![]() Normalisation function to be given within a simply typed metatheory. A new complete characterization of -strong normalization is given, both in the classical and in the lazy -calculus. Semantics of the typed lambda calculus that allows the definition of the It is called strongly normalizable (SN) iff all reductions starting at X are finite. Technical development includes an algebraic treatment of the syntax and Definition A3.1 (Normalizable terms) A typed or untyped CL-or -term X is called normalizable or weakly normalizable or WN with respect to a given reduction concept, iff it reduces to a normal form. It is the canonical and simplest example of a typed lambda calculus. Im having trouble understanding how to reduce lambda terms to normal form. Inspired by a recent graphical formalism for lambda-calculus based on linear logic technology, we introduce an untyped structural lambda-calculus. In the second part of the paper theĪnalysis is refined further by considering intensional Kripke relations (in theįorm of Artin glueing) and shown to provide a function for normalising terms,Ĭasting normalisation by evaluation in the context of categorical glueing. The simply typed lambda calculus ( ), a form of type theory, is a typed interpretation of the lambda calculus with only one type constructor ( ) that builds function types. Shows how it can be adapted to unify definability and normalisation, yieldingĪn extensional normalisation result. I plan to add a section on normalisation by evaluation for -equality in a future version of these notes. ![]() Lambda definability result of Jung and Tiuryn via Kripke logical relations and ![]() Download a PDF of the paper titled Semantic Analysis of Normalisation by Evaluation for Typed Lambda Calculus, by Marcelo Fiore Download PDF Abstract: This paper studies normalisation by evaluation for typed lambda calculus fromĪ categorical and algebraic viewpoint.
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