This paper gives a purely syntactical proof, based on proof normalization techniques, of an extension of Chew's theorem. The main theorem is that a weakly compatible TRS is uniquely normalizing. Roughly speaking, the weakly compatible condition allows possibly nonlinear TRSs to have nonroot overlapping rules that return the same results. This result implies the consistency of CL-pc which is an ...

We present a typing system for the π-calculus which guarantees that every well-typed term is strongly normalizing. Our typing system is an extension of that presented in Strong normalisation in the π-calculus by Yoshida, Honda and Berger [23] and it is able to type more term than that presented there.

We investigate (co-)induction in Classical Logic under the propositions-as-types paradigm, considering propositional, second-order, and (co-)inductive types. Specifically, we introduce an extension of the Dual Calculus with a Mendler-style (co-)iterator that remains strongly normalizing under head reduction. We prove this using a non-constructive realizability argument.

In the first part of this paper, we define two resource aware typing systems for the λμ-calculus based on non-idempotent intersection and union types. The nonidempotent approach provides very simple combinatorial arguments –based on decreasing measures of type derivations– to characterize head and strongly normalizing terms. Moreover, typability provides upper bounds for the lengths of the head...

We introduce λμ→∧∨⊥, an extension of Parigot’s λμ-calculus where disjunction is taken as a primitive. The associated reduction relation, which includes the permutative conversions related to disjunction, is Church-Rosser, strongly normalizing, and such that the normal deductions satisfy the subformula property. From a computer science point of view, λμ→∧∨⊥ may be seen as the core of a typed cbn...

We study inductive characterizations of the sets of terms, the subset of strongly normalizing terms and normal forms in order to give short proofs of weak and strong normalization for the simply-typed-calculus and for an extension by sum types with permutative conversions. In contrast to the strong computability/candidate style a la Tait and Girard this proof can be formalized in primitive recu...

We define and studyco-Noetherian dimension of rings for which the injective envelopeof simple modules have finite Krull-dimension. This  is a Moritainvariant dimension that measures how far the ring is from beingco-Noetherian. The co-Noetherian dimension of certain rings,including commutative rings, are determined. It is shown that the class ${mathcal W}_n$ of rings with co-Noetherian dimension...