Some Programming Languages Suggested by Game Models (Extended Abstract)

We consider a simple and well-known category of alternating games (also known as sequential data structures) and several categories derived from it. In each case, we present an extension of Plotkin's language FPC (or a suitable linearization thereof) which defines all computable strategies of appropriate types. The quest for such languages results in a novel selection of language primitives for state encapsulation, coroutining and backtracking.

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

[2]  Pierre-Louis Curien.  On the Symmetry of Sequentiality , 1993, MFPS.

[3]  Nicholas Wolverson,et al.  Game semantics for an object-oriented language , 2009 .

[4]  Pierre-Louis Curien,et al.  A Semantic Characterization of Full Abstraction for Typed Lambda Calculi , 1984, FOCS.

[5]  Martín Hötzel Escardó,et al.  Infinite sets that admit fast exhaustive search , 2007, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007).

[6]  AbramskySamson,et al.  Games and full completeness for multiplicative linear logic , 1994 .

[7]  Paul-André Melliès.  Comparing hierarchies of types in models of linear logic , 2004, Inf. Comput..

[8]  John Longley,et al.  Universal Types and What They are Good For , 2003 .

[9]  Samson Abramsky,et al.  Call-by-Value Games , 1997, CSL.

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

[11]  Andrew M. Pitts,et al.  Semantics and Logics of Computation: List of Contributors , 1997 .

[12]  John Longley.  Eriskay : a programming language based on game semantics , 2008 .

[13]  Martin Hyland.  Semantics and Logics of Computation: Game Semantics , 1997 .

[14]  Guy McCusker.  Games and Full Abstraction for FPC , 2000, Inf. Comput..

[15]  S. Abramsky.  Game Semantics , 1999 .

[16]  Samson Abramsky,et al.  A fully abstract game semantics for general references , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[17]  James Laird.  A Categorical Semantics of Higher Order Store , 2002, CTCS.

[18]  Matthias Felleisen,et al.  Observable sequentiality and full abstraction , 1992, POPL '92.

[19]  James Laird.  Locally Boolean domains , 2005, Theor. Comput. Sci..

[20]  Radha Jagadeesan,et al.  Games and Full Completeness for Multiplicative Linear Logic , 1994, J. Symb. Log..

[21]  Gordon Plotkin,et al.  Logical Full Abstraction and PCF , 2000 .

[22]  John Longley.  The sequentially realizable functionals , 2002, Ann. Pure Appl. Log..

[23]  Russell Harmer,et al.  Categorical Combinatorics for Innocent Strategies , 2007, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007).