By Giorgio Bacci, Vincent Danos, Ohad Kammar (auth.), Andrea Corradini, Bartek Klin, Corina Cîrstea (eds.)
This publication constitutes the refereed lawsuits of the 4th foreign convention on Algebra and Coalgebra in computing device technological know-how, CALCO 2011, held in Winchester, united kingdom, in August/September 2011. The 21 complete papers provided including four invited talks have been rigorously reviewed and chosen from forty-one submissions. The papers document result of theoretical paintings at the arithmetic of algebras and coalgebras, the way in which those effects can help equipment and strategies for software program improvement, in addition to adventure with the move of the ensuing applied sciences into business perform. They conceal themes within the fields of summary types and logics, really expert types and calculi, algebraic and coalgebraic semantics, and approach specification and verification. The publication additionally contains 6 papers from the CALCO-tools Workshop, colocated with CALCO 2011 and devoted to instruments in keeping with algebraic and/or coalgebraic principles.
Read or Download Algebra and Coalgebra in Computer Science: 4th International Conference, CALCO 2011, Winchester, UK, August 30 – September 2, 2011. Proceedings PDF
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Additional resources for Algebra and Coalgebra in Computer Science: 4th International Conference, CALCO 2011, Winchester, UK, August 30 – September 2, 2011. Proceedings
Luttenberger Theorem 3 ([EKL10]). For every i ≥ 1, there is a yield-preserving bijection between T (H [i] ) and the trees of T (G) of dimension at most i. According to this theorem, the tree above must belong to T (H  ) and indeed this is the case, as shown by the derivation tree on the right. Note that along any path from the root to a leaf the sequence of numbers in the superscripts drops atmost by one in each step. One the other hand, moving from a leaf to the root, the superscript only increases from i to i + 1 at a given node if this very node has at least a second child with superscript i.
For instance, X = X + 1 has no solution over the reals. However, if we extend the reals with a maximal element ∞ (correspondingly adapting addition and multiplication so that these operations still are monotone), we can consider ∞ a solution of this equation. We restrict ourselves to semirings with these “limit” elements. Definition 2. Given a semiring S, define the binary relation a by b :⇔ ∃d ∈ S : a + d = b. , the supremum supi∈N ai of any ω-chain a0 a1 . . t. , for any ω-chain (ai )i∈N and semiring element a: a + sup ai = sup(a + ai ) i∈N and i∈N a · sup ai = sup(a · ai ) i∈N i∈N and symmetrically in the other argument.
9, vol. 1, pp. 609– 677. : An extension of Parikh’s theorem. : Solving Systems of Polynomial Equations: A Generalization of Newton’s Method. : Principles of Program Analysis. : A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math. : Characterizing derivation trees of context-free grammars through a generalization of finite automata theory. J. Comput. Syst. Sci. 1(4), 317–322 (1967) Abstract Local Reasoning for Program Modules Thomas Dinsdale-Young, Philippa Gardner, and Mark Wheelhouse Imperial College London Extended Abstract Hoare logic () is an important tool for formally proving correctness properties of programs.
Algebra and Coalgebra in Computer Science: 4th International Conference, CALCO 2011, Winchester, UK, August 30 – September 2, 2011. Proceedings by Giorgio Bacci, Vincent Danos, Ohad Kammar (auth.), Andrea Corradini, Bartek Klin, Corina Cîrstea (eds.)