Attribute Grammars and Categorical Semantics

We give a new formulation of attribute grammars (AG for short) called monoidalAGsin traced symmetric monoidal categories. Monoidal AGs subsume existing domain-theoretic, graph-theoretic and relational formulations of AGs. Using a 2-categorical aspect of monoidal AGs, we also show that every monoidal AG is equivalent to a synthesised one when the underlying category is closed, and that there is a sound and complete translation from local dependency graphs to relational AGs.

[1]  E. S. Bainbridge.  Feedback and Generalized Logic , 1976, Inf. Control..

[2]  Bruno Courcelle,et al.  Proofs of Partial Correctness for Attribute Grammars with Applications to Recursive Procedures and Logic Programming , 1988, Inf. Comput..

[3]  Z. Ésik,et al.  Iteration Theories: The Equational Logic of Iterative Processes , 1993 .

[4]  G. M. Kelly,et al.  Coherence for compact closed categories , 1980 .

[5]  Samson Abramsky,et al.  Geometry of Interaction and linear combinatory algebras , 2002, Mathematical Structures in Computer Science.

[6]  Masahito Hasegawa,et al.  Models of Sharing Graphs , 1999, Distinguished Dissertations.

[7]  John Tang Boyland,et al.  Conditional attribute grammars , 1996, TOPL.

[8]  Samson Abramsky,et al.  Retracing some paths in Process Algebra , 1996, CONCUR.

[9]  Ross Street,et al.  Traced monoidal categories , 1996 .

[10]  Henk Alblas,et al.  Attribute Grammars, Applications and Systems , 1991, Lecture Notes in Computer Science.

[11]  真人 長谷川.  Models of sharing graphs : a categorical semantics of let and letrec , 1999 .

[12]  Masahito Hasegawa,et al.  On traced monoidal closed categories , 2009, Mathematical Structures in Computer Science.

[13]  Donald E. Knuth,et al.  Semantics of context-free languages , 1968, Mathematical systems theory.

[14]  David F. Martin,et al.  An order-algebraic definition of knuthian semantics , 1979, Mathematical systems theory.

[15]  Pierre Deransart,et al.  Attribute Grammars: Definitions, Systems and Bibliography , 1988 .

[16]  Radha Jagadeesan,et al.  New foundations for the geometry of interaction , 1992, [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science.

[17]  Tom Leinster.  Higher Operads, Higher Categories , 2003 .

[18]  S. Doaitse Swierstra,et al.  Higher order attribute grammars , 1989, PLDI '89.

[19]  S. Lane.  Categories for the Working Mathematician , 1971 .

[20]  Zoltán Ésik,et al.  Fixed-Point Operations on ccc's. Part I , 1996, Theor. Comput. Sci..

[21]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[22]  Johan Jeuring,et al.  A translation from attribute grammars to catamorphisms , 1991 .

[23]  Bart Jacobs,et al.  Semantics of Grammars and Attributes via Initiality , 2007 .

[24]  Tom Leinster,et al.  Higher Operads, Higher Categories: Opetopes , 2004 .

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