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### System Demonstration of Spiral: Generator for High-Performance Linear Transform Libraries [chapter]

Yevgen Voronenko, Franz Franchetti, Frédéric de Mesmay, Markus Püschel
2008 Lecture Notes in Computer Science
rewriting framework.  ...  Optimization includes various forms of parallelization. Even though Spiral provides complete automation, its generated libraries run often faster than any existing hand-written code.  ...  The system is based on a set of techniques from different disciplines including linear algebra, algorithms, programming languages, generative programming, rewriting systems, and compilers.  ...

### Computer Generation of General Size Linear Transform Libraries

Yevgen Voronenko, Frédéric de Mesmay, Markus Püschel
2009 2009 International Symposium on Code Generation and Optimization
In this paper we show how to automatically generate general input-size libraries for the domain of linear transforms.  ...  The input to our generator is a formal specification of the transform and the recursive algorithms the library should use; the output is a library that supports general input size, is vectorized and multithreaded  ...  To find the recursion steps automatically, we introduce a "function tag" into P -SPL that identifies those parts of a formula that are to be implemented as separate functions and use rewriting rules that  ...

### Recognizing Strategies

Bastiaan Heeren, Johan Jeuring
2009 Electronical Notes in Theoretical Computer Science
With such a strategy, we can automatically generate worked-out solutions, track the progress of a student by inspecting submitted intermediate answers, and report back suggestions in case the student deviates  ...  A strategy describes valid sequences of transformation rules that solve the exercise at hand, which turns tracking intermediate steps into a parsing problem.  ...  Each symbol of s is either a rewrite rule or a labeled strategy (see the type definition of Strategy): a rewrite rule becomes a symbol with a step, and a labeled strategy is handled by calling the function  ...

### PAM: A process algebra manipulator [chapter]

Huimin Lin
1992 Lecture Notes in Computer Science
The logic that PAM implements is equational logic plus recursion, with some features tailored to the particular requirements of process algebras.  ...  Equational reasoning is implemented by rewriting, while recursion is dealt with by induction. Proofs are constructed interactively, giving users the freedom to control the proof processes.  ...  in formulating the expansion law, to Robin Milner for remarks on fair abstraction rule and on the integration with the Concurrency Workbench, to Faron Moller for detailed comments on the paper, to Simon  ...

### An automatic parallelization framework for OpenAxiom

Yue Li, Gabriel Dos Reis
2011 ACM Communications in Computer Algebra
: T Figure 1 : 1 The workflow of the automatic parallelization framework. a reduction function call.  ...  The framework rewrites reductions in algebraic libraries with their parallel versions.  ...

### A unique formalism for VLSI logical and electrical synthesis

J. Frehel, J.-C. Longchambon, P. Malardier
1987 Revue de Physique Appliquée
Abstract. 2014 This paper presents a unique formalism of knowledge representation of a MOS digital designer in terms of sets of rewriting rules.  ...  Corresponding inference origines extensively use a general commutative unification process with variable arity of operators. Revue Phys.  ...  Let us start again with carry formula (9). we want to automatically find : which can be achieved through the use of the following rewriting rules : These rewriting rules have to be dynamically generated  ...

### Parallelization of Termination Checkers for Algebraic Software

Rui Ding, Haruhiko Sato, Masahito Kurihara
2014 Transactions on Machine Learning and Artificial Intelligence
(or rewrite rules) is called a term rewriting system, which can be interpreted as a functional program executed by the pattern matching and term rewriting.  ...  automatically.  ...  A term rewriting system is a set of rewrite rules used for rewriting a term to another, and can be interpreted as a functional program executed by the pattern matching and term rewriting.  ...

### Dynamic task mapping onto multi-core architectures through stream rewriting

Lars Middendorf, Christian Zebelein, Christian Haubelt
2013 2013 International Conference on Embedded Computer Systems: Architectures, Modeling, and Simulation (SAMOS)
Both the topology of the graph and the state of the tasks are encoded as a stream of tokens, which is iteratively rewritten at multiple positions in parallel.  ...  In this paper, we present a novel approach for mapping the class of series-parallel task graphs onto multicore architectures based on pattern matching.  ...  Fig. 7 . 7 Execution phases of the parallel stream rewriting with 3 cores. Fig. 8 . 8 Topology of the generic parallel and sequential task graphes.  ...

### Mechanically verifying the correctness of the Fast Fourier Transform in ACL2 [chapter]

Ruben A. Gamboa
1998 Lecture Notes in Computer Science
In [10] , Misra introduced the powerlist data structure, which is well suited to express recursive, data-parallel algorithms.  ...  Such simplicity in presentation facilitates reasoning about the resulting algorithms, and in fact Misra was able to give a stunningly simple proof of the correctness of the FFT.  ...  First, if we use a rewrite rule with a false forced hypothesis, the proof attempt will subsequently fail -even if some other rewrite rule could have been applied at that time.  ...

### Parallelising An Erlang Multi-Agent System

Adam D. Barwell, Kevin Hammond, Aleksander Byrski, Wojciech Turek
2016 Zenodo
We present a series of generic Program Shaping rewrite rules, and their implementation as refactorings, and demonstrate their application to an Erlang Multi-Agent System (MAS).  ...  of parallelism.  ...  Conditions are given as predicates to each rule. Each rewrite rule operates within an environment γ allowing access and reference to the current scope of the rewrite rule within the source program.  ...

### Machine Learning for Inductive Theorem Proving [chapter]

Yaqing Jiang, Petros Papapanagiotou, Jacques Fleuriot
2018 Lecture Notes in Computer Science
Over the past few years, machine learning has been successfully combined with automated theorem provers to prove conjectures from proof assistants.  ...  In this work, we explore a combination of machine learning, a simple Boyer-Moore model and ATPs as a means of improving the automation of inductive proofs in the proof assistant HOL Light.  ...  Acknowledgements This research was supported by EPSRC grants: Proof-Peer: Collaborative Theorem Proving EP/L011794/1 and The Integration and Interaction of Multiple Mathematical Reasoning Processes EP/  ...

### A Language for Describing Optimization Strategies [article]

Bastian Hagedorn, Johannes Lenfers, Thomas Koehler, Sergei Gorlatch, Michel Steuwer
2020 arXiv   pre-print
We show how user-defined optimization strategies in Elevate enable the effective optimization of programs expressed in a functional data-parallel language demonstrating competitive performance with Halide  ...  Elevate follows a tradition of prior systems used in different contexts that express optimization strategies as composition of rewrites.  ...  F is a small functional language capable of automatically computing the derivative of arbitrary F functions.  ...

### Using term rewriting to verify software

S. Antoy, J. Gannon
1994 IEEE Transactions on Software Engineering
Verifications are performed with the aid of a program that incorporates term rewriting, structural induction, and heuristics based on ideas used in the Boyer-Moore prover.  ...  This paper describes a uniform approach to the automation of verification tasks associated with while statements, representation functions for abstract data types, generic program units and abstract base  ...  The recursive reduction strategy consists in defining the right sides of rules using only functional composition of symbols of a terminating term rewriting system and the recursive reduction of the corresponding  ...

### Combining interaction and automation in process algebra verification [chapter]

Albert Camilleri, Paola Inverardi, Monica Nesi
1991 Lecture Notes in Computer Science
Most existing verification tools for process algebras allow the correctness of specifications to be checked in a fully automatic fashion.  ...  To achieve our goal, we use the interactive theorem prover ItOL as a framework for supporting the theory of observational congruence of ccs, and provide a set of automatic proof tools, based on the algebraic  ...  Acknowledgements We are grateful to Rocco De Nicola of IEI-CNR for his technical advice and continuous encouragement, and to Robin Gallimore and Roger Fleming of Hewlett-Packard Laboratories for supporting  ...

### Reachability Analysis for Spatial Concurrent Constraint Systems with Extrusion [article]

Miguel Romero, Camilo Rocha
2018 arXiv   pre-print
This work presents an executable rewriting logic semantics of SCCP with extrusion (i.e., process mobility) that uses rewriting modulo SMT, a novel technique that combines the power of term rewriting, matching  ...  The approach is illustrated with examples about the automatic verification of fault-tolerance, consistency, and privacy in distributed spatial and hierarchical systems.  ...  , parallel composition of processes, recursion, and extrusion.  ...
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