Analysing Parallel Complexity of Term Rewriting

We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques to derive both upper and lower bounds on parallel complexity of rewriting that enable a direct reuse of existing techniques for sequential complexity. The applicability and the precision of the method are demonstrated by the relatively light effort in extending the program analysis tool AProVE and by experiments on numerous benchmarks from the literature.Comment: Extended authors' accepted manuscript for a paper accepted for publication in the Proceedings of the 32nd International Symposium on Logic-based Program Synthesis and Transformation (LOPSTR 2022). 27 page

On Complexity Bounds and Confluence of Parallel Term Rewriting

We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques to derive both upper and lower bounds on parallel complexity of rewriting that enable a direct reuse of existing techniques for sequential complexity. Our approach to find lower bounds requires confluence of the parallel-innermost rewrite relation, thus we also provide effective sufficient criteria for proving confluence. The applicability and the precision of the method are demonstrated by the relatively light effort in extending the program analysis tool AProVE and by experiments on numerous benchmarks from the literature.Comment: Under submission to Fundamenta Informaticae. arXiv admin note: substantial text overlap with arXiv:2208.0100

Knit&Frog: Pattern matching compilation for custom memory representations (doctoral session)

National audienceInitially present only in functional languages such as OCaml and Haskell, Algebraic Data Types have now become pervasive in mainstream languages, providing nice data abstractions and an elegant way to express functions though pattern-matching. Numerous approaches have been designed to compile rich pattern matching to cleverly designed, efficient decision trees. However, these approaches are specific to a choice of internal memory representation which must accommodate garbage-collection and polymorphism. ADTs now appear in languages more liberal in their memory representation such as Rust. Notably, Rust is now introducing more and more optimizations of the memory layout of Algebraic Data Types. As memory representation and compilation are interdependent, it raises the question of pattern matching compilation in the presence of non-regular, potentially customized, memory layouts. In this article, we present Knit&Frog, a framework to compile pattern-matching for monomorphic ADTs, parametrized by an arbitrary memory representation. We propose a novel way to describe choices of memory representation along with a validity condition under which we prove the correctness of our compilation scheme. The approach is implemented in a prototype tool ribbit

On Confluence of Parallel-Innermost Term Rewriting

International audienceWe revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures. We propose a simple sufficient criterion for confluence of parallelinnermost rewriting based on non-overlappingness. Our experiments on a large benchmark set indicate the practical usefulness of our criterion. We close with a challenge to the community to develop more powerful dedicated techniques for this problem

Knit&Frog: Pattern matching compilation for custom memory representations

Initially present only in functional languages such as OCaml and Haskell, Algebraic Data Types have now become pervasive in mainstream languages, providing nice data abstractions and an elegant way to express functions though pattern-matching. Numerous approaches have been designed to compile rich pattern matching to cleverly designed, ecient decision trees. However, these approaches are specic to a choice of internal memory representation which must accommodate garbage-collection and polymorphism. ADTs now appear in languages more liberal in their memory representation such as Rust. Notably, Rust is now introducing more and more optimizations of the memory layout of Algebraic Data Types. As memory representation and compilation are interdependent, it raises the question of pattern matching compilation in the presence of non-regular, potentially customized, memory layouts. In this report, we present Knit&Frog, a framework to compile pattern-matching for monomorphic ADTs, parametrized by an arbitrary memory representation. We propose a novel way to describe choices of memory representation along with a validity condition under which we prove the correctness of our compilation scheme. The approach is implemented in a prototype tool ribbit.Initialement présents dans les langages fonctionnels comme Ocaml et Haskell, les types algébriques sont maintenant de plus en plus présents dans les langages mainstream comme Rust. Ils permettent une abstraction commode des données et une façon élégante de décrire des fonctions via le fitrage de motifs (pattern-matching). Ce rapport de recherche présente Knit&Frog, un cadre formel pour décrire des représentations mémoires de types algébrique paramétré par la représentation mémoire. La correction de l'algorithme est prouvée sous une hypothèse de validité de la représentation. L'algorithme est implémenté dans l'outil ribbit. Le principal avantage de l'approche est l'indépendance de l'algorithme et de sa représentation mémoire,qui permettra à terme de décrire des représentations optimisées sans perdre de l'expressivité

Ribbit

Ribbit is a compiler for pattern languagescwith algebraic data types which is parameterized by the memory representation of types. Given a memory representation, it generates efficient and correct code for pattern matching clauses

Knit&Frog: Pattern matching compilation for custom memory representations (doctoral session)

National audienceInitially present only in functional languages such as OCaml and Haskell, Algebraic Data Types have now become pervasive in mainstream languages, providing nice data abstractions and an elegant way to express functions though pattern-matching. Numerous approaches have been designed to compile rich pattern matching to cleverly designed, efficient decision trees. However, these approaches are specific to a choice of internal memory representation which must accommodate garbage-collection and polymorphism. ADTs now appear in languages more liberal in their memory representation such as Rust. Notably, Rust is now introducing more and more optimizations of the memory layout of Algebraic Data Types. As memory representation and compilation are interdependent, it raises the question of pattern matching compilation in the presence of non-regular, potentially customized, memory layouts. In this article, we present Knit&Frog, a framework to compile pattern-matching for monomorphic ADTs, parametrized by an arbitrary memory representation. We propose a novel way to describe choices of memory representation along with a validity condition under which we prove the correctness of our compilation scheme. The approach is implemented in a prototype tool ribbit

On Confluence of Parallel-Innermost Term Rewriting

International audienceWe revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures. We propose a simple sufficient criterion for confluence of parallelinnermost rewriting based on non-overlappingness. Our experiments on a large benchmark set indicate the practical usefulness of our criterion. We close with a challenge to the community to develop more powerful dedicated techniques for this problem

Analysing Parallel Complexity of Term Rewriting

International audienceWe revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques to derive both upper and lower bounds on parallel complexity of rewriting that enable a direct reuse of existing techniques for sequential complexity. The applicability and the precision of the method are demonstrated by the relatively light effort in extending the program analysis tool AProVE and by experiments on numerous benchmarks from the literature

Analysing Parallel Complexity of Term Rewriting

International audienceWe revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques to derive both upper and lower bounds on parallel complexity of rewriting that enable a direct reuse of existing techniques for sequential complexity. The applicability and the precision of the method are demonstrated by the relatively light effort in extending the program analysis tool AProVE and by experiments on numerous benchmarks from the literature