Economic OutlookVolume 46, Issue 1 p. 28-31 Feature articleFree to Read Normalising money growth is reducing inflation risks First published: 29 January 2022 https://doi.org/10.1111/1468-0319.12602AboutPDF ToolsRequest permissionExport citationAdd favoritesTrack citation ShareShare Give accessShare full text full-text accessPlease review our Terms and Conditions of Use check box below share ver...

We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting ⊥ is strongly normalising provided all its ‘stratified approximations’ are. From this we derive a general normalisation theorem for applied typed λ-calculi: If all constants have a total value, then all typeable terms are strongly nor...

In this paper we present a strongly normalising cut-elimination procedure for classical logic. This procedure adapts Gentzen’s standard cut-reductions, but is less restrictive than previous strongly normalising cut-elimination procedures. In comparison, for example, with works by Dragalin and Danos et al., our procedure requires no special annotations on formulae and allows cut-rules to pass ov...

We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting ⊥ is strongly normalising provided all its ‘stratified approximations’ are. From this we derive a general normalisation theorem for applied typed λ-calculi: If all constants have a total value, then all typeable terms are strongly nor...

We propose a method for realising the proofs of Intuitionistic Zermelo-Fraenkel set theory (IZF) by strongly normalising λ-terms. This method relies on the introduction of a Curry-style type theory extended with specific subtyping principles, which is then used as a low-level language to interpret IZF via a representation of sets as pointed graphs inspired by Aczel’s hyperset theory. As a conse...

Inspired by the Curry-Howard correspondence, we study normalisation procedures in the depth-bounded intuitionistic sequent calculus of Hudelmaier (1988) for the implicational case, thus strengthening existing approaches to Cut-admissibility. We decorate proofs with proofterms and introduce various term-reduction systems representing proof transformations. In contrast to previous papers which ga...

We provide a characterisation of strongly normalising terms of the λμ-calculus by means of a type system with intersection and product types. The presence of the latter and a restricted use of the type ω enable us to represent the particular notion of continuation used in the literature for the definition of semantics for the λμ-calculus. This makes it possible to lift the well-known characteri...