Algebra and Coalgebra in Computer Science: 4th International by Giorgio Bacci, Vincent Danos, Ohad Kammar (auth.), Andrea

By Giorgio Bacci, Vincent Danos, Ohad Kammar (auth.), Andrea Corradini, Bartek Klin, Corina Cîrstea (eds.)

This e-book constitutes the refereed court cases of the 4th overseas convention on Algebra and Coalgebra in laptop technological know-how, CALCO 2011, held in Winchester, united kingdom, in August/September 2011. The 21 complete papers awarded including four invited talks have been rigorously reviewed and chosen from forty-one submissions. The papers record result of theoretical paintings at the arithmetic of algebras and coalgebras, the best way those effects can aid equipment and methods for software program improvement, in addition to adventure with the move of the ensuing applied sciences into business perform. They disguise themes within the fields of summary versions and logics, really expert versions and calculi, algebraic and coalgebraic semantics, and process specification and verification. The ebook additionally contains 6 papers from the CALCO-tools Workshop, colocated with CALCO 2011 and devoted to instruments in accordance with algebraic and/or coalgebraic principles.

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Extra info for Algebra and Coalgebra in Computer Science: 4th International Conference, CALCO 2011, Winchester, UK, August 30 – September 2, 2011. Proceedings

Example text

Stream(X). will systematically produce all finite streams one by one, starting from the [] stream. Suppose now we remove the base case and obtain the program P2: stream([H|T]) :- number(H), stream(T). - stream(X). fails, since the model of P2 does not contain any instances of stream/1. The problems are two-fold: (i) the Herbrand universe does not contain infinite terms; (ii) the least Herbrand model does not allow for infinite proofs, such as the proof of stream(X); yet these concepts are commonplace in computer science, and a sound mathematical foundation exists for them in the field of hyperset theory [2].

N ≤n ≤n ≤n ≤n ≤n ≤n ≤n Fig. 2. An example of the structure of a bamboo: it consists of a stem of unbounded length from which subtrees of height at most n sprout; on the right it is shown with its stem straightened Figure 2 illustrates the definition. The definition of “bamboo” directly leads to an unfolding rule for G: in every rule we limit the recursion depth of all but one terminal to n in the same way as we did in the case of the Kleene approximation. Notice that, since V (G) = V (L) by idempotence, we do not need to ensure that each derivation tree of the unfolded grammars uniquely corresponds to a derivation tree of G.

Let us “unfold” the grammar G of (4) by augmenting the nonterminal X with a counter keeping track of the height of a derivation: 24 J. Esparza and M. Luttenberger X 1 X [1] X 2 X [2] X 3 X [3] →c →X 1 → aX 1 X 1 | bX 1 → X 2 | X [1] → aX 2 X 2 | aX [1] X → X 3 | X [2] .. 2 2 | aX X h → aX h−1 X h−1 | aX [h−2] X X [h] → X h | X [h−1] .. X [1] | bX h−1 | aX 2 h−1 X [h−2] | bX h−1 Let G[h] (G h ) be the grammar consisting of those “unfolded” rules whose left-hand side is given by one of the variables of X [h] = {X 0 , X [0] , .

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