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Explicit substitution on the edge of strong normalization

Roel Bloo, Herman Geuvers
1999 Theoretical Computer Science  
We use the recursive path ordering (RPO) technique 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.  ... 
doi:10.1016/s0304-3975(97)00183-7 fatcat:fzefifua6fhshc2im22dl3agxe

Strong Normalization of $\overline{\lambda}\mu\widetilde{\mu}$ -Calculus with Explicit Substitutions [chapter]

Emmanuel Polonovski
2004 Lecture Notes in Computer Science  
Here we prove the 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).  ... 
doi:10.1007/978-3-540-24727-2_30 fatcat:7zbsfvgh4ne3fbklq3er2cyiwi

Simple Proofs of Characterizing Strong Normalization for Explicit Substitution Calculi [chapter]

Kentaro Kikuchi
Lecture Notes in Computer Science  
We present a method 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.  ... 
doi:10.1007/978-3-540-73449-9_20 fatcat:vixskitpqvbrpdsz4e3dk5bqx4

Strong normalization of explicit substitutions via cut elimination in proof nets

R. Di Cosmo, D. Kesner
Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science  
in the field 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  ... 
doi:10.1109/lics.1997.614927 dblp:conf/lics/CosmoK97 fatcat:szddpc4bxfck5jzzyyrymp6szi

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

H. Herbelin
2001 Journal of Logic and Computation  
To illustrate this point, we give a proof 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).  ... 
doi:10.1093/logcom/11.3.431 fatcat:ul7rqhzkpzfqbplxlj674r74fa

Evolution of transport properties of BaFe2−xRuxAs2in a wide range of isovalent Ru substitution

M. J. Eom, S. W. Na, C. Hoch, R. K. Kremer, J. S. Kim
2012 Physical Review B  
The effects 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.  ... 
doi:10.1103/physrevb.85.024536 fatcat:rwkoeod6izgdtlvjbvhyinfnfy

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]

René David
2009 arXiv   pre-print
We give an elementary and purely arithmetical proof 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  ... 
arXiv:0905.1557v1 fatcat:bioduzoperhl3houk33xky2ggu

COALITION-PROOF NASH EQUILIBRIA IN A NORMAL-FORM GAME AND ITS SUBGAMES

RYUSUKE SHINOHARA
2010 International Game Theory Review  
Ray (2001) also established that a 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) .  ... 
doi:10.1142/s0219198910002659 fatcat:qj5bzpdyybgqpekax4sj3j3iji

Reductions, intersection types, and explicit substitutions

DAN DOUGHERTY, PIERRE LESCANNE
2003 Mathematical Structures in Computer Science  
Given the central place that 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  ... 
doi:10.1017/s0960129502003821 fatcat:myfnrtvfvrgm5iuselws3yo3pe

A short proof of Curry's normal form theorem

Roger Hindley, Bruce Lercher
1970 Proceedings of the American Mathematical Society  
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  ...  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  ... 
doi:10.1090/s0002-9939-1970-0255405-x fatcat:awxjpbdcibcendavpcrfkoepfu

A Short Proof of Curry's Normal Form Theorem

Roger Hindley, Bruce Lercher
1970 Proceedings of the American Mathematical Society  
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  ...  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  ... 
doi:10.2307/2037329 fatcat:yj4b2x2kmrghdfu5otsreked5a

Extracting a Normalization Algorithm in Isabelle/HOL [chapter]

Stefan Berghofer
2006 Lecture Notes in Computer Science  
Unlike many other proofs 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.  ... 
doi:10.1007/11617990_4 fatcat:pe2szgcl2vbqzemfy2ukhtjlne

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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