Jan-Willem Klop. Combinatory Reduction Systems. PhD thesis, Mathematical Centre Tracts 127, CWI, Amsterdam, 1980. Home/Search Document Not in Database Summary Related Articles Check |
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Four Equivalent Equivalences of Reductions - van Oostrom, de Vrijer (2002) (Correct)
....= #, then src(#) src(#) and tgt(#) tgt(#) and similarly for reductions (i.e. modulo the reduction identities) Remark 3.5 Permutation equivalence is of a relatively recent origin. It was introduced for the # calculus in [24] Some important further developments of the notion can be traced in [21,16,5,18,27,23,30,2]. Owing to the tight connexion between permutation equivalence and concurrency, permutation equivalence appears in many guises in areas where concurrency is important. For instance, in trace theory the notion of Mazurkiewicz trace as a trace up to the order of independent actions was introduced in ....
....finally yields the sorted list [1, 2, 3] not containing any inversions. Similarly, parallel standardisation by inversion consists in repeatedly and non deterministically permuting any pair of adjacent steps which are in the wrong, inside out, order. Such pairs are called anti standard pairs ([21]) and a reduction where no anti standard pairs remain, is called parallel standard. The permutation process can be most easily described as a rewriting process, where the rules are oriented versions of the inner and outer permutation identities, which are applied modulo the structural equivalence ....
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J.W. Klop. Combinatory Reduction Systems. PhD thesis, Rijksuniversiteit Utrecht, June 1980.
De Bruijn's syntax and reductional behaviour of λ-terms - Kamareddine, Bloo (Correct)
....[20] and [4] use whereas [16] uses to reduce the problem of strong normalization to the problem of weak normalization (WN) for related reductions. 14] uses and to reduce typability in the rank 2 restriction of the 2nd order calculus to the problem of acyclic semi uni cation. [18, 28, 26, 17] use related reductions to reduce SN to WN and [12] uses similar notions in SN proofs. 9] uses a more extended version of (called term reshu ing) and of g (called generalised reduction) where C and N are not only separated by the redex ( x : B but by many redexes (ordinary and generalised) ....
J. W. Klop. Combinatory Reduction Systems. Mathematical Center Tracts, 27, 1980. CWI.
Dependent Types and Explicit Substitutions - Muñoz (1999) (Correct)
....# y: T x) x:nat. #. Therefore, the type of 1[S] S) is not preserved by rule (SCons) The problem here is not the type system but the substitution calculus. Non left linear rules like (SCons) are not only harmful for typing, but are also usually responsible for non confluence problems [26, 7]. Nadathur [35] has remarked that in ## with meta variables of terms, but without meta variables of substitutions, rule (SCons) is admissible when the following scheme of rule is added to the system: 1[# n 1 # . Since is a shorthand, an infinite set of rules is represented by this ....
J.-W. Klop, Combinatory reduction systems, Mathematical Center Tracts, (1980).
Calculi of Generalized beta-Reduction and Explicit.. - Kamareddine, Ríos, Wells (1998) (Correct)
....[KW95b] used fl to reduce the problem of fi strong normalization to the problem of weak normalization (WN) for related reductions. Kfoury and Wells used and fl to reduce typability in the rank 2 restriction of system F to the problem of acyclic semi unification [KW94] Klop, Srensen, and Xi [Klo80, Xi96, Sr97] used related reductions to reduce SN to WN. Finally, 95] used (called let C ) as a part of an analysis of how to represent sharing in a call by need language implementation in a formal calculus. 1.2 The Calculus with Explicit Substitution Most literature on the calculus treats ....
....a = fi c; hence b = fi c. By confluence of fi, 9d 2 where b fi d, and c fi d. By Remark 1, b gfi d, and c gfi d. There are, as we mentioned in the introduction, various notions of generalized reduction. For other proofs of confluence of some of these notions, we refer the reader to [AFM 95, dG93, Kam96, KW95b, Klo80]. Finally, the following ensures the good passage of gfi reduction through ff gg and U k : Lemma 5 Let a; b; c; d 2 . The following hold: 1. If c gfi d, then U k (c) gfi U k (d) 2. If c gfi d, then affn cgg gfi affn dgg. 3. If a gfi b, then affn cgg gfi bffn cgg. 15 ....
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J. W. Klop. Combinatory Reduction Systems. PhD thesis, Mathematical Centre Tracts. Mathematisch Centrum, Amsterdam, 1980.
De Bruijn's syntax and reductional equivalence of.. - Kamareddine, Bloo, al. (2001) (Correct)
....with . 16] and [4] use whereas [12] uses to reduce the problem of strong normalization to the problem of weak normalization (WN) for related reductions. 10] uses and to reduce typability in the rank 2 restriction of the 2nd order calculus to the problem of acyclic semi uni cation. [14, 22, 20, 13] use related reductions to reduce SN to WN and [8] uses similar notions in SN proofs. 6] uses a more extended version of (called termreshu ing) and of g (called generalised reduction) where Q and N are not only separated by the redex ( x : P but by many redexes (ordinary and generalised) ....
J. W. Klop. Combinatory Reduction Systems. Mathematical Center Tracts, 27, 1980. CWI.
Adjoint Rewriting - Ghani (2 citations) (Correct)
....sequences u and v are independent iff u 6 v and v 6 u. These operations on sequences are extended pointwise to sets of sequences e.g. X=u = fw j u Delta w 2 Xg. Relations Relations are a convenient framework to define some abstract properties of term rewriting systems and the reader may consult [21,42,43,53]. A homogeneous relation on a set X is a subset R X Theta X. If (x; x ) 2 R then x is called the redex, x the reduct and we say that x rewrites or reduces to x . This is often written x )R x and the subscript R is omitted if the relation is clear from the context. Given a ....
J. W. Klop. Combinatory reduction systems. Mathematical Center Tracts, 27, 1980.
Type Assigment Systems for Lambda Calculi and for the Lambda.. - Liquori (1996) (Correct)
....The notion of reduction, as presented in Definition 3.1.5, satisfies the Church Rosser property. Theorem 3.3.1 (Church Rosser Property for type assignment systems) If A fi A and B fi B , then there exists C, such that A fi C and B fi C. Proof: In the terminology of Klop [Klo80] our fi reduction is a regular combinatory reduction system, and thus the Church Rosser Property follows from Theorem 3.11 in [Klo80] As an illustration, and to give some details about how the Church Rosser property is obtained, we now present another proof, that uses the technique of ....
....for type assignment systems) If A fi A and B fi B , then there exists C, such that A fi C and B fi C. Proof: In the terminology of Klop [Klo80] our fi reduction is a regular combinatory reduction system, and thus the Church Rosser Property follows from Theorem 3. 11 in [Klo80] As an illustration, and to give some details about how the Church Rosser property is obtained, we now present another proof, that uses the technique of parallel reduction developed by Tait and Martin Lof. Intuitively, parallel reduction reduces a number of fi redexes simultaneously. ....
W. Klop, J. Combinatory Reduction Systems. PhD thesis, Department of Computer Science, Rijksuniversiteit Utrecht, 1980.
Descendants and Origins in Term Rewriting - Bethke, Klop, de Vrijer (1999) Self-citation (Klop) (Correct)
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J.W. Klop, V. van Oostrom, and F. van Raamsdonk. Combinatory reduction systems, introduction and survey. Theoretical Computer Science, 121:279--308, 1993.
Descendants and Origins in Term Rewriting - Bethke, Klop, de Vrijer (1999) Self-citation (Klop) (Correct)
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J.W. Klop. Combinatory Reduction Systems. Mathematical Centre Tracts Nr. 127. CWI, Amsterdam, 1980. PhD Thesis.
Pure Pattern Calculus - Jay, Kesner (2005) (Correct)
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Jan-Willem Klop. Combinatory Reduction Systems. PhD thesis, Mathematical Centre Tracts 127, CWI, Amsterdam, 1980.
Intersection Types, λ-models, and Böhm Trees - Dezani-Ciancaglini.. (Correct)
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J.W. Klop, "Combinatory Reduction Systems", Math. Center Tracts 129, Amsterdam, 1980.
An Standardisation Theorem - Georges Gonthier Jean-Jacques (Correct)
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J. W. Klop, "Combinatory reduction systems," tech. rep., CWI, 1980. Math. Center Tracts 129, Amsterdam.
A Generic Normalisation Proof for Pure Type Systems.. - Paulm Dcs Ed (Correct)
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J. W. Klop, Combinatory Reduction Systems. Ph.D. Thesis, Utrecht University, 1980.
Axiomatic Rewriting Theory IV - A stability theorem in Rewriting.. - Mellies (1998) (1 citation) (Correct)
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J.W. Klop, "Combinatory Reduction Systems". Volume 127 of Mathematical Centre Tracts, CWI, Amsterdam, 1980. PhD thesis.
Axiomatic Rewriting Theory III - A factorisation theorem in.. - Mellies (1997) (2 citations) (Correct)
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J. W. Klop, "Combinatory Reduction Systems". PhD thesis, Rijksuniversiteit Utrecht, Mathematics Centre Tract, volume 127, June 1980.
A Linearization of the Lambda-Calculus and Consequences - Kfoury (2000) (Correct)
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Klop, J. W., Combinatory Reduction Systems, PhD thesis, Utrecht University, Amsterdam 1980. Volume 127 of CWI Tract.
A Canonical Calculus of Residuals - Bertot (1991) (2 citations) (Correct)
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J. W. Klop, Combinatory Reduction Systems, Mathematisch Centrum, Amsterdam, 1980.
Conservation and Uniform Normalization in Lambda Calculi.. - Neergaard, Sørensen (2002) (2 citations) (Correct)
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J. W. Klop, Combinatory Reduction Systems, Mathematisch Centrum, Amsterdam, 1980, ph.D. Thesis.
A Linearization of the Lambda-Calculus and Consequences - Kfoury (2000) (Correct)
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Klop, J. W., Combinatory Reduction Systems, PhD thesis, Utrecht University, Amsterdam 1980. Volume 127 of CWI Tract.
Weak and Strong Normalization, K-redexes, and First-Order Logic - Neergaard (1999) (Correct)
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J. W. Klop. Combinatory Reduction Systems. PhD thesis, Utrecht University, Amsterdam, 1980. Volume 127 of CWI Tract. Cited on pages 2, 77, and 78.
Non Deterministic Extensions of Untyped λ-calculus - de'Liguoro, Piperno (1995) (Correct)
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J.W. Klop, "Combinatory reduction systems", PhD thesis, Mathematisch Centrum, Amsterdam 1980. 64
The Dynamics of Information Exchange Dialogues - Cate (2001) (Correct)
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Klop, J., \Combinatory Reduction Systems," Mathematical centre tracts 127, Mathematisch Centrum, Amsterdam, 1980.
DEA SEMANTIQUE, PREUVES et - Langages Cours De (Correct)
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Klop J.W. , Combinatory Reduction Systems, Math. Center Tracts 129, Amsterdam, 1980. These de J. W. Klop, assez dicile a trouver. Lecture recommandee comme complement au cours.
Parametric Parameter Passing λ-calculus - Paolini, Rocca (2003) (Correct)
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Klop J.W., \Combinatory Reduction Systems", Mathematical Center Tracts 129, 1980, Amsterdam.
A Calculus of Lambda Calculus Contexts - Bognar, de Vrijer (2001) (4 citations) (Correct)
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Klop, J.: 1980, Combinatory Reduction Systems, Mathematical Centre Tracts Nr. 127. Amsterdam: CWI. PhD Thesis.
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