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Explicit substitution on the edge of strong normalization

1999
*
Theoretical Computer Science
*

We use the recursive path ordering (RPO) technique

doi:10.1016/s0304-3975(97)00183-7
fatcat:fzefifua6fhshc2im22dl3agxe
*of*semantic labelling to show the preservation*of**strong**normalization*(PSN) property for several calculi*of*explicit*substitution*. ... PSN states that if a term M is strongly*normalizing*under ordinary p-reduction (using 'global'*substitutions*), then it is strongly*normalizing*if the*substitution*is made explicit ('local'). ... Acknowledgements Thanks to Thomas Arts for making us aware*of*current notations for the recursive path orders, using semantic labelling. ...##
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Strong Normalization of $\overline{\lambda}\mu\widetilde{\mu}$ -Calculus with Explicit Substitutions
[chapter]

2004
*
Lecture Notes in Computer Science
*

Here we prove the

doi:10.1007/978-3-540-24727-2_30
fatcat:7zbsfvgh4ne3fbklq3er2cyiwi
*strong**normalization*(SN)*of*simply typed λµμ-calculus with explicit*substitutions*. ...*of**strong**normalization*), and we prove PSN by the perpetuality technique, as formalized by Bonelli [5] . ... We present here some usual results on*substitution*calculi [5] . Lemma 6 (*Strong**normalization**of*x). x is strongly*normalizing*and its*normal*forms are pure objects (i.e. without*substitutions*). ...##
###
Simple Proofs of Characterizing Strong Normalization for Explicit Substitution Calculi
[chapter]

*
Lecture Notes in Computer Science
*

We present a method

doi:10.1007/978-3-540-73449-9_20
fatcat:vixskitpqvbrpdsz4e3dk5bqx4
*of*lifting to explicit*substitution*calculi some characterizations*of*the strongly*normalizing*terms*of*λ-calculus by means*of*intersection type systems. ... Then we present a new intersection type system in the style*of*sequent calculus, and show that it characterizes the strongly*normalizing*terms*of*Dyckhoff and Urban's extension*of*Herbelin's explicit*substitution*... This research was partially supported by the Japanese Ministry*of*Education, Culture, Sports, Science and Technology, Grant-in-Aid for Young Scientists (B) 17700003. ...##
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Strong normalization of explicit substitutions via cut elimination in proof nets

*
Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science
*

in the field

doi:10.1109/lics.1997.614927
dblp:conf/lics/CosmoK97
fatcat:szddpc4bxfck5jzzyyrymp6szi
*of*explicit*substitutions*. ... This correspondence allows us to prove that a typed version*of*the λx-calculus [34, 5] is strongly*normalizing*, as well as*of*all the calculi that can be translated to it keeping*normalization*properties ...*Strong**normalization**of*the calculus*of*explicit*substitutions*alone, called the σ-calculus, is proved in [8] , but the σ-calculus together with the Beta rule does not preserve β-*strong**normalization*...##
###
Page 244 of Journal of Personality Vol. 10, Issue 3
[page]

1942
*
Journal of Personality
*

expression

*of*very*strong*and asocial aggression is pro- vided. ... SUMMARY An interrupted task technique has been described for the investi- gation*of*the centrality*of*tasks as a determinant*of**substitute*value in*normal*and schizophrenic persons. ...##
###
Explicit Substitutions and Reducibility

2001
*
Journal of Logic and Computation
*

To illustrate this point, we give a proof

doi:10.1093/logcom/11.3.431
fatcat:ul7rqhzkpzfqbplxlj674r74fa
*of**strong**normalization*(SN) for simply-typed call-by-name -calculus enriched with operators*of*explicit unary*substitutions*. ... We consider reducibility sets defined not by induction on types but by induction on sequents as a tool to prove*strong**normalization**of*systems with explicit*substitution*. ...*Strong**normalization*proofs The traditional approach to*strong**normalization*(SN) in -calculi with explicit*substitution*is through the property*of*preservation*of**strong**normalization*(PSN). ...##
###
Evolution of transport properties of BaFe2−xRuxAs2in a wide range of isovalent Ru substitution

2012
*
Physical Review B
*

The effects

doi:10.1103/physrevb.85.024536
fatcat:rwkoeod6izgdtlvjbvhyinfnfy
*of*isovalent Ru*substitution*at the Fe sites*of*BaFe2-xRuxAs2 are investigated by measuring resistivity and Hall coefficient on high-quality single crystals in a wide range*of*doping (0 < x ... Ru*substitution*weakens the antiferromagnetic (AFM) order, inducing superconductivity for relatively high doping level*of*0.4 < x < 0.9. ... Having established the phase diagram*of*BaFe 2−x Ru x As 2 , we discuss the effects*of*Ru*substitution*on the*normal*state electrical transport properties for a wide range*of*x. ...##
###
Page 751 of Mathematical Reviews Vol. , Issue 2004b
[page]

2004
*
Mathematical Reviews
*

One important application

*of*uniform*normalization*is in prov- ing*strong**normalization*in systems*of*type assignment, since it is often easier to prove that weak*normalization*holds than to prove*strong*... in a reduction path and a*substitution*instance*of*P has an infinite reduction path, then so does that same*substitution*instance*of*Q (for*substitutions*satisfying a certain technical condition). ...##
###
A short proof of the strong normalization of the simply typed λμ-calculus
[article]

2009
*
arXiv
*
pre-print

We give an elementary and purely arithmetical proof

arXiv:0905.1557v1
fatcat:bioduzoperhl3houk33xky2ggu
*of*the*strong**normalization**of*Parigot's simply typed λμ-calculus. ... This proof is based on a proof*of*the*strong**normalization**of*the simply typed λ-calculus due to the first author (see [2] ) which, itself, is a simplification*of*the one given by R. ... The first proof*of*the the*strong**normalization**of*the λµ-calculus for the types*of*Girard's system F was done by Parigot in [6] in two different ways : by using reducibility candidates and by a CPS ...##
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COALITION-PROOF NASH EQUILIBRIA IN A NORMAL-FORM GAME AND ITS SUBGAMES

2010
*
International Game Theory Review
*

Ray (2001) also established that a

doi:10.1142/s0219198910002659
fatcat:qj5bzpdyybgqpekax4sj3j3iji
*strong*equilibrium (Aumann, 1959)*of*a subgame is a*strong*equilibrium*of*the original game under the condition*of*no coalitional benefit. ... A subgame*of*a*normal*-form game is a game in which the strategy sets*of*all players in the subgame are subsets*of*those in the*normal*-form game. ... In the following, the equilibrium concepts*of*a*normal*-form game are introduced. The first is the notion*of**strong*equilibrium introduced by Aumann (1959) . ...##
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Reductions, intersection types, and explicit substitutions

2003
*
Mathematical Structures in Computer Science
*

Given the central place that

doi:10.1017/s0960129502003821
fatcat:myfnrtvfvrgm5iuselws3yo3pe
*strong**normalization*occupies in the theory and application*of*classical lambda calculus, it is important to study this property in systems*of*explicit*substitutions*. ... The first is to define classes*of*reduction strategies in the original calculus which support*strong**normalization*; a notable example*of*work in this area is that*of*Eike Ritter [34] . ... Acknowledgements The authors are grateful to Norman Danner, Frédéric Lang, Simona Ronchi della Rocca, and Kristoffer Rose for many helpful discussions and the referees*of*the conferences LATIN'02 and TCS ...##
###
A short proof of Curry's normal form theorem

1970
*
Proceedings of the American Mathematical Society
*

In Chapter 6

doi:10.1090/s0002-9939-1970-0255405-x
fatcat:awxjpbdcibcendavpcrfkoepfu
*of*their book [l] Curry and Feys define a notion*of*reduction (*strong*reduction) for the extensional theory*of*equality in combinatory logic, show [l, Theorem 3, p. 221 ] that*strong*reduction ... Curry's*normal*form theorem [l, Theorem 7, p. 230] asserts that if a term ("ob")*of*combinatory logic is in*normal*form, it is irreducible, so that if X has*normal*form X*, then X reduces to X* by a process ... In Chapter 6*of*their book [l] Curry and Feys define a notion*of*reduction (*strong*reduction) for the extensional theory*of*equality in combinatory logic, show [l, Theorem 3, p. 221 ] that*strong*reduction ...##
###
A Short Proof of Curry's Normal Form Theorem

1970
*
Proceedings of the American Mathematical Society
*

In Chapter 6

doi:10.2307/2037329
fatcat:yj4b2x2kmrghdfu5otsreked5a
*of*their book [l] Curry and Feys define a notion*of*reduction (*strong*reduction) for the extensional theory*of*equality in combinatory logic, show [l, Theorem 3, p. 221 ] that*strong*reduction ... Curry's*normal*form theorem [l, Theorem 7, p. 230] asserts that if a term ("ob")*of*combinatory logic is in*normal*form, it is irreducible, so that if X has*normal*form X*, then X reduces to X* by a process ... In Chapter 6*of*their book [l] Curry and Feys define a notion*of*reduction (*strong*reduction) for the extensional theory*of*equality in combinatory logic, show [l, Theorem 3, p. 221 ] that*strong*reduction ...##
###
Extracting a Normalization Algorithm in Isabelle/HOL
[chapter]

2006
*
Lecture Notes in Computer Science
*

Unlike many other proofs

doi:10.1007/11617990_4
fatcat:pe2szgcl2vbqzemfy2ukhtjlne
*of*weak*normalization*based on Tait's*strong*computability predicates, which require a logic supporting*strong*eliminations and can give rise to dependent types in the extracted ... We present a formalization*of*a constructive proof*of*weak*normalization*for the simply-typed λ-calculus in the theorem prover Isabelle/HOL, and show how a program can be extracted from it. ... Although weak*normalization*follows from*strong**normalization*as a corollary, proofs*of*weak*normalization*are interesting in their own right. ...##
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Page 134 of Psychoanalytic Review Vol. 13, Issue 2
[page]

1926
*
Psychoanalytic Review
*

I would like here to point out, that the neurotic generally shows the reversed result

*of*this*normal*genital accomplishment, namely, with the man, a*strong*mother identification mainly shown in uncon- ... In the case*of*the boy, the finger*substituting*the nipple is replaced by the whole hand (forming a hole), which first*of*all*substitutes*the mouth (as hole), when the displacement to the genitals takes ...
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