In this paper we prove that any lambda-term that is strongly normalising for beta-reduction is also strongly normalising for beta,assoc-reduction. assoc is a call-by-value rule that has been used in works by Moggi, Joachimsky, Espirito Santo and others. The result has often been justified with incomplete or incorrect proofs. Here we give one in full details.

I outline a new proof of strong normalisation for system F, by direct calculation of the size of a normalisation tree. The system F itself is used as a formulism for representing these calculations, and any reasonably sensible model of the calculus can be used to verify that the correctness of the calculations. The method works for a variety of calculi, and seems reasonably general. Discussion ...

Objectives To examine the effect of patients’ causal attributions of common somatic symptoms on recognition by general practitioners of cases of depression and anxiety and to test the hypothesis that normalising attributions make recognition less likely. Design Cross sectional survey. Setting One general practice of eight doctors in Bristol. Subjects 305 general practice attenders. Main outcome...

We present a strongly normalising and confluent term rewrite system which describes addition, subtraction, and multiplication of positive and negative integers represented in base 10. We prove a general theorem giving an easily checkable syntactic condition on term rewrite systems which implies strong normalisation. The rewrite system for decimal arithmetic satisfies the condition. The method i...

Poor communication is widely acknowledged as a causal factor in healthcare failures and adverse events.1Makary M.A. Daniel M. Medical error—the third leading cause of death the US.BMJ. 2016; 353: i2139Crossref PubMed Scopus (1465) Google Scholar Modern complex sociotechnical system, which effective between clinical personnel patients critical to delivery safe appropriate healthcare. At negative...

An auxiliary notion of reduction ρ on the λ-terms preserves strong normalisation if all strongly normalising terms for β are also strongly normalising for β∪ρ. We give a sufficient condition for ρ to preserve strong normalisation. As an example of application, we check easily the sufficient condition for Regnier’s σ-reduction rules and the “assoc”-reduction rule inspired by calculi with let-exp...

We present a recursive algorithm to compute a collection of normalising constants which can be used in a straightforward manner to sample a realisation from a Markov random field. Further we present important consequences of this result which renders possible tasks such as maximising Markov random fields, computing marginal distributions, exact inference for certain loss functions and computing...