Comparing Higher-Order Encodings in Logical Frameworks and Tile Logic

Abstract In recent years, logical frameworks and tile logic have been separately proposed by our research groups, respectively in Udine and in Pisa, as suitable metalanguages with higher-order features for encoding and studying nominal calculi. This paper discusses the main features of the two approaches, tracing differences and analogies on the basis of two case studies: late π-calculus and lazy simply typed Λ-calculus.

[1]  Roberto Bruni,et al.  Executable Tile Specifications for Process Calculi , 1999, FASE.

[2]  Roberto Bruni,et al.  Bisimilarity Congruences for Open Terms and Term Graphs via Tile Logic , 2000, CONCUR.

[3]  G. Plotkin,et al.  Proof, language, and interaction: essays in honour of Robin Milner , 2000 .

[4]  Frank Pfenning,et al.  Higher-order abstract syntax , 1988, PLDI '88.

[5]  José Meseguer,et al.  Mapping tile logic into rewriting logic , 1997, WADT.

[6]  Robert Pollack.  The theory of LEGO , 1995 .

[7]  J. Meseguer,et al.  IMPLEMENTING TILE SYSTEMS : SOME EXAMPLES FROM PROCESS CALCULIR , 1998 .

[8]  H. Barendregt.  Lambda Calculus kHV its Hovels , 1984 .

[9]  Fabio Gadducci,et al.  The tile model , 2000, Proof, Language, and Interaction.

[10]  R. Bruni.  Tile Logic for Synchronized Rewriting of Concurrent Systems , 1999 .

[11]  Roberto Bruni,et al.  Internal strategies in a rewriting implementation of tile systems , 1998, WRLA.

[12]  Fabio Gadducci,et al.  Comparing cospan-spans and tiles via a Hoare-style process calculus , 2001, Electron. Notes Theor. Comput. Sci..

[13]  M. LenisaUniversit.  Final Semantics for the -calculus , 1998 .

[14]  Roberto Bruni,et al.  Cartesian closed double categories, their lambda-notation, and the pi-calculus , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[15]  C.-H. Luke Ong,et al.  Full Abstraction in the Lazy Lambda Calculus , 1993, Inf. Comput..

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

[17]  Robin Milner,et al.  A Calculus of Mobile Processes, II , 1992, Inf. Comput..

[18]  Marina Lenisa.  Themes in Final Semantics , 1998 .

[19]  Roberto Bruni,et al.  Symmetric monoidal and cartesian double categories as a semantic framework for tile logic , 2002, Mathematical Structures in Computer Science.

[20]  Peter Schroeder-Heister,et al.  A natural extension of natural deduction , 1984, Journal of Symbolic Logic.

[21]  José Meseguer,et al.  Rewriting as a unified model of concurrency , 1990, OOPSLA/ECOOP '90.

[22]  Julian Rathke,et al.  Towards a theory of bisimulation for local names , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[23]  Furio Honsell,et al.  pi-calculus in (Co)inductive-type theory , 2001, Theor. Comput. Sci..

[24]  P. Martin-Lof,et al.  ON THE MEANINGS OF THE LOGICAL CONSTANTS AND THE JUSTIFICATIONS OF THE LOGICAL LAWS(Logic and the Foundations of Mathematics) , 1986 .

[25]  Frank Pfenning,et al.  The Practice of Logical Frameworks , 1996, CAAP.

[26]  Furio Honsell,et al.  A framework for defining logics , 1993, JACM.

[27]  Roberto Bruni,et al.  An interactive semantics of logic programming , 2001, Theory and Practice of Logic Programming.

[28]  Robin Milner,et al.  The Polyadic π-Calculus: a Tutorial , 1993 .

[29]  Marco Pistore,et al.  Final semantics for the pi-calculus , 1998, PROCOMET.

[30]  Reiko Heckel,et al.  Compositional SOS and beyond: a coalgebraic view of open systems , 2002, Theor. Comput. Sci..