Kat + B!

Grathwohl, Niels Bjørn Bugge; Kozen, Dexter; Mamouras, Konstantinos

doi:10.1145/2603088.2603095

Cited by 15 publications

(3 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An interesting question is whether a complete axiomatization can be provided for the basic dataflow combinators of Sect. 5, similarly to how Kleene Algebra (KA) [62,63] and its extensions [49,64,79,83] (as well as other program logics [65,66,78,[80][81][82]) capture properties of imperative programs at the propositional level. We also leave for future work the development of the coalgebraic approach [96][97][98] for reasoning about the equivalence of stream transducers.…”

Section: Algebraic Reasoning For Optimizing Transformationsmentioning

confidence: 99%

Semantic Foundations for Deterministic Dataflow and Stream Processing

Mamouras

2020

Programming Languages and Systems

Self Cite

View full text Add to dashboard Cite

We propose a denotational semantic framework for deterministic dataflow and stream processing that encompasses a variety of existing streaming models. Our proposal is based on the idea that data streams, stream transformations, and stream-processing programs should be classified using types. The type of a data stream is captured formally by a monoid, an algebraic structure with a distinguished binary operation and a unit. The elements of a monoid model the finite fragments of a stream, the binary operation represents the concatenation of stream fragments, and the unit is the empty fragment. Stream transformations are modeled using monotone functions on streams, which we call stream transductions. These functions can be implemented using abstract machines with a potentially infinite state space, which we call stream transducers. This abstract typed framework of stream transductions and transducers can be used to (1) verify the correctness of streaming computations, that is, that an implementation adheres to the desired behavior, (2) prove the soundness of optimizing transformations, e.g. for parallelization and distribution, and (3) inform the design of programming models and query languages for stream processing. In particular, we show that several useful combinators can be supported by the full class of stream transductions and transducers: serial composition, parallel composition, and feedback composition.

show abstract

Section: Algebraic Reasoning For Optimizing Transformationsmentioning

confidence: 99%

Semantic Foundations for Deterministic Dataflow and Stream Processing

Mamouras

2020

Programming Languages and Systems

Self Cite

View full text Add to dashboard Cite

show abstract

“…The two experiments reported were both with commutative semirings, for which NPA-TP is not needed. Grathwohl et al [2014] developed an extension of Kleene algebra with tests to allow a finite amount of mutable state. They noted that one model of their extension could be represented using Kronecker products of 2 × 2 Boolean matrices, but did not make further use of that fact.…”

Section: Related Workmentioning

confidence: 99%

Newtonian Program Analysis via Tensor Product

Reps

Turetsky

Prabhu

2017

ACM Trans. Program. Lang. Syst.

View full text Add to dashboard Cite

Recently, Esparza et al. generalized Newton's method-a numerical-analysis algorithm for finding roots of real-valued functions-to a method for finding fixed-points of systems of equations over semirings. Their method provides a new way to solve interprocedural dataflow-analysis problems. As in its real-valued counterpart, each iteration of their method solves a simpler "linearized" problem.One of the reasons this advance is exciting is that some numerical analysts have claimed that " 'all' effective and fast iterative [numerical] methods are forms (perhaps very disguised) of Newton's method." However, there is an important difference between the dataflow-analysis and numerical-analysis contexts: when Newton's method is used on numerical-analysis problems, multiplicative commutativity is relied on to rearrange expressions of the form "c * X + X * d" into "(c + d) * X." Such equations correspond to path problems described by regular languages. In contrast, when Newton's method is used for interprocedural dataflow analysis, the "multiplication" operation involves function composition, and hence is non-commutative: "c * X + X * d" cannot be rearranged into "(c + d) * X." Such equations correspond to path problems described by linear context-free languages (LCFLs).In this paper, we present an improved technique for solving the LCFL sub-problems produced during successive rounds of Newton's method. Our method applies to predicate abstraction, on which most of today's software model checkers rely.

show abstract

“…The problem can be recast using an LCFL equation system to which the algorithm of the present paper can be applied. Grathwohl et al [2014] developed an extension of Kleene algebra with tests to allow a finite amount of mutable state. They noted that one model of their extension could be represented using Kronecker products of 2 × 2 Boolean matrices but did not make further use of that fact.…”

Section: Related Workmentioning

confidence: 99%

Untitled

2017

ACM Trans. Program. Lang. Syst.

View full text Add to dashboard Cite

Recently, Esparza et al. generalized Newton's method-a numerical-analysis algorithm for finding roots of real-valued functions-to a method for finding fixed-points of systems of equations over semirings. Their method provides a new way to solve interprocedural dataflow-analysis problems. As in its real-valued counterpart, each iteration of their method solves a simpler "linearized" problem. One of the reasons this advance is exciting is that some numerical analysts have claimed that "'all' effective and fast iterative [numerical] methods are forms (perhaps very disguised) of Newton's method." However, there is an important difference between the dataflow-analysis and numerical-analysis contexts: When Newton's method is used in numerical-analysis problems, commutativity of multiplication is relied on to rearrange an expression of the form "a * X * b + c * X * d" into "(a * b + c * d) * X." Equations with such expressions correspond to path problems described by regular languages. In contrast, when Newton's method is used for interprocedural dataflow analysis, the "multiplication" operation involves function composition and hence is non-commutative: "a * X * b + c * X * d" cannot be rearranged into "(a * b + c * d) * X." Equations with such expressions correspond to path problems described by linear context-free languages (LCFLs). In this article, we present an improved technique for solving the LCFL sub-problems produced during successive rounds of Newton's method. Our method applies to predicate abstraction, on which most of today's software model checkers rely.

show abstract

Kat + B!

Cited by 15 publications

References 18 publications

Semantic Foundations for Deterministic Dataflow and Stream Processing

Semantic Foundations for Deterministic Dataflow and Stream Processing

Newtonian Program Analysis via Tensor Product

Untitled

Contact Info

Product

Resources

About