Normalization property

Abstract: We present a notion of η-long β-normal term for the typed lambda calculus with sums and prove, using Grothendieck logical relations, that every term is equivalent to one in normal form. Based on this development we give the first type-directed partial evaluator that constructs %able to construct normal forms of terms in this calculus.

Abstract: We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (ie, no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead In particular, weak call-by-value beta-reduction can be simulated by an orthogonal constructor term rewrite system in the same number of reduction steps Conversely, each reduction in an orthogonal term rewrite system can be simulated by a constant number of weak call-by-value beta-reduction steps This is relevant to implicit computational complexity, because the number of beta steps to normal form is polynomially related to the actual cost (that is, as performed on a Turing machine) of normalization, under weak call-by-value reduction Orthogonal constructor term rewrite systems and lambda-calculus are thus both polynomially related to Turing machines, taking as notion of cost their natural parameters

Abstract: Since Mellies showed that λσ (a calculus of explicit substitutions) does not preserve the strong normalization of the β-reduction, it has become a challenge to find a calculus satisfying the following properties: step-by-step simulation of the β-reduction, confluence on terms with metavariables, strong normalization of the calculus of substitutions and preservation of the strong normalization of the λ-calculus. We present here such a calculus. The main novelty of this calculus (given with de Bruijn indices) is the use of labels that represent updating functions and correspond to explicit weakening. A typed version is also presented.

Abstract: Lighting apparatus provides emergency illumination independent of power source in compact attractive configuration. A capped circular and longitudinally slotted tube (10) contains a power supply (25) and charging electronics. Cylindrical outer envelopes (12) rotatably enclosing the tube (10) each have pivotally mounted lamp shells (15) at opposing ends. A spider plate attachable canopy (11) having integrally molded apertured inner lugs (52) has an outer integrally molded arm supported overhanging portion (56), the arm (56) of substantial cross section for supporting the tube weight centrally supporting the lighting fixture. The tube (10) has a longitudinal support slot (120) receiving a rectangular support piece (57) terminating from the canopy arm (56). End caps (19, 20) enclosing tube ends each have a circumferential groove (42) for receiving guide nubs (44) are disposed in spaced apart relationship on the inner circumference of the envelopes (12).