Binding in Nominal Equational Logic

Many formal systems, particularly in computer science, may be expressed through equations modulated by assertions regarding the 'freshness of names'. It is the presence of binding operators that make such structure non-trivial. Clouston and Pitts's Nominal Equational Logic presented a formalism for this style of reasoning in which support for name binding was implicit. This paper extends this logic to offer explicit support for binding and then demonstrates that such an extension does not in fact add expressivity.

[1]  Andrew M. Pitts,et al.  A New Approach to Abstract Syntax with Variable Binding , 2002, Formal Aspects of Computing.

[2]  Peter Burmeister,et al.  Partial Algebras — An Introductory Survey , 1993 .

[3]  Carl A. Gunter.  Semantics of programming languages: structures and techniques , 1993, Choice Reviews Online.

[4]  James Cheney.  Toward a general theory of names: binding and scope , 2005, MERLIN '05.

[5]  Murdoch James Gabbay,et al.  Nominal (Universal) Algebra: Equational Logic with Names and Binding , 2009, J. Log. Comput..

[6]  Andrew M. Pitts.  Nominal system T , 2010, POPL '10.

[7]  Christian Urban,et al.  Nominal unification , 2004, Theor. Comput. Sci..

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

[9]  Andrew M. Pitts,et al.  Nominal Equational Logic , 2007, Electron. Notes Theor. Comput. Sci..

[10]  Riccardo Pucella,et al.  SIGACT news logic column 14 , 2005, SIGA.

[11]  Andrew M. Pitts,et al.  A First Order Theory of Names and Binding , 2001 .

[12]  Sam Staton,et al.  A Congruence Rule Format for Name-Passing Process Calculi from Mathematical Structural Operational Semantics , 2006, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06).

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

[14]  Joseph A. Goguen,et al.  An Oxford survey of order sorted algebra , 1994, Mathematical Structures in Computer Science.

[15]  Christian Urban,et al.  A Head-to-Head Comparison of de Bruijn Indices and Names , 2007, Electron. Notes Theor. Comput. Sci..

[16]  Gordon D. Plotkin,et al.  Abstract syntax and variable binding , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[17]  Harold F. Schiffman.  The Nominal System , 1999 .

[18]  Ranald Alexander Clouston.  Equational logic for names and binders , 2010 .

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

[20]  Jozef Gruska.  Foundations of Computing , 1997 .