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A Universal Innocent Game Model for the Böhm Tree Lambda Theory [chapter]

Andrew D. Ker, Hanno Nickau, C. -H. Luke Ong
1999 Lecture Notes in Computer Science  
We present a game model of the untyped λ-calculus, with equational theory equal to the Böhm tree λ-theory B, which is universal (i.e. every element of the model is definable by some term).  ...  We build on our earlier work, which uses the methods of innocent game semantics to develop a universal model inducing the maximal consistent sensible theory H * .  ...  This paper answers that question by constructing a universal game model for the Böhm tree lambda-theory.  ... 
doi:10.1007/3-540-48168-0_29 fatcat:ugf73gheyzcqdbf3vptytftgbe

Game Semantics and Normalization by Evaluation [chapter]

Pierre Clairambault, Peter Dybjer
2015 Lecture Notes in Computer Science  
We use the bijective correspondence between innocent well-bracketed strategies and PCF Böhm trees, and show how operations on PCF Böhm trees, such as composition, can be computed lazily and simply by nbe  ...  As an illustration, we give a Haskell program computing the application of innocent strategies.  ...  The first author acknowledges the support of French ANR Project RAPIDO, ANR-14-CE25-0007.  ... 
doi:10.1007/978-3-662-46678-0_4 fatcat:r4x2bi7cqngqbplmifgehweq54

Adapting innocent game models for the Böhm tree λ-theory

Andrew D. Ker, Hanno Nickau, C.-H.Luke Ong
2003 Theoretical Computer Science  
We present a game model of the untyped -calculus, with equational theory equal to the B ohm tree -theory B, which is universal (i.e. every element of the model is deÿnable by some term).  ...  We build on our earlier work, which uses the methods of innocent game semantics to develop a universal model inducing the maximal consistent sensible theory H * .  ...  This paper answers that question by constructing a universal game model for the B ohm tree -theory.  ... 
doi:10.1016/s0304-3975(02)00849-6 fatcat:nxbgcuruujhypkf2visykun3lq

Designs, Disputes and Strategies [chapter]

Claudia Faggian, Martin Hyland
2002 Lecture Notes in Computer Science  
Important progresses in logic are leading to interactive and dynamical models. Geometry of Interaction and Games Semantics are two major examples.  ...  A design can be described as the skeleton of a sequent calculus derivation, where we do not manipulate formulas, but their location (the address where the formula is stored).  ...  In particular, one can define a type (a game, a behaviour) in an internal way, that is without setting special rules for each type: Definition 6.2 (Behaviours / Games) A game G on the arena <> is a set  ... 
doi:10.1007/3-540-45793-3_30 fatcat:dixoqfearje6fo756leiztgjhi

On Berry's conjectures about the stable order in PCF

Fritz Müller, Luke Ong
2012 Logical Methods in Computer Science  
And we restrict the syntax to "game terms", with a graphical representation.  ...  : If a is less than b in the stable order of the model, for finite a and b, then there are normal form terms A and B with the semantics a, resp. b, such that A is less than B in the syntactic order."  ...  I thank the anonymous referees for their valuable suggestions.  ... 
doi:10.2168/lmcs-8(4:7)2012 fatcat:ykhrphlbn5dwnjabmvsdgdiyz4

Game semantics for first-order logic

Olivier Laurent, Samson Abramsky
2010 Logical Methods in Computer Science  
We use a Church style extension of Parigot's lambda-mu-calculus to represent proofs of first-order classical logic.  ...  We refine HO/N game semantics with an additional notion of pointer (mu-pointers) and extend it to first-order classical logic with completeness results.  ...  I also thank the anonymous referees for their useful suggestions.  ... 
doi:10.2168/lmcs-6(4:3)2010 fatcat:wrl5xva6ynhcpgypaea6y5lf4i

Page 74 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
Luke) A universal innocent game model for the Bohm tree lambda theory. (English summary) (see 2002b:68003) Kfoury, Assaf J. A linearization of the lambda-calculus and consequences.  ...  (see 2002h:03004) Spreen, Dieter A new model construction for the polymorphic lambda calculus.  ... 

Page 78 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
Luke) Innocent game models of untyped /-calculus. (English summary) 2003b:03012 Kerth, Rainer On the construction of stable models of untyped /-calculus.  ...  (English summary) 2003h:03023 Miquel, Alexandre A model for impredicative type systems, universes, intersection types and subtyping.  ... 

Page 1901 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
Luke) A universal innocent game model for the Bohm tree lambda theory. (English summary) (see 2002b:68003) Kfoury, Assaf J. A linearization of the lambda-calculus and consequences.  ...  (English summary) 2002d:68065 Sittampalam, Ganesh see de Moor, Oege, 2002h:68082 Spreen, Dieter A new model construction for the polymorphic lambda calculus.  ... 

Page 1473 of Mathematical Reviews Vol. , Issue Author Index [page]

Mathematical Reviews  
Luke (with Ker, Andrew D.; Nickau, Hanno) A universal innocent game model for the Bohm tree lambda theory. (English summary) Computer science logic (Madrid, 1999), 405-419, Lecture Notes in Comput.  ...  Evolving games and essential nets for affine polymorphism. (English summary) Typed lambda calculi and applications (Krakéw, 2001), 360-375, Lecture Notes in Comput.  ... 

This Week's Finds in Mathematical Physics (1-50) [article]

John C. Baez
2022 arXiv   pre-print
(I already know the cover page looks weird).  ...  These issues focus on quantum gravity, topological quantum field theory, knot theory, and applications of n-categories to these subjects.  ...  We introduce a path-dependent hamiltonian representation (the path representation) for SU (2) with fermions in 3 + 1 dimensions.  ... 
arXiv:2101.04168v3 fatcat:kh5eurusrjevbkttpuq24p3s4q

Physics of brain-mind interaction

John C. Eccles
1990 Behavioral and Brain Sciences  
Penrose has produced an accessible, Information-packed compilation over a wide-ranging selection of difficult topics. One  ...  as Einstein, Schrodinger, de Broglie, Dirac, Bohm, and Bell have all expressed the need for a new theory).  ...  Chess is a finite game, so there is an algorithm "for" either checkmate or draw: the brute force algorithm that draws the entire decision tree for chess and works backwards from the last nodes.  ... 
doi:10.1017/s0140525x00080778 fatcat:hsnvygzhgnckdk3wqswlr3b63y

Betting your life on an algorithm

Daniel C. Dennett
1990 Behavioral and Brain Sciences  
as Einstein, Schrodinger, de Broglie, Dirac, Bohm, and Bell have all expressed the need for a new theory).  ...  Chess is a finite game, so there is an algorithm "for" either checkmate or draw: the brute force algorithm that draws the entire decision tree for chess and works backwards from the last nodes.  ...  For a given word problem this can be done by finding a property that is present in the input, is conserved by each transformation, but is absent in the output.  ... 
doi:10.1017/s0140525x00080742 fatcat:oksxbigvojgmfnrkc73qgp3qmq

On confluence and semantic full abstraction of lambda calculus languages [article]

Fritz Müller, Universität Des Saarlandes, Universität Des Saarlandes
2016
This thesis joins my four articles: (1) Confluence of the lambda calculus with left-linear algebraic rewriting, where we show that a lambda calculus with additional algebraic term rewrite rules that are  ...  This is a model of syntactic entities.  ...  And there is the game model consisting of all denotations of (infinite) PCF-Böhm-trees, i.e. the sequential functionals.  ... 
doi:10.22028/d291-26678 fatcat:5jzj74ijbjbhhi3msy2eslcmvq

Games, Mobile Processes, and Functions

Guilhem Jaber, Davide Sangiorgi, Florin Manea, Alex Simpson
2022
We establish a tight connection between two models of the λ-calculus, namely Milner's encoding into the π-calculus (precisely, the Internal π-calculus), and operational game semantics (OGS).  ...  We do so for various LTSs: the standard LTS for π and a new "concurrent" LTS for OGS; an "output-prioritised" LTS for π and the standard alternating LTS for OGS.  ...  of Böhm Trees (or Lévy-Longo Trees).  ... 
doi:10.4230/lipics.csl.2022.25 fatcat:rsstjtqwnjatjd23h3v3h4rdoy
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