Some characteristics of strong innermost normalization

Some Applications of Strong Product

Let G and H be graphs. The strong product GH of graphs G and H is the graph with vertex set V(G)V(H) and u=(u1, v1) is adjacent with v= (u2, v2) whenever (v1 = v2 and u1 is adjacent with u2) or (u1 = u2 and v1 is adjacent with v2) or (u1 is adjacent with u2 and v1 is adjacent with v2). In this paper, we first collect the earlier results about strong product and then we present applications of ...

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

Short Proofs of Strong Normalization

This paper presents simple, syntactic strong normalization proofs for the simply-typed λ-calculus and the polymorphic λ-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The normalization proofs use translations of terms and types of λ→,∧,∨,⊥ to terms and types of λ→ and from F∀,∃,→,∧,∨,⊥ to F∀,→.

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...