University of Pennsylvania  ...  The method we propose proceeds first with a translation of Fun into an extended polymorphic lambda calculus with recursive types.  ... 
doi:10.1016/0890-5401(91)90055-7 fatcat:qlzvfdnfpfhgxggyfkdbpxorta


Solomon Feferman
1995 Erkenntnis: An International Journal of Scientific Philosophy  
It begins with a general logic of "partial terms", continues with partial combinatory and lambda calculi, and concludes with an expressively rich theory of partial functions and polymorphic types, where  ...  termination of functional programs can be established in a natural way.  ...  The partial lambda calculus. We now turn to a version of the lambda calculus in LPT.  ... 
doi:10.1007/bf01135376 fatcat:vwmphjirsfglfh65voamsyuira

Page 75 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
(English summary) (see 2002c:03005) Altenkirch, Thorsten (with Coquand, Thierry) A finitary subsystem of the polymorphic A- calculus.  ...  lambda proof of the P-W theorem.  ... 

Page 1899 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
., (2002c:68012) Altenkirch, Thorsten (with Coquand, Thierry) A finitary subsystem of the polymorphic A- calculus.  ...  (English summary) 2002i:68026 Di Gianantonio, Pietro Game semantics for the pure lazy A-calculus.  ... 

Subject index volumes 1–200

1999 Theoretical Computer Science  
-, 858 Girard-Reynolds calculus, 13 12 polymorphic lambda calculus, 1122 second-order polymorphic h-calculus, 1664 Girard's linear logic, 2148, 2188, 2203 model of polymorphism, 1294 proof nets  ...  polymorphic lambda calculus, 1552 result, 2321 strong NP-completeness, 249, 3306 NP-complete problems, 249 polymorphic typing, 2957 polynomial-time reducibilities, 1638 Prolog fixpoint semantics  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Around finite second-order coherence spaces [article]

Lê Thành Dũng Nguyên
2019 arXiv   pre-print
We exhibit such a finite semantics for a polymorphic purely linear language: more precisely, we show that in Girard's semantics of second-order linear logic using coherence spaces and normal functors,  ...  the denotations of multiplicative-additive formulas are finite.  ...  deg(F ) is the supremum of a finite subset of N and is therefore finite.  ... 
arXiv:1902.00196v3 fatcat:vyvzyqyuhvc7heye3pjewgbide

Domain Theory and the Logic of Observable Properties [article]

Samson Abramsky
2011 arXiv   pre-print
Moreover, the underlying logic is geometric, which can be computationally interpreted as the logic of observable properties---i.e. properties which can be determined to hold of a process on the basis of  ...  Given a denotational description of a computational situation in our meta-language, we can turn the handle to obtain a logic for that situation.  ...  Finally, we consider some extensions and variations of the theory. The Lazy Lambda-Calculus We begin with the syntax, which is standard.  ... 
arXiv:1112.0347v1 fatcat:dtnbwwmcrret5lgh2yusnmtq4m

Proof Theory in Computer Science (Dagstuhl Seminar 01411)

Reinhard Kahle, Peter Schröder-Heister, Robert F. Stärk
A finitary subsystem of polymorphic λ-calculus by Thierry Coquand, University of Göteborg (joint work with Thorsten Altenkirch) Polymorphic λ-calculus, or system F, has a simple interpretation where types  ...  We present a natural subsystem of system F (no nested products), which has a finitary interpretation. This is essentially the previous interpretation above but over a suitable Kripke models.  ...  We reprove the result for a variant ΛJ of λ-calculus which allows to define the interpolants by a single recursion on the build-up of normal terms of ΛJ: It has a generalized application r ρ→σ (s ρ , z  ... 
doi:10.4230/dagsemrep.322 fatcat:uilk6uqqbjdqth5hbtjfcccogq

Real interpolation with logarithmic functors

WD Evans, Bohumír Opic, Luboš Pick
2002 Journal of Inequalities and Applications  
We give the first sub-polynomial upper bound in a type system with impredicative polymorphism; adding restrictions on quantifiers yields a characterization of logarithmic space, for which extensional completeness  ...  Queries in the λ-calculus Hillebrand's PhD thesis [18] is a junction point between implicit and descriptive complexity.  ...  Semantic Evaluation, Intersection Types and Complexity of Simply Typed Lambda Calculus.  ... 
doi:10.1155/s1025583402000127 fatcat:jveevfbrk5bdpap5cbz3s5dwx4

Teaching machines to understand data science code by semantic enrichment of dataflow graphs [article]

Evan Patterson, Ioana Baldini, Aleksandra Mojsilovic, Kush R. Varshney
2019 arXiv   pre-print
The semantic enrichment algorithm is undergirded by a new ontology language for modeling computer programs and a new ontology about data science, written in this language.  ...  Throughout the paper, we focus on code written by data scientists and we locate our work within a larger movement towards collaborative, open, and reproducible science.  ...  Church's invention of the lambda calculus.  ... 
arXiv:1807.05691v2 fatcat:cmgrc2ku3jbabctmhngxtknunu


2016 Bulletin of Symbolic Logic  
When one attempts to develop the model theory of a logic generalizing first order logic, one runs into the problem that model theoretic properties of the logic like compactness, Löwenheim-Skolem Theorem  ...  In set theory, a reflection principle says that a proposition true in the universe holds already in a smaller set.  ...  We prove that for some sequence of tautologies ϕn the proof steps and the proof sizes in  ... 
doi:10.1017/bsl.2016.22 fatcat:cm4a5yyvgfajzm4qvlszviblni

Induction and inductive definitions in fragments of second order arithmetic

Klaus Aehlig
2005 Journal of Symbolic Logic (JSL)  
The underlying language allows only up to n + 1 nested second order quantifications and those are in such a way. that no second order variable occurs free in the scope of another second order quantifier  ...  The amount of induction on arithmetical formulae only affects the arithmetical consequences of these theories, whereas adding induction for arbitrary formulae increases the strength by one inductive definition  ...  Acknowledgements The author wishes to gratefully acknowledge the anonymous referee for the many very helpful comments on an earlier draft of this article.  ... 
doi:10.2178/jsl/1129642116 fatcat:qs6hrkuxlvc2hamlvy6foqdwfa
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