A Category Theoretic View of Nondeterministic Recursive Program Schemes

Daniel Schwencke, Marc Herbstritt
2011 Annual Conference for Computer Science Logic  
Deterministic recursive program schemes (RPS's) have a clear category theoretic semantics presented by Ghani et al. and by Milius and Moss. Here we extend it to nondeterministic RPS's. We provide a category theoretic notion of guardedness and of solutions. Our main result is a description of the canonical greatest solution for every guarded nondeterministic RPS, thereby giving a category theoretic semantics for nondeterministic RPS's. We show how our notions and results are connected to
more » ... l work. Different semantics of RPS's have been investigated in the 1970's and 80's: for deterministic RPS's see for example Courcelle [8], Guessarian [10] and Nivat [19]; for nondeterministic RPS's we mention Boudol [7], Arnold and Nivat [4] and Poigné [20]. In Section 5 we compare our work in particular with [4] to see how we cover the classical definitions and results. A 1 http://www.tu-braunschweig.de/iti/mitarbeiter/ehemalige/schwencke C S L ' 1 1 Definition 2.5. The Kleisli category A M of a monad (M, η, µ) on a category A is given as follows: the objects of A M are the same objects as the ones of A; the morphisms of A M between X and Y are all morphisms X → M Y from A; the identity morphism on X is η X : X → M X; composition of f : X → M Y and g : Y → M Z is given by Furthermore, there is a canonical inclusion functor J : A → A M given as the identity on objects and by Jf = η Y · f : X → M Y on morphisms f : X → Y .
doi:10.4230/lipics.csl.2011.496 dblp:conf/csl/Schwencke11 fatcat:eemeg2qyybahzj5p2cx2uebusu