Tracing sharing in an imperative pure calculus

10.26686/wgtn.13174967.v1 ◽

2020 ◽

Author(s):

P Giannini ◽

T Richter ◽

Marco Servetto ◽

E Zucca

Keyword(s):

Standard Model ◽

Equivalence Relation ◽

Free Variables ◽

Execution Model ◽

Natural Way

© 2018 Elsevier B.V. We introduce a type and effect system, for an imperative object calculus, which infers sharing possibly introduced by the evaluation of an expression, represented as an equivalence relation among its free variables. This direct representation of sharing effects at the syntactic level allows us to express in a natural way, and to generalize, widely-used notions in literature, notably uniqueness and borrowing. Moreover, the calculus is pure in the sense that reduction is defined on language terms only, since they directly encode store. The advantage of this non-standard execution model with respect to a behaviorally equivalent standard model using a global auxiliary structure is that reachability relations among references are partly encoded by scoping.

Download Full-text

On the Groups of Cobordism Ωk

Nagoya Mathematical Journal ◽

10.1017/s0027763000023588 ◽

1958 ◽

Vol 13 ◽

pp. 135-156 ◽

Cited By ~ 1

Author(s):

Masahisa Adachi

Keyword(s):

Equivalence Relation ◽

Differentiable Manifold ◽

Equivalence Classes ◽

Graded Algebra ◽

Differentiable Manifolds ◽

Free Part ◽

Natural Way

In the papers [11] and [18] Rohlin and Thom have introduced an equivalence relation into the set of compact orientable (not necessarily connected) differentiable manifolds, which, roughly speaking, is described in the following manner: two differentiable manifolds are equivalent (cobordantes), when they together form the boundary of a bounded differentiable manifold. The equivalence classes can be added and multiplied in a natural way and form a graded algebra Ω relative to the addition, the multiplication and the dimension of manifolds. The precise structures of the groups of cobordism Ωk of dimension k are not known thoroughly. Thom [18] has determined the free part of Ω and also calculated explicitly Ωk for 0 ≦ k ≦ 7.

Download Full-text

When are Two Algorithms the Same?

Bulletin of Symbolic Logic ◽

10.2178/bsl/1243948484 ◽

2009 ◽

Vol 15 (2) ◽

pp. 145-168 ◽

Cited By ~ 13

Author(s):

Andreas Blass ◽

Nachum Dershowitz ◽

Yuri Gurevich

Keyword(s):

Equivalence Relation ◽

Equivalence Classes ◽

Natural Way

AbstractPeople usually regard algorithms as more abstract than the programs that implement them. The natural way to formalize this idea is that algorithms are equivalence classes of programs with respect to a suitable equivalence relation. We argue that no such equivalence relation exists.

Download Full-text

Onp-Convergence in Measure of a Sequence of Measurable Functions

Abstract and Applied Analysis ◽

10.1155/2011/582576 ◽

2011 ◽

Vol 2011 ◽

pp. 1-7

Author(s):

A. Boccuto ◽

Ch. Papachristodoulos ◽

N. Papanastassiou

Keyword(s):

Equivalence Relation ◽

Metric Space ◽

Quotient Space ◽

Compact Metric Space ◽

Convergence In Measure ◽

Measurable Functions ◽

Natural Way

In the study by Papanastassiou and Papachristodoulos, 2009 the notion ofp-convergence in measure was introduced. In a natural wayp-convergence in measure induces an equivalence relation on the spaceMof all sequences of measurable functions converging in measure to zero. We show that the quotient spaceℳis a complete but not compact metric space.

Download Full-text

Indirect measurements in micro-space with the EM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100139366 ◽

1995 ◽

Vol 53 ◽

pp. 598-599

Author(s):

Sterling P. Newberry

Keyword(s):

Electron Microscope ◽

Standard Model ◽

Particle Physics ◽

Information Storage ◽

Storage Space ◽

Indirect Measurements ◽

Storage And Retrieval ◽

Adequate Information ◽

Compelling Reason ◽

The Standard Model

At the 1958 meeting of our society, then known as EMSA, the author introduced the concept of microspace and suggested its use to provide adequate information storage space and the use of electron microscope techniques to provide storage and retrieval access. At this current meeting of MSA, he wishes to suggest an additional use of the power of the electron microscope.The author has been contemplating this new use for some time and would have suggested it in the EMSA fiftieth year commemorative volume, but for page limitations. There is compelling reason to put forth this suggestion today because problems have arisen in the “Standard Model” of particle physics and funds are being greatly reduced just as we need higher energy machines to resolve these problems. Therefore, any techniques which complement or augment what we can accomplish during this austerity period with the machines at hand is worth exploring.

Download Full-text