Mathematical Synthesis of Equational Deduction Systems
Our view of computation is still evolving. The concrete theories for specific computational phenomena that are emerging encompass three aspects: specification and programming languages for describing computations, mathematical structures for modelling computations, and logics for reasoning about properties of computations. To make sense of this complexity, and also to compare and/or relate different concrete theories, meta-theories have been built. These metatheories are used for the study, formalisation, specification, prototyping, and testing of concrete theories.
- 1.Fiore, M., Hur, C.-K.: On the construction of free algebras for equational systems. In: Special issue for Automata, Languages and Programming (ICALP 2007). Theoretical Computer Science, vol. 410, pp. 1704–1729. Elsevier, Amsterdam (2009)Google Scholar
- 2.Fiore, M., Hur, C.-K.: Term equational systems and logics. In: Proceedings of the 24th Conference on the Mathematical Foundations of Programming Semantics (MFPS XXIV). Electronic Notes in Theoretical Computer Science, vol. 218, pp. 171–192. Elsevier, Amsterdam (2008)Google Scholar
- 3.Fiore, M.: Algebraic theories and equational logics. In: Invited tutorial at the 24th Conference on the Mathematical Foundations of Programming Semantics, MFPS XXIV (2008), http://www.cl.cam.ac.uk/~mpf23/
- 5.Hur, C.-K.: Categorical Equational Systems: Algebraic Models and Equational Reasoning. Forthcoming PhD thesis. Computer Laboratory, University of Cambridge (2009)Google Scholar