A mathematical approach towards hardware design

Today the hardware for embedded systems is often specified in VHDL. However, VHDL describes the system at a rather low level, which is cumbersome and may lead to design faults in large real life applications. There is a need of higher level abstraction mechanisms. In the embedded systems group of the University of Twente we are working on systematic and transformational methods to design hardware architectures, both multi core and single core. The main line in this approach is to start with a straightforward (often mathematical) specification of the problem. The next step is to find some adequate transformations on this specification, in particular to find specific optimizations, to be able to distribute the application over different cores. The result of these transformations is then translated into the functional programming language Haskell since Haskell is close to mathematics and such a translation often is straightforward. Besides, the Haskell code is executable, so one immediately has a simulation of the intended system. Next, the resulting Haskell specification is given to a compiler, called CëaSH (for CAES LAnguage for Synchronous Hardware) which translates the specification into VHDL. The resulting VHDL is synthesizable, so from there on standard VHDL-tooling can be used for synthesis. In this work we primarily focus on streaming applications: i.e. applications that can be modeled as data-flow graphs. At the moment the CëaSH system is ready in prototype form and in the presentation we will give several examples of how it can be used. In these examples it will be shown that the specification code is clear and concise. Furthermore, it is possible to use powerful abstraction mechanisms, such as polymorphism, higher order functions, pattern matching, lambda abstraction, partial application. These features allow a designer to describe circuits in a more natural and concise way than possible with the language elements found in the traditional hardware description languages. In addition we will give some examples of transformations that are possible in a mathematical specification, and which do not suffer from the problems encountered in, e.g., automatic parallelization of nested for-loops in C-programs

Predicativity and parametric polymorphism of Brouwerian implication

A common objection to the definition of intuitionistic implication in the Proof Interpretation is that it is impredicative. I discuss the history of that objection, argue that in Brouwer's writings predicativity of implication is ensured through parametric polymorphism of functions on species, and compare this construal with the alternative approaches to predicative implication of Goodman, Dummett, Prawitz, and Martin-L\"of.Comment: Added further references (Pistone, Poincar\'e, Tabatabai, Van Atten

Strategic polymorphism requires just two combinators!

In previous work, we introduced the notion of functional strategies: first-class generic functions that can traverse terms of any type while mixing uniform and type-specific behaviour. Functional strategies transpose the notion of term rewriting strategies (with coverage of traversal) to the functional programming paradigm. Meanwhile, a number of Haskell-based models and combinator suites were proposed to support generic programming with functional strategies. In the present paper, we provide a compact and matured reconstruction of functional strategies. We capture strategic polymorphism by just two primitive combinators. This is done without commitment to a specific functional language. We analyse the design space for implementational models of functional strategies. For completeness, we also provide an operational reference model for implementing functional strategies (in Haskell). We demonstrate the generality of our approach by reconstructing representative fragments of the Strafunski library for functional strategies.Comment: A preliminary version of this paper was presented at IFL 2002, and included in the informal preproceedings of the worksho

Relational Parametricity and Control

We study the equational theory of Parigot's second-order λμ-calculus in connection with a call-by-name continuation-passing style (CPS) translation into a fragment of the second-order λ-calculus. It is observed that the relational parametricity on the target calculus induces a natural notion of equivalence on the λμ-terms. On the other hand, the unconstrained relational parametricity on the λμ-calculus turns out to be inconsistent with this CPS semantics. Following these facts, we propose to formulate the relational parametricity on the λμ-calculus in a constrained way, which might be called ``focal parametricity''.Comment: 22 pages, for Logical Methods in Computer Scienc