CLF: A Dependent Logical Framework for Concurrent Computations∗

We present CLF, a dependently typed logical framework with several novel features supporting concurrent computations, in particular monads and synchronous linear connectives. We illustrate its representation methodology of concurrent computations as monadic expressions via the encoding of an asynchronous π-calculus with correspondence assertions, including its dynamic semantics, safety criterion, and a type system with latent effects due to Gordon and Jeffrey. We also explain a new, general methodology for defining dependently-typed logical frameworks in the LF family. The methodology involves defining the terms of the framework directly in canonical form and greatly simplifies much of the metatheory of these frameworks, which has been notoriously difficult in the past. We have used the methodology to show that CLF has a number of key properties including decidability of type checking.

[1]  Andrew D. Gordon,et al.  Ðð Blockinøöóòò Aeóøø× Ò Ìììóööøø Blockin Blockinð Óñôùøøö Ë Blockin , 2007 .

[2]  Thomas F. Melham.  A Mechanized Theory of the Pi-Calculus in HOL , 1994, Nord. J. Comput..

[3]  Frank Pfenning,et al.  System Description: Twelf - A Meta-Logical Framework for Deductive Systems , 1999, CADE.

[4]  Frank Pfenning,et al.  A judgmental reconstruction of modal logic , 2001, Mathematical Structures in Computer Science.

[5]  Dale Miller,et al.  A multiple-conclusion meta-logic , 1994, Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science.

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

[7]  Eugenio Moggi,et al.  Notions of Computation and Monads , 1991, Inf. Comput..

[8]  Frank Pfenning,et al.  A linear logical framework , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[9]  Daniel Hirschkoff.  A Full Formalisation of pi-Calculus Theory in the Calculus of Constructions , 1997, TPHOLs.

[10]  David Walker,et al.  A Concurrent Logical Framework II: Examples and Applications , 2003 .

[11]  Frank Pfenning.  Structural Cut Elimination: I. Intuitionistic and Classical Logic , 2000, Inf. Comput..

[12]  JEAN-MARC ANDREOLI,et al.  Logic Programming with Focusing Proofs in Linear Logic , 1992, J. Log. Comput..

[13]  David J. Pym,et al.  A Relevant Analysis of Natural Deduction , 1998, J. Log. Comput..

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

[15]  D. Walker,et al.  A concurrent logical framework I: Judgments and properties , 2003 .

[16]  Dale Miller,et al.  A proof theory for generic judgments , 2005, TOCL.

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

[18]  John H. Reppy,et al.  Concurrent programming in ML , 1999 .

[19]  Simon S. Lam,et al.  A semantic model for authentication protocols , 1993, Proceedings 1993 IEEE Computer Society Symposium on Research in Security and Privacy.

[20]  Stefan Berghofer,et al.  Higher-Order Abstract Syntax with Induction in Isabelle/HOL: Formalizing the pi-Calculus and Mechanizing the Theory of Contexts , 2001, FoSSaCS.

[21]  Jawahar Chirimar,et al.  Proof theoretic approach to specification languages , 1995 .

[22]  J. Hannan,et al.  A logical framework for reasoning about logical specifications , 2004 .

[23]  David Walker,et al.  A Concurrent Logical Framework: The Propositional Fragment , 2003, TYPES.