Modeling Permutations in Coq for Coccinelle

Contejean, Evelyne

doi:10.1007/978-3-540-73147-4_13

Cited by 4 publications

(7 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to validate Definitions 7 and 12, we show that they are equivalent and that they are equivalent to a permutation relation on lists given by Contejean [6] (and thanks to Theorem 1 this will also validate Definition 8).…”

Section: Equivalence Proofs Between the Definitionsmentioning

confidence: 82%

See 1 more Smart Citation

Permutations in Coinductive Graph Representation

Picard

Matthes

2012

Coalgebraic Methods in Computer Science

View full text Add to dashboard Cite

In the proof assistant Coq, one can model certain classes of graphs by coinductive types. The coinductive aspects account for infinite navigability already in finite but cyclic graphs, as in rational trees. Coq's static checks exclude simple-minded definitions with lists of successors of a node. In previous work, we have shown how to mimic lists by a type of functions and built a Coq theory for such graphs. Naturally, these coinductive structures have to be compared by a bisimulation relation, and we defined it in a generic way. However, there are many cases in which we would not like to distinguish between graphs that are constructed differently and that are thus not bisimilar, in particular if only the order of elements in the lists of successors is not the same. We offer a wider bisimulation relation that allows permutations. Technical problems arise with their specification since (1) elements have to be compared by a not necessarily decidable relation and (2) coinductive types are mixed with inductive ones. Still, a formal development has been carried out in Coq, by using its built-in language for proof automation. Another extension of the original bisimulation relation based on cycle analysis provides indifference concerning the root node of the term graphs. This work has been funded by the project CLIMT of the French Agence Nationale de la Recherche (ANR-11-BS02-016).

show abstract

Section: Equivalence Proofs Between the Definitionsmentioning

confidence: 82%

“…Equivalence with Contejean. In [6], Contejean treats the same problem as ours but on lists. She bases her solution on the classical one presented in [20] but adds a base relation.…”

Section: Equivalence Proofs Between the Definitionsmentioning

confidence: 99%

Permutations in Coinductive Graph Representation

Picard

Matthes

2012

Coalgebraic Methods in Computer Science

View full text Add to dashboard Cite

show abstract

“…Many definitions of bag equivalence and related concepts are available in the literature, including classical definitions of permutations; definitions of bag equivalence for lists in the Coq [19], Ssreflect [7] and Coccinelle [5] libraries; and definitions of the type of bags in the Boom hierarchy [14], in terms of quotient containers [2], and in terms of combinatorial species [21,13]. However, I want to propose another definition, based on bijections between sets of membership proofs (Sect.…”

Section: Herementioning

confidence: 99%

“…Contejean [5] defines bag equivalence for lists inductively by, in effect, enumerating where every element in the left list occurs in the right one. It seems likely that this definition can be adapted to streams, but it is not obvious how to generalise it to branching structures such as binary trees.…”

Section: Related Workmentioning

confidence: 99%

Bag Equivalence via a Proof-Relevant Membership Relation

Danielsson

2012

Interactive Theorem Proving

View full text Add to dashboard Cite

Abstract. Two lists are bag equivalent if they are permutations of each other, i.e. if they contain the same elements, with the same multiplicity, but perhaps not in the same order. This paper describes how one can define bag equivalence as the presence of bijections between sets of membership proofs. This definition has some desirable properties:-Many bag equivalences can be proved using a flexible form of equational reasoning. -The definition generalises easily to arbitrary unary containers, including types with infinite values, such as streams. -By using a slight variation of the definition one gets set equivalence instead, i.e. equality up to order and multiplicity. Other variations give the subset and subbag preorders. -The definition works well in mechanised proofs.

show abstract

“…The deep part of the modelling is formalised in a public COQ library called COC-CINELLE [6]. To start with, it contains a modelling of the mathematical notions needed for rewriting, such as term algebras, generic rewriting, generic and AC equational theories and RPO with status.…”

Section: The Coccinelle Librarymentioning

confidence: 99%

Certification of Automated Termination Proofs

Contejean

Courtieu

Forest

et al. 2007

Frontiers of Combining Systems

Self Cite

View full text Add to dashboard Cite

Abstract. Nowadays, formal methods rely on tools of different kinds: proof assistants with which the user interacts to discover a proof step by step; and fully automated tools which make use of (intricate) decision procedures. But while some proof assistants can check the soundness of a proof, they lack automation. Regarding automated tools, one still has to be satisfied with their answers Yes/No/Do not know, the validity of which can be subject to question, in particular because of the increasing size and complexity of these tools. In the context of rewriting techniques, we aim at bridging the gap between proof assistants that yield formal guarantees of reliability and highly automated tools one has to trust. We present an approach making use of both shallow and deep embeddings. We illustrate this approach with a prototype based on the CiME rewriting toolbox, which can discover involved termination proofs that can be certified by the COQ proof assistant, using the COCCINELLE library for rewriting.

show abstract

Modeling Permutations in Coq for Coccinelle

Cited by 4 publications

References 5 publications

Permutations in Coinductive Graph Representation

Permutations in Coinductive Graph Representation

Bag Equivalence via a Proof-Relevant Membership Relation

Certification of Automated Termination Proofs

Contact Info

Product

Resources

About