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A Simplified Suspension Calculus and its Relationship to Other Explicit Substitution Calculi
"... This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this calculus provides a cumbersome encoding of substitution compos ..."
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This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this calculus provides a cumbersome encoding of substitution
Comparing Calculi of Explicit . . .
 ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE 67 (2002)
, 2002
"... The past decade has seen an explosion of work on calculi of explicit substitutions. Numerous work has illustrated the usefulness of these calculi for practical notions like the implementation of typed functional programming languages and higher order proof assistants. Three styles of explicit substi ..."
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substitutions are treated in this paper: the and the s e which have proved useful for solving practical problems like higher order uni cation, and the suspension calculus related to the implementation of the language Prolog. We enlarge the suspension calculus with an adequate etareduction which we show
Comparing and Implementing Calculi of Explicit Substitutions with Eta Reduction
 Annals of Pure and Applied Logic
, 2005
"... The past decade has seen an explosion of work on calculi of explicit substitutions. Numerous work has illustrated the usefulness of these calculi for practical notions like the implementation of typed functional programming languages and higher order proof assistants. It has also been shown that e ..."
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Cited by 10 (8 self)
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that eta reduction is useful for adapting substitution calculi for practical problems like higher order uni cation. This paper concentrates on rewrite rules for eta reduction in three dierent styles of explicit substitution calculi: , se and the suspension calculus. Both and se when extended with eta
R.: Moduli of suspension spectra
 arXiv:math.AT/0210258, toappearinTrans. Amer. Math. Soc
"... Abstract. For a 1connected spectrum E, we study the moduli space of suspension spectra which come equipped with a weak equivalence to E. We construct a spectral sequence converging to the homotopy of the moduli space in positive degrees. In the metastable range, we get a complete homotopical classi ..."
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Cited by 5 (4 self)
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Abstract. For a 1connected spectrum E, we study the moduli space of suspension spectra which come equipped with a weak equivalence to E. We construct a spectral sequence converging to the homotopy of the moduli space in positive degrees. In the metastable range, we get a complete homotopical
Rational Homotopy Calculus of Functors by
, 2005
"... We construct a homotopy calculus of functors in the sense of Goodwillie for the categories of rational homotopy theory. More precisely, given a homotopy functor between any of the categories of differential graded vector spaces (DG), reduced differential graded vector spaces, differential graded Lie ..."
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We construct a homotopy calculus of functors in the sense of Goodwillie for the categories of rational homotopy theory. More precisely, given a homotopy functor between any of the categories of differential graded vector spaces (DG), reduced differential graded vector spaces, differential graded
SUBSEXPL: a Tool for Simulating and Comparing Explicit Substitutions Calculi
 Proc. 6th IEEE Symp
, 2006
"... Abstract In this tutorial we present the system SUBSEXPL that is used for simulating and comparing explicit substitutions calculi. This framework was developed in Ocaml, a language of the ML family, and it allows the manipulation of expressions of the λcalculus and of several styles of explicit su ..."
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, the λs e , the suspension calculus and a refinement of the suspension calculus called combining suspension calculus which allows for combination of steps of βcontraction; other explicit substitutions calculi can be easily incorporated into the system. An implementation of the ηreduction is provided
Algebraic goodwillie calculus and a cotriple model for the remainder
 Trans. Amer. Math. Soc
"... Abstract. Goodwillie has defined a tower of approximations for a functor from spaces to spaces that is analogous to the Taylor series of a function. His nth order approximation PnF at a space X depends on the values of F on coproducts of large suspensions of the space: F (∨ΣM X). We define an “algeb ..."
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Abstract. Goodwillie has defined a tower of approximations for a functor from spaces to spaces that is analogous to the Taylor series of a function. His nth order approximation PnF at a space X depends on the values of F on coproducts of large suspensions of the space: F (∨ΣM X). We define
The Suspension Notation for Lambda Terms and its Use in Metalanguage Implementations
 Proc. 9th Workshop on Logic, Language, Information and Computation (WoLLIC 2002), volume 67 of ENTCS
, 2003
"... Many metalanguages and logical frameworks have emerged in recent years that use the terms of the lambda calculus as data structures. A common set of questions govern the suitability of a representation for lambda terms in the implementation of such systems: convertibility must be easily recognizabl ..."
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Cited by 5 (0 self)
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Many metalanguages and logical frameworks have emerged in recent years that use the terms of the lambda calculus as data structures. A common set of questions govern the suitability of a representation for lambda terms in the implementation of such systems: convertibility must be easily
Iterates of the suspension map and Mitchell’s finite spectra with Ak free cohomology
, 1998
"... Abstract. We study certain crosseects of the unstable homotopy of spheres. These crosseects were constructed by Weiss, for dierent purposes, in the context of \Orthogonal calculus". We show that Mithchell’s nite spectra with Akfree cohomology (constructed in [Mt85]) arise naturally as stabi ..."
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Abstract. We study certain crosseects of the unstable homotopy of spheres. These crosseects were constructed by Weiss, for dierent purposes, in the context of \Orthogonal calculus". We show that Mithchell’s nite spectra with Akfree cohomology (constructed in [Mt85]) arise naturally
Results 1  10
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