By Gordon Plotkin (auth.), Alexander Kurz, Marina Lenisa, Andrzej Tarlecki (eds.)
This booklet constitutes the court cases of the 3rd foreign convention on Algebra and Coalgebra in computing device technology, CALCO 2009, shaped in 2005 via becoming a member of CMCS and WADT. This 12 months the convention used to be held in Udine, Italy, September 7-10, 2009.
The 23 complete papers have been rigorously reviewed and chosen from forty two submissions. they're offered including 4 invited talks and workshop papers from the CALCO-tools Workshop. The convention used to be divided into the next classes: algebraic results and recursive equations, thought of coalgebra, coinduction, bisimulation, stone duality, video game conception, graph transformation, and software program improvement techniques.
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Extra info for Algebra and Coalgebra in Computer Science: Third International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009. Proceedings
T. the combination of effects . Acknowledgement. We thank Erwin R. Catesbeiana for finite discussions about infinite iterations. : Computational types from a logical perspective. J. Funct. Prog. : A confluent reduction for the lambda-calculus with surjective pairing and terminal object. J. Funct. Program. : Linear regions are all you need. In: Sestoft, P. ) ESOP 2006. LNCS, vol. 3924, pp. 7–21. : Deriving backtracking monad transformers. : Combining effects: Sum and tensor. Theoret. Comput. Sci.
Xkm : T Akm ) ✄ a : T B occurring in p, q, whose return value is either bound to some variable xk or propagated to the top of the term. In the latter case, we just assume k = n + 1. Now put a ˆ(z) = do x ← a πk1 z, . . , πkn z ; ret π1 z, . . , πk−1 z, x, πk+1 , . . , πn+1 z . Having defined the interpretation of all the symbols a ˆ in this manner, we obtain an equation over the original signature Σ. It can be shown by induction that the original equation p = q can by obtained from it by application of the operator λt.
We next require some auxiliary machinery for additive monads, which as a side product induces a simple normalisation-based algorithm for deciding equality over additive monads. Consider the following rewriting system, inspired by . (p : 1n ) fst(p), n n , snd(p) fst(p), snd(p) do x ← (p : T 1n ); ret n do x ← p; ret x n p p p p p fst p, q snd p, q do x ← ret p; q do x ← (do y ← p; q); r p q q[p/x] (∗) do x ←p; y ← q; r 26 S. Goncharov, L. Schr¨oder, and T. Mossakowski Basic monad laws: do x ← (do y ← p; q); r = do x ← p; y ← q; r (bind) (eta1 ) do x ← ret a; p = p[a/x] (eta2 ) do x ← p; ret x = p Extra axioms for nondeterminism: (plus∅) p+∅ =p (comm) p+q =q+p (idem) p+p=p (assoc) p + (q + r) = (p + q) + r (bind∅1 ) do x ← p; ∅ = ∅ (bind∅2 ) do x ← ∅; p = ∅ (distr1 ) do x ← p; (q + r) = do x ← p; q + do x ← p; r (distr2 ) do x ← (p + q); r = do x ← p; r + do x ← q; r Extra axioms and rules for Kleene star: (unf1 ) init x ← p in q ∗ = p + do x ← (init x ← p in q ∗ ); q (unf2 ) init x ← p in q ∗ = p + init x ← (do x ← p; q) in q ∗ (init) (ind1 ) init x ← (do y ← p; q) in r ∗ = do y ← p; init x ← q in r ∗ do x ← p; q ≤ p init x ← p in q ∗ ≤ p (ind2 ) (y ∈ / F V (r)) do x ← q; r ≤ r do x ← (init x ← p in q ∗ ); r ≤ do x ← p; r Fig.
Algebra and Coalgebra in Computer Science: Third International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009. Proceedings by Gordon Plotkin (auth.), Alexander Kurz, Marina Lenisa, Andrzej Tarlecki (eds.)