Abstract machines for dialogue games

The notion of abstract Boehm tree has arisen as an operationally-oriented distillation of works on game semantics, and has been investigated in two papers. This paper revisits the notion, providing more syntactic support and more examples (like call-by-value evaluation) illustrating the generality of the underlying computing device. Precise correspondences between various formulations of the evaluation mechanism of abstract Boehm trees are established.

[1]  Cheng-Shang Chang Calculus , 2020, Bicycle or Unicycle?.

[2]  G.D. Plotkin,et al.  LCF Considered as a Programming Language , 1977, Theor. Comput. Sci..

[3]  Michel Parigot,et al.  Lambda-Mu-Calculus: An Algorithmic Interpretation of Classical Natural Deduction , 1992, LPAR.

[4]  Roberto M. Amadio,et al.  Domains and lambda-calculi , 1998, Cambridge tracts in theoretical computer science.

[5]  Jean-Jacques Lévy,et al.  Full abstraction for sequential languages : The states of the art , 1983 .

[6]  Hugo Herbelin,et al.  Computing with Abstract Böhm Trees , 1998, Fuji International Symposium on Functional and Logic Programming.

[7]  Pierre-Louis Curien,et al.  Sequential Algorithms on Concrete Data Structures , 1982, Theor. Comput. Sci..

[8]  Thierry Coquand,et al.  A semantics of evidence for classical arithmetic , 1995, Journal of Symbolic Logic.

[9]  Jean-Yves Girard,et al.  Geometry of Interaction 1: Interpretation of System F , 1989 .

[10]  François Maurel Un cadre quantitatif pour la ludique , 2004 .

[11]  Pierre-Louis Curien Abstract Böhm trees , 1998, Math. Struct. Comput. Sci..

[12]  Walter Felscher,et al.  Dialogues, strategies, and intuitionistic provability , 1985 .

[13]  Jean-Louis Krivine,et al.  A call-by-name lambda-calculus machine , 2007, High. Order Symb. Comput..

[14]  Henk Barendregt,et al.  The Lambda Calculus: Its Syntax and Semantics , 1985 .

[15]  Patrick Lincoln,et al.  Linear logic , 1992, SIGA.

[16]  Jean-Yves Girard Locus Solum: From the Rules of Logic to the Logic of Rules , 2001, CSL.

[17]  Thierry Joly Codages, separabilite et representation de fonctions en lambda-calcul simplement type et dans d'autres systemes de types , 2000 .

[18]  de Ng Dick Bruijn,et al.  Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem , 1972 .

[19]  Nobuko Yoshida,et al.  Game-Theoretic Analysis of Call-by-Value Computation , 1997, Theor. Comput. Sci..

[20]  Hugo Herbelin Games and Weak-Head Reduction for Classical PCF , 1997, TLCA.

[21]  Pierre Boudes Desequentialization of Games and Experiments on Proof-nets , 2005 .

[22]  Hugo Herbelin,et al.  The duality of computation , 2000, ICFP '00.

[23]  Radha Jagadeesan,et al.  Full Abstraction for PCF , 1994, Inf. Comput..

[24]  Matthias Felleisen,et al.  Fully Abstract Semantics for Observably Sequential Languages , 1994, Inf. Comput..

[25]  Gordon D. Plotkin,et al.  Call-by-Name, Call-by-Value and the lambda-Calculus , 1975, Theor. Comput. Sci..

[26]  Pierre-Louis Curien Sur l'-expansion infinie , 2002 .

[27]  Pierre-Louis Curien Introduction to linear logic and ludics, part I , 2005, ArXiv.

[28]  U. Sehrt Dialogues , 2004, MMW, Munchener medizinische Wochenschrift.