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Proof of termination of the rewriting system subst on CCL

Thérèse Hardin, Alain Laville
1986 Theoretical Computer Science  
The rewriting system SUBST simulates in particular the substitution of the Xe-calculus. This system is locally confluent. We shall show here that it is also noetherian.  ...  Curien (1985) defines a translation of the Ac-calculus in the Pure Combinatory Categorical Logic and establishes an equivalence theorem between these two theories.  ...  Acknowledgment We would like to thank the members of the project FORMEL at INRIA for the fruitful discussions we have had with them.  ... 
doi:10.1016/0304-3975(86)90035-6 fatcat:63swrohasfam7jzo2b7twwvmme

Confluence results for the pure strong categorical logic CCL. λ-calculi as subsystems of CCL

Thérèse Hardin
1989 Theoretical Computer Science  
Here we study the confluence properties of (CCL, CCLpqSP) and of several of its subsystems, and the relationship between untyped Lambda-calculi and (CCL, CCLpqSP) as rewriting systems.  ...  The Strong Categorical Combinatory Logic (CCL, CCLpqSP), developed by Curien (1986) is, when typed and augmented with a rule defining a terminal object, a presentation of Cartesian Closed Categories.  ...  Subst is terminating. We say only a few words about the proof of this result.  ... 
doi:10.1016/0304-3975(89)90105-9 fatcat:skfsyolxrzf5db3vgmrmr7elpe

Author index volume 46 (1986)

1986 Theoretical Computer Science  
Laville, Proof of termination of the rewriting system SUBST on CCL (1) 83-89 Latteux, M. and E. Timmerman, Two characterizations of rational adherences (Note) (1).101-106 Laville, A., see T.  ...  ., An algebraic and algorithmic method for analysing transition systems , (2, 3) 285-303 Diekert, V., On some variants of the Ehrenfeucht Conjecture (Note) (2, 3) 313-318 Diekert, V., Commutative monoids  ... 
doi:10.1016/0304-3975(86)90039-3 fatcat:aturjbxhkbav5bvv4w7a3sunti

Page 4316 of Mathematical Reviews Vol. , Issue 88h [page]

1988 Mathematical Reviews  
{For the entire collection see MR 88e:68009.} 88h:68053 68Q50 03B40 03B70 68T15 Hardin, Thérése (F-REIMS); Laville, Alain (F-REIMS) Proof of termination of the rewriting system SUBST on CCL. Theoret.  ...  The rewriting system SUBST simu- lates, in particular, the substitution of the Ac-calculus. This system is locally confluent.  ... 

Page 4046 of Mathematical Reviews Vol. , Issue 97G [page]

1997 Mathematical Reviews  
We present here an independent proof of the termination of several subsitution calculi, including o and SUBST.” 97g:03017 03B40 03B15 68Q42 Springintveld, Jan (NL-NIJMC-CS; Nijmegen) Third-order matching  ...  The strong normalization of a, the subcalculus which computes substitutions, may be inferred from the strong normalization of the similar subsystem SUBST of CCL.  ... 

Rewriting UNITY [chapter]

Adam Granicz, Daniel M. Zimmerman, Jason Hickey
2003 Lecture Notes in Computer Science  
Phobos uses term rewriting to define the syntax and semantics of programming languages, and automates their translation to an internal compiler representation.  ...  In this paper we describe the implementation of the UNITY formalism as an extension of general-purpose languages and show its translation to C abstract syntax using Phobos, our generic front-end in the  ...  On the other hand, we have ignored rewriting termination or Church-Rosser properties of our implementation.  ... 
doi:10.1007/3-540-44881-0_11 fatcat:oj5aah52yjg2vjujlcbyxtyiva

An Algorithmic Interpretation of a Deep Inference System [chapter]

Kai Brünnler, Richard McKinley
2008 Lecture Notes in Computer Science  
Starting from natural deduction for the conjunction-implication fragment of intuitionistic logic we design a corresponding deep inference system together with reduction rules on proofs that allow a fine-grained  ...  simulation of beta-reduction.  ...  However, since we only have a subset of the defining equations of the adjunctions this will not lead to an embedding of Curien's system (not even the one called CCL β since it contains a bit of surjective  ... 
doi:10.1007/978-3-540-89439-1_34 fatcat:s2onuy4y3fh35avd64ngy3y67q

On equality up-to constraints over finite trees, context unification, and one-step rewriting [chapter]

Joachim Niehren, Manfred Pinkal, Peter Ruhrberg
1997 Lecture Notes in Computer Science  
The positive existential fragment of the theory of one-step rewriting is decidable. The 9 8 9 fragment of the theory of context uni cation is undecidable.  ...  Equality up-to constraints subsume equality constraints, subtree constraints, and one-step rewriting constraints.  ...  However, at the time of submitting this paper, the termination proof given there has not been agreed on to be complete.  ... 
doi:10.1007/3-540-63104-6_4 fatcat:oij25wzpvjbnvnfknmnl5bjyl4

A HOL Basis for Reasoning about Functional Programs

Sten Agerholm
1994 BRICS Report Series  
and proof infrastructure already available in the HOL system.  ...  This thesis presents a formalization of domain theory in the Higher Order Logic (HOL) theorem proving system along with a mechanization of proof functions and other tools to support reasoning about the  ...  The proof of termination of strict addition requires much more thought in LCF though it can be proved by a one-line LCF tactic, induction then rewriting.  ... 
doi:10.7146/brics.v1i44.21598 fatcat:5aowedoqnbdlxnjcfplcsygyum

Subject index volumes 1–200

1999 Theoretical Computer Science  
systems. 3385 rewriting, 727 termination preservation of -. 2598 problems, 2687 proof of -, 900 termination proofs, 367, 1755. 2062, 2379, 2646 automatizing -. 2580 simphfication orderings in  ...  assumption, 3587 subspace of the rule space of CA's corresponding to NN's, 3253 subspaces of projective space, 1203 subspecifications, 1639 SUBST (rewriting system),900 substitution, 982, 1033, 1134,  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Reference list of indexed articles

1999 Theoretical Computer Science  
Laville, Proof of termination of the rewriting system SUBST on CCL 46 (2-3) (1986) 305-3 12 901. V. Diekert, On some variants of the Ehrenfeucht Conjecture 46 (2-3) (1986) 313-318 902. V.  ...  Yen, On the complexity of deciding fair termination of probabilistic concurrent finite-state programs 58 (1-3) (1988) 263-324 1116. K.  ... 
doi:10.1016/s0304-3975(98)00320-x fatcat:bdgg2ekzdjahdo7g2gtwbdye6m

Combining Symbolic Constraint Solvers on Algebraic Domains

Hélène Kirchner, Christophe Ringeissen
1994 Journal of symbolic computation  
In the context of constraint logic programming and theorem proving, the development of constraint solvers on algebraic domains and their combination is of prime interest.  ...  The set V(c) of free variables of the constraint c is de ned as follows: { V(T) = V(F) = ;, { V(p ?  ...  The set of all these symbolic solutions is denoted by SS < Ai (c i ; V j ). Variables in V j ; j 6 = i are said frozen. 2.  ... 
doi:10.1006/jsco.1994.1040 fatcat:p5wmq3jefrcxzp3gydfz7x6vvq

Cumulative index volumes 1–100

1992 Theoretical Computer Science  
Laville, Proof of termination of the rewriting system SUBST on CCL (Note) 46 (2-3) (1986) 305-312 Hardin, T.. Confluence results for the pure Strong Categorical Logic CCL.  ...  Fischer, On describing the behavior and implementation Madlener, K. and F. Otto, About the descriptive power of certain classes of finite string-rewriting Maon. Y., B. Schieber and U.  ... 
doi:10.1016/0304-3975(92)90292-n fatcat:ekwes6owtrco3lkfkiqagnketq

Page 1088 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
system SUBST on CCL. 88h:68053 Heilbrunner, Stephan (with Holidobler, Steffen) The undecidability of the unification and matching problem for canonical theories. 88j:68100 Herold, Alexander (with Sickmann  ...  (See 88f:68008) Haraguchi, Makoto (with Arikawa, Setsuo) Reasoning by analogy as a partial identity between models. 88h:03037 Hardin, Thérése (with Laville, Alain) Proof of termination of the rewriting  ... 

An Algorithmic Interpretation of a Deep Inference System [article]

Kai Brünnler, Richard McKinley, Helmut Veith, Andrei Voronkov, Iliano Cervesato
2008
Starting from natural deduction for the conjunction-implication fragment of intuitionistic logic we design a corresponding deep inference system together with reduction rules on proofs that allow a fine-grained  ...  simulation of beta-reduction.  ...  However, since we only have a subset of the defining equations of the adjunctions this will not lead to an embedding of Curien's system (not even the one called CCL β since it contains a bit of surjective  ... 
doi:10.7892/boris.37187 fatcat:7arr5legjvbkfee5tz3aba3iaq
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