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FOSSACS
2010
Springer

CIA Structures and the Semantics of Recursion

9 years 2 months ago
CIA Structures and the Semantics of Recursion
Final coalgebras for a functor serve as semantic domains for state based systems of various types. For example, formal languages, streams, nonwell-founded sets and behaviors of CCS processes form final coalgebras. We present a uniform account of the semantics of recursive definitions in final coalgebras by combining two ideas: (1) final coalgebras are also initial completely iterative algebras (cia); (2) additional algebraic operations on final coalgebras may be presented in terms of a distributive law λ. We first show that a distributive law leads to new extended cia structures on the final coalgebra. Then we formalize recursive function definitions involving operations given by λ as recursive program schemes for λ, and we prove that unique solutions exist in the extended cias. We illustrate our results by the four concrete final coalgebras mentioned above, e. g., a finite stream circuit defines a unique stream function and we show how to define new process combinators ...
Stefan Milius, Lawrence S. Moss, Daniel Schwencke
Added 18 May 2010
Updated 18 May 2010
Type Conference
Year 2010
Where FOSSACS
Authors Stefan Milius, Lawrence S. Moss, Daniel Schwencke
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