Mary Sheeran

Checking Safety Properties Using Induction and a SAT-Solver

We take a fresh look at the problem of how to check safety properties of finite state machines. We are particularly interested in checking safety properties with the help of a SAT-solver. We describe some novel induction-based methods, and show how they are related to more standard fixpoint algorithms for invariance checking. We also present preliminary experimental results in the verification of FPGA cores. This demonstrates the practicality of combining a SAT-solver with induction for safety property checking of hardware in a real design flow.

Lava: hardware design in Haskell

Lava is a tool to assist circuit designers in specifying, designing, verifying and implementing hardware. It is a collection of Haskell modules. The system design exploits functional programming language features, such as monads and type classes, to provide multiple interpretations of circuit descriptions. These interpretations implement standard circuit analyses such as simulation, formal verification and the generation of code for the production of real circuits.Lava also uses polymorphism and higher order functions to provide more abstract and general descriptions than are possible in traditional hardware description languages. Two Fast Fourier Transform circuit examples illustrate this.

A Tutorial on Stålmarck‘s Proof Procedure for PropositionalLogic

We explain Stålmarcks proof procedure for classical propositional logic. The method is implemented in a commercial tool that has been used successfully in real industrial verification projects. Here, we present the proof system underlying the method, and motivate the various design decisions that have resulted in a system that copes well with the large formulas encountered in industrial-scale verification.

Feldspar: A domain specific language for digital signal processing algorithms

A new language, Feldspar, is presented, enabling high-level and platform-independent description of digital signal processing (DSP) algorithms. Feldspar is a pure functional language embedded in Haskell. It offers a high-level dataflow style of programming, as well as a more mathematical style based on vector indices. The key to generating efficient code from such descriptions is a high-level optimization technique called vector fusion. Feldspar is based on a low-level, functional core language which has a relatively small semantic gap to machine-oriented languages like C. The core language serves as the interface to the back-end code generator, which produces C. For very small examples, the generated code performs comparably to hand-written C code when run on a DSP target. While initial results are promising, to achieve good performance on larger examples, issues related to memory access patterns and array copying will have to be addressed.

A Tutorial on Stålmarcks's Proof Procedure for Propositional Logic

We explain St?lmarcks proof procedure for classical propositional logic. The method is implemented in a commercial tool that has been used successfully in real industrial verification projects. Here, we present the proof system underlying the method, and motivate the various design decisions that have resulted in a system that copes well with the large formulas encountered in industrial-scale verification. We also discuss possible applications in Computer Aided Design of electronic circuits.

Expressive array constructs in an embedded GPU kernel programming language

Graphics Processing Units (GPUs) are powerful computing devices that with the advent of CUDA/OpenCL are becomming useful for general purpose computations. Obsidian is an embedded domain specific language that generates CUDA kernels from functional descriptions. A symbolic array construction allows us to guarantee that intermediate arrays are fused away. However, the current array construction has some drawbacks; in particular, arrays cannot be combined efficiently. We add a new type of push arrays to the existing Obsidian system in order to solve this problem. The two array types complement each other, and enable the definition of combinators that both take apart and combine arrays, and that result in efficient generated code. This extension to Obsidian is demonstrated on a sequence of sorting kernels, with good results. The case study also illustrates the use of combinators for expressing the structure of parallel algorithms. The work presented is preliminary, and the combinators presented must be generalised. However, the raw speed of the generated kernels bodes well.

The design and implementation of feldspar an embedded language for digital signal processing

Feldspar is a domain specific language, embedded in Haskell, for programming digital signal processing algorithms. The final aim of a Feldspar program is to generate low level code with good performance. Still, we chose to provide the user with a purely functional DSL. The language is implemented as a minimal, deeply embedded core language, with shallow extensions built upon it. This paper presents full details of the essential parts of the implementation. Our initial conclusion is that this approach works well in our domain, although much work remains.

Obsidian: a domain specific embedded language for parallel programming of graphics processors

We present a domain specific language, embedded in Haskell, for general purpose parallel programming on GPUs. Our intention is to explore the use of connection patterns in parallel programming. We briefly present our earlier work on hardware generation, and outline the current state of GPU architectures and programming models. Finally, we present the current status of the Obsidian project, which aims to make GPU programming easier, without relinquishing detailed control of GPU resources. Both a programming example and some details of the implementation are presented. This is a report on work in progress.

Multiplier reduction tree with logarithmic logic depth and regular connectivity

A novel partial-product reduction circuit for use in integer multiplication is presented. The high-performance multiplier (HPM) reduction tree has the ease of layout of a simple carry-save reduction array, but is in fact a high-speed low-power Dadda-style tree having a worst-case delay which depends on the logarithm (O(log TV)) of the word length N

Designing Arithmetic Circuits by Refinement in Ruby

This paper presents in some detail the systematic derivation of a static bit-level parallel algorithm to implement multiplication of integers, that is to say one which might be implemented as an electronic circuit. The circuit is well known, but the derivation shows that its design can be seen as the consequence of decisions made (and explained) in terms of the abstract algorithm. The systematic derivation serves both as an explanation of the circuit, and as a demonstration that it is correct ‘by construction’. We believe that the technique is applicable to a wide range of similar algorithms.