By René Ahn (auth.), Peter Dybjer, Bengt Nordström, Jan Smith (eds.)
This publication provides a strictly refereed selection of revised complete papers chosen from the papers approved for the categories '94 Workshop, held less than the auspices of the ESPRIT uncomplicated examine motion 6453 varieties for Proofs and courses in Bastad, Sweden, in June 1994.
The 10 papers integrated deal with a number of elements of constructing computer-assisted proofs and courses utilizing a logical framework. kind concept and 3 logical frameworks in accordance with it are handled: ALF, Coq, and LEGO; different subject matters coated are metatheory, the Isabelle procedure, 2-calculus, facts checkers, and ZF set theory.
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Additional info for Types for Proofs and Programs: International Workshop TYPES '94 Båstad, Sweden, June 6–10, 1994 Selected Papers
Example text
Agent rules : = −→ 1. P revi =⊥ ∨ (Brief casei = (down, hop)) ∧ (θ(Γi , colorP revi ) ⊥) parent ← P rev i i N exti ← θ(Γi , colori ) colori ← colori if P revi =⊥, hop = 0 Brief casei ← (down, hop + 1) (* going down *) = ∧ (Brief casei = (down, hop)) ∧ (θ(Γi , colorP revi ) =⊥) −→ 2. (P revi ⊥) parenti ← P revi N exti ← P revi Brief casei ← (up, hop + 1) colori ← colori (* reaching a dead-end *) = ∧ (Brief casei = (up, hop)) ∧ (θ(Γi , colori ) ⊥) = −→ 3. (P revi ⊥) N exti ← θ(Γi , colori ) Brief casei ← (down, hop + 1) (* done one branch, go down for others *) = ∧ (Brief casei = (up, hop)) ∧ (θ(Γi , colori ) =⊥) −→ 4.
Corollary 2 (Propagation of k-Fairness). Let A B be the cross-over composition between the algorithms A and B. If B is k-fair under a scheduler D then A B is k-fair under D. The proof of the following Lemma is similar to the proof of the Lemma 1. Cross-Over Composition - Enforcement of Fairness under Unfair Adversary 25 Lemma 2 (Propagation of Convergence Properties). Let A B be the cross-over composition between the algorithms A and B. Let P be a predicate on the B’s configurations. If any maximal computation of B under the scheduler D reaches a configuration which satisfies the predicate P then any maximal computation of A B under D reaches a configuration which satisfies P .
Finally, the independence property is also satisfied since every agent-free execution with a legitimate initial configuration is correct. 3 Token Circulation on a Bidirectional Uniform Oriented Ring As it was shown in [5] a simple non self-stabilizing algorithm for achieving token circulation on a ring with a leader can be made easily agent-stabilizing, assuming that the agent is always installed at the leader. We will prove that this assumption can be removed. Furthermore, we propose a token circulation algorithm on a bidirectional uniform oriented ring which is agent-stabilizing.