Comodels and Effects in Mathematical Operational Semantics

In the mid-nineties, Turi and Plotkin gave an elegant categorical treatment of denotational and operational semantics for process algebra-like languages, proving compositionality and adequacy by defining operational semantics as a distributive law of syntax over behaviour. However, its applications to stateful or effectful languages, incorporating (co)models of a countable Lawvere theory, have been elusive so far. We make some progress towards a coalgebraic treatment of such languages, proposing a congruence format related to the evaluation-in-context paradigm. We formalise the denotational semantics in suitable Kleisli categories, and prove adequacy and compositionality of the semantic theory under this congruence format.

[1]  Bartek Klin.  Bialgebraic Methods in Structural Operational Semantics: Invited Talk , 2007, Electron. Notes Theor. Comput. Sci..

[2]  Robin Milner,et al.  Theories for the Global Ubiquitous Computer , 2004, FoSSaCS.

[3]  Daniele Turi,et al.  Categorical Modelling of Structural Operational Rules: Case Studies , 1997, Category Theory and Computer Science.

[4]  Ian Stark,et al.  Free-Algebra Models for the pi-Calculus , 2005, FoSSaCS.

[5]  John Power,et al.  Discrete Lawvere theories and computational effects , 2006, Theor. Comput. Sci..

[6]  John Power,et al.  A Coalgebraic Foundation for Linear Time Semantics , 1999, CTCS.

[7]  Ana Sokolova,et al.  Generic Trace Semantics via Coinduction , 2007, Log. Methods Comput. Sci..

[8]  Luís Monteiro.  A Coalgebraic Characterization of Behaviours in the Linear Time - Branching Time Spectrum , 2008, WADT.

[9]  A. Kock.  Strong functors and monoidal monads , 1972 .

[10]  Gordon D. Plotkin,et al.  Adequacy for Algebraic Effects , 2001, FoSSaCS.

[11]  Gordon D. Plotkin,et al.  Combining effects: Sum and tensor , 2006, Theor. Comput. Sci..

[12]  John Power,et al.  Category theory for operational semantics , 2004, Theor. Comput. Sci..

[13]  Gordon D. Plotkin,et al.  Towards a mathematical operational semantics , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[14]  Martin Wirsing,et al.  Extraction of Structured Programs from Specification Proofs , 1999, WADT.

[15]  J. Adámek,et al.  Locally Presentable and Accessible Categories: Bibliography , 1994 .

[16]  Jirí Adámek.  Recursive Data Types in Algebraically omega-Complete Categories , 1995, Inf. Comput..

[17]  E. Riehl.  Basic concepts of enriched category theory , 2014 .

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

[19]  John Power,et al.  From Comodels to Coalgebras: State and Arrays , 2004, CMCS.

[20]  D. Turi,et al.  Functional Operational Semantics and its Denotational Dual , 1996 .

[21]  John Power,et al.  Semantics for Local Computational Effects , 2006, MFPS.

[22]  Gordon D. Plotkin,et al.  Notions of Computation Determine Monads , 2002, FoSSaCS.

[23]  Patricia Johann,et al.  A Generic Operational Metatheory for Algebraic Effects , 2010, 2010 25th Annual IEEE Symposium on Logic in Computer Science.

[24]  Dirk Pattinson,et al.  Towards Effects in Mathematical Operational Semantics , 2011, MFPS.

[25]  Sam Staton.  Completeness for Algebraic Theories of Local State , 2010, FoSSaCS.

[26]  Gordon D. Plotkin,et al.  Tensors of Comodels and Models for Operational Semantics , 2008, MFPS.

[27]  John Power,et al.  Countable Lawvere Theories and Computational Effects , 2006, MFCSIT.