Exactly estimating functionals and strong normalization

HOAS and strong normalization

We develop some Higher-Order Abstract Syntax (HOAS) concepts and proof principles as a collection of definitions and propositions on top of the original syntax with bindings. Our approach brings together hassle-free (i.e., bindingand substitution-free) manipulation of the objects on the one hand, and inductive reasoning about the same objects on the other. We present our approach by providing a...

Linear Logic and Strong Normalization

Strong normalization for linear logic requires elaborated rewriting techniques. In this paper we give a new presentation of MELL proof nets, without any commutative cut-elimination rule. We show how this feature induces a compact and simple proof of strong normalization, via reducibility candidates. It is the first proof of strong normalization for MELL which does not rely on any form of conflu...

Lazy Strong Normalization

Among all the reduction strategies for the untyped λ-calculus, the so called lazy β-evaluation is of particular interest due to its large applicability to functional programming languages (e.g. Haskell [3]). This strategy reduces only redexes not inside a lambda abstraction. The lazy strongly βnormalizing terms are the λ-terms that don’t have infinite lazy β-reduction sequences. This paper pres...

Strong Normalization with Singleton

Strong Normalization Proofs

We deene an equivalent variant LK sp of the Gentzen sequent calculus LK. In LK sp weakenings or contractions can be performed in parallel. This modiication allows us to interpret a symmetrical system of mix elimination rules E LKsp by a nite rewriting system; the termination of this rewriting system can be machine checked. We give also a self-contained strong normalization proof by structural i...