From Reduction-Based to Reduction-Free Normalization

From Reduction-Based to Reduction-Free Normalization

We present a systematic construction of a reduction-free normalization function. Starting from a reduction-based normalization function, i.e., the transitive closure of a one-step reduction function, we successively subject it to refocusing (i.e., deforestation of the intermediate reduced terms), simplification (i.e., fusing auxiliary functions), refunctionalization (i.e., Church encoding), and...

Categorical Reconstruction of a Reduction Free Normalization Proof

Smoothing, Normalization, Correction and Reduction

In this paper we analyze a variety of standard techniques used in corpus linguistics and examine a number of issues relating to incorrect usage, the computational infeasibility of various approaches, and the inevitable sampling errors. We motivate much of the paper with applications from information retrieval but the techniques discussed and introduced are far more widely applicable, and some a...

Taylor Expansion, β-Reduction and Normalization

We introduce a notion of reduction on resource vectors, i.e. infinite linear combinations of resource λ-terms. The latter form the multilinear fragment of the differential λ-calculus introduced by Ehrhard and Regnier, and resource vectors are the target of the Taylor expansion of λ-terms. We show that the reduction of resource vectors contains the image, through Taylor expansion, of β-reduction...

Relative Normalization in Orthogonal Expression Reduction Systems

We study reductions in orthogonal (left-linear and non-ambiguous) Expression Reduction Systems, a formalism for Term Rewriting Systems with bound variables and substitutions. To generalise the normalization theory of Huet and Lévy, we introduce the notion of with respect to a set of reductions or a set of terms so that each existing notion of neededness can be given by specifying or . We impose...