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336 % There should be no need to do such things with IEEEtran.cls V1.6 and later.
337 % (Unless specifically asked to do so by the journal or conference you plan
338 % to submit to, of course. )
340 % correct bad hyphenation here
341 \hyphenation{op-tical net-works semi-conduc-tor}
343 % Macro for certain acronyms in small caps. Doesn't work with the
344 % default font, though (it contains no smallcaps it seems).
345 \def\acro#1{{\small{#1}}}
346 \def\acrop#1{\acro{#1}s}
347 \def\acrotiny#1{{\scriptsize{#1}}}
348 \def\VHDL{\acro{VHDL}}
350 \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}}
351 \def\CLaSHtiny{{\scriptsize{C}}$\lambda$a{\scriptsize{SH}}}
353 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
354 % we'll get something more complex later on.
355 \def\hs#1{\texttt{#1}}
356 \def\quote#1{``{#1}"}
358 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
360 \settowidth{\labelwidth}{#1:}
361 \setlength{\labelsep}{0.5em}
362 \setlength{\leftmargin}{\labelwidth}
363 \addtolength{\leftmargin}{\labelsep}
364 \addtolength{\leftmargin}{\parindent}
365 \setlength{\rightmargin}{0pt}
366 \setlength{\listparindent}{\parindent}
367 \setlength{\itemsep}{0 ex plus 0.2ex}
368 \renewcommand{\makelabel}[1]{##1:\hfil}
373 \usepackage{paralist}
375 \def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}
377 \usepackage{cleveref}
378 \crefname{figure}{figure}{figures}
379 \newcommand{\fref}[1]{\cref{#1}}
380 \newcommand{\Fref}[1]{\Cref{#1}}
382 \usepackage{epstopdf}
384 \epstopdfDeclareGraphicsRule{.svg}{pdf}{.pdf}{rsvg-convert --format=pdf < #1 > \noexpand\OutputFile}
386 %include polycode.fmt
392 % can use linebreaks \\ within to get better formatting as desired
393 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
396 % author names and affiliations
397 % use a multiple column layout for up to three different
399 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards}%, Bert Molenkamp, Sabih H. Gerez}
400 \IEEEauthorblockA{%Computer Architecture for Embedded Systems (CAES)\\
401 Department of EEMCS, University of Twente\\
402 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
403 c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl, j.kuper@@utwente.nl}
404 % \thanks{Supported through the FP7 project: S(o)OS (248465)}
407 % \IEEEauthorblockN{Homer Simpson}
408 % \IEEEauthorblockA{Twentieth Century Fox\\
410 % Email: homer@thesimpsons.com}
412 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
413 % \IEEEauthorblockA{Starfleet Academy\\
414 % San Francisco, California 96678-2391\\
415 % Telephone: (800) 555--1212\\
416 % Fax: (888) 555--1212}}
418 % conference papers do not typically use \thanks and this command
419 % is locked out in conference mode. If really needed, such as for
420 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
421 % after \documentclass
423 % for over three affiliations, or if they all won't fit within the width
424 % of the page, use this alternative format:
426 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
427 %Homer Simpson\IEEEauthorrefmark{2},
428 %James Kirk\IEEEauthorrefmark{3},
429 %Montgomery Scott\IEEEauthorrefmark{3} and
430 %Eldon Tyrell\IEEEauthorrefmark{4}}
431 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
432 %Georgia Institute of Technology,
433 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
434 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
435 %Email: homer@thesimpsons.com}
436 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
437 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
438 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
443 % use for special paper notices
444 %\IEEEspecialpapernotice{(Invited Paper)}
449 % make the title area
454 \CLaSH\ is a functional hardware description language that borrows both its
455 syntax and semantics from the functional programming language Haskell.
456 Polymorphism and higher-order functions provide a level of abstraction and
457 generality that allow a circuit designer to describe circuits in a more
458 natural way than possible in a traditional hardware description language.
460 Circuit descriptions can be translated to synthesizable VHDL using the
461 prototype \CLaSH\ compiler. As the circuit descriptions, simulation code, and
462 test input are also valid Haskell, complete simulations can be compiled as an
463 executable binary by a Haskell compiler allowing high-speed simulation and
466 Stateful descriptions are supported by explicitly making the current state an
467 argument of the function, and the updated state part of the result. In this
468 sense, \CLaSH\ descriptions are the combinational parts of a mealy machine.
470 % IEEEtran.cls defaults to using nonbold math in the Abstract.
471 % This preserves the distinction between vectors and scalars. However,
472 % if the conference you are submitting to favors bold math in the abstract,
473 % then you can use LaTeX's standard command \boldmath at the very start
474 % of the abstract to achieve this. Many IEEE journals/conferences frown on
475 % math in the abstract anyway.
482 % For peer review papers, you can put extra information on the cover
484 % \ifCLASSOPTIONpeerreview
485 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
488 % For peerreview papers, this IEEEtran command inserts a page break and
489 % creates the second title. It will be ignored for other modes.
490 \IEEEpeerreviewmaketitle
492 \section{Introduction}
493 Hardware description languages (\acrop{HDL}) have allowed the productivity of
494 hardware engineers to keep pace with the development of chip technology.
495 Standard \acrop{HDL}, like \VHDL~\cite{VHDL2008} and Verilog~\cite{Verilog},
496 allowed an engineer to describe circuits using a `programming' language. These
497 standard languages are very good at describing detailed hardware properties
498 such as timing behavior, but are generally cumbersome in expressing
499 higher-level abstractions. In an attempt to raise the abstraction level of the
500 descriptions, a great number of approaches based on functional languages has
501 been proposed \cite{Cardelli1981, muFP,DAISY,FHDL,T-Ruby,Hydra,HML2,Hawk1,
502 Lava,ForSyDe1,Wired,reFLect}. The idea of using functional languages for
503 hardware descriptions started in the early 1980s \cite{Cardelli1981,muFP,
504 DAISY,FHDL}, a time which also saw the birth of the currently popular hardware
505 description languages such as \VHDL. Functional languages are especially well
506 suited to describe hardware because combinational circuits can be directly
507 modeled as mathematical functions. Furthermore, functional languages are very
508 good at describing and composing mathematical functions.
510 In an attempt to decrease the amount of work involved in creating all the
511 required tooling, such as parsers and type-checkers, many functional
512 \acrop{HDL} \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired} are embedded as a domain
513 specific language (\acro{DSL}) inside the functional language Haskell
514 \cite{Haskell}. This means that a developer is given a library of Haskell
515 functions and types that together form the language primitives of the
516 \acro{DSL}. The primitive functions used to describe a circuit do not actually
517 process any signals, but instead compose a large domain-specific datatype
518 (which is usually hidden from the designer). This datatype is then further
519 processed by an embedded circuit compiler. This circuit compiler actually
520 runs in the same environment as the description; as a result compile-time and
521 run-time become hard to define, as the embedded circuit compiler is usually
522 compiled by the same Haskell compiler as the circuit description itself.
523 Though the embedded language approach still allows for the support of
524 polymorphism and higher-order functions, it impossible to capture Haskell's
525 choice elements within a circuit description.
527 The approach taken in this research is not to make another \acro{DSL} embedded
528 in Haskell, but to use (a subset of) the Haskell language \emph{itself} for
529 the purpose of describing hardware. By taking this approach, we \emph{can}
530 capture certain language constructs, such as Haskell's choice elements
531 (\hs{if}-expressions, \hs{case}-expressions, pattern matching, etc.), within
532 circuit descriptions. To the best knowledge of the authors, supporting
533 polymorphism, higher-order functions and such an extensive array of
534 choice-elements is new in the domain of functional \acrop{HDL}.
535 % As the hardware descriptions are plain Haskell
536 % functions, these descriptions can be compiled to an executable binary
537 % for simulation using an optimizing Haskell compiler such as the Glasgow
538 % Haskell Compiler (\GHC)~\cite{ghc}.
540 Where descriptions in a conventional \acro{HDL} have an explicit clock for the
541 purposes state and synchronicity, the clock is implied in the context of the
542 research presented in this paper. A circuit designer describes the behavior of
543 the hardware between clock cycles. Many functional \acrop{HDL} model signals
544 as a stream of all values over time; state is then modeled as a delay on this
545 stream of values. The approach taken in this research is to make the current
546 state of a circuit part of the input of the function and the updated state
547 part of the output. The current abstraction of state and time limits the
548 descriptions to synchronous hardware, there is however room within the
549 language to eventually add a different abstraction mechanism that will allow
550 for the modeling of asynchronous systems.
552 Like the traditional \acrop{HDL}, descriptions made in a functional \acro{HDL}
553 must eventually be converted into a netlist. This research also features a
554 prototype translator, which has the same name as the language:
555 \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES} Language for Synchronous Hardware}
556 (pronounced: clash). This compiler converts the Haskell code to equivalently
557 behaving synthesizable \VHDL\ code, ready to be converted to an actual netlist
558 format by an (optimizing) \VHDL\ synthesis tool.
560 Besides trivial circuits such as variants of both the \acro{FIR} filter and
561 the simple \acro{CPU} shown in \Cref{sec:usecases}, the \CLaSH\ compiler has
562 also been able to successfully translate non-trivial functional descriptions
563 such as a streaming reduction circuit~\cite{reductioncircuit} for floating
566 \section{Hardware description in Haskell}
568 \subsection{Function application}
569 Two basic syntactic elements of a functional program are functions
570 and function application. These have a single obvious translation to a
573 \item every function is translated to a component,
574 \item every function argument is translated to an input port,
575 \item the result value of a function is translated to an output port,
577 \item function applications are translated to component instantiations.
579 The result value can have a composite type (such as a tuple), so having
580 just a single result value does not pose any limitation. The actual
581 arguments of a function application are assigned to signals, which are
582 then mapped to the corresponding input ports of the component. The output
583 port of the function is also mapped to a signal, which is used as the
584 result of the application itself. Since every top level function generates
585 its own component, the hierarchy of function calls is reflected in the
586 final netlist, creating a hierarchical description of the hardware.
587 % The separation in different components makes it easier for a developer
588 % to understand and possibly hand-optimize the resulting \VHDL\ output of
589 % the \CLaSH\ compiler.
591 The short example demonstrated below gives an indication of the level of
592 conciseness that can be achieved with functional hardware description
593 languages when compared with the more traditional hardware description
594 languages. The example is a combinational multiply-accumulate circuit that
595 works for \emph{any} word length (this type of polymorphism will be
596 further elaborated in \Cref{sec:polymorhpism}). The corresponding netlist
597 is depicted in \Cref{img:mac-comb}.
600 mac a b c = add (mul a b) c
604 \centerline{\includegraphics{mac.svg}}
605 \caption{Combinatorial Multiply-Accumulate}
609 The use of a composite result value is demonstrated in the next example,
610 where the multiply-accumulate circuit not only returns the accumulation
611 result, but also the intermediate multiplication result. Its corresponding
612 netlist can be see in \Cref{img:mac-comb-composite}.
615 mac a b c = (z, add z c)
621 \centerline{\includegraphics{mac-nocurry.svg}}
622 \caption{Combinatorial Multiply-Accumulate (composite output)}
623 \label{img:mac-comb-composite}
627 In Haskell, choice can be achieved by a large set of syntactic elements,
628 consisting of: \hs{case} expressions, \hs{if-then-else} expressions,
629 pattern matching, and guards. The most general of these are the \hs{case}
630 expressions (\hs{if} expressions can be very directly translated to
631 \hs{case} expressions). A \hs{case} expression is translated to a
632 multiplexer, where the control value is fed into a number of
633 comparators and their output is used to compose the selection port
634 of the multiplexer. The result of each alternative is linked to the
635 corresponding input port on the multiplexer.
636 % A \hs{case} expression can in turn simply be translated to a conditional
637 % assignment in \VHDL, where the conditions use equality comparisons
638 % against the constructors in the \hs{case} expressions.
639 We can see two versions of a contrived example below, the first
640 using a \hs{case} expression and the other using an \hs{if-then-else}
641 expression. Both examples sums two values when they are
642 equal or non-equal (depending on the given predicate, the \hs{pred}
643 variable) and returns 0 otherwise. The \hs{pred} variable has the
644 following, user-defined, enumeration datatype:
647 data Pred = Equal | NotEqual
650 The naive netlist corresponding to both versions of the example is
651 depicted in \Cref{img:choice}. Note that the \hs{pred} variable is only
652 compared to the \hs{Equal} value, as an inequality immediately implies
653 that the \hs{pred} variable has a \hs{NotEqual} value.
656 sumif pred a b = case pred of
657 Equal -> case a == b of
660 NotEqual -> case a != b of
667 if pred == Equal then
668 if a == b then a + b else 0
670 if a != b then a + b else 0
674 \centerline{\includegraphics{choice-case.svg}}
675 \caption{Choice - sumif}
679 A user-friendly and also very powerful form of choice that is not found in
680 the traditional hardware description languages is pattern matching. A
681 function can be defined in multiple clauses, where each clause corresponds
682 to a pattern. When an argument matches a pattern, the corresponding clause
683 will be used. Expressions can also contain guards, where the expression is
684 only executed if the guard evaluates to true, and continues with the next
685 clause if the guard evaluates to false. Like \hs{if-then-else}
686 expressions, pattern matching and guards have a (straightforward)
687 translation to \hs{case} expressions and can as such be mapped to
688 multiplexers. A third version of the earlier example, using both pattern
689 matching and guards, can be seen below. The guard is the expression that
690 follows the vertical bar (\hs{|}) and precedes the assignment operator
691 (\hs{=}). The \hs{otherwise} guards always evaluate to \hs{true}.
693 The version using pattern matching and guards corresponds to the same
694 naive netlist representation (\Cref{img:choice}) as the earlier two
695 versions of the example.
698 sumif Equal a b | a == b = a + b
700 sumif NotEqual a b | a != b = a + b
705 % \centerline{\includegraphics{choice-ifthenelse}}
706 % \caption{Choice - \emph{if-then-else}}
711 Haskell is a statically-typed language, meaning that the type of a
712 variable or function is determined at compile-time. Not all of Haskell's
713 typing constructs have a clear translation to hardware, this section will
714 therefore only deal with the types that do have a clear correspondence
715 to hardware. The translatable types are divided into two categories:
716 \emph{built-in} types and \emph{user-defined} types. Built-in types are
717 those types for which a fixed translation is defined within the \CLaSH\
718 compiler. The \CLaSH\ compiler has generic translation rules to
719 translated the user-defined types described below.
721 The \CLaSH\ compiler is able to infer unspecified types,
722 meaning that a developer does not have to annotate every function with a
723 type signature (even if it is good practice to do so).
725 % Translation of two most basic functional concepts has been
726 % discussed: function application and choice. Before looking further
727 % into less obvious concepts like higher-order expressions and
728 % polymorphism, the possible types that can be used in hardware
729 % descriptions will be discussed.
731 % Some way is needed to translate every value used to its hardware
732 % equivalents. In particular, this means a hardware equivalent for
733 % every \emph{type} used in a hardware description is needed.
735 % The following types are \emph{built-in}, meaning that their hardware
736 % translation is fixed into the \CLaSH\ compiler. A designer can also
737 % define his own types, which will be translated into hardware types
738 % using translation rules that are discussed later on.
740 \subsubsection{Built-in types}
741 The following types have fixed translations defined within the \CLaSH\
745 the most basic type available. It can have two values:
746 \hs{Low} or \hs{High}.
747 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
749 this is a basic logic type. It can have two values: \hs{True}
751 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
752 % type (where a value of \hs{True} corresponds to a value of
754 Supporting the Bool type is required in order to support the
755 \hs{if-then-else} expression, which requires a \hs{Bool} value for
757 \item[\bf{SizedWord}, \bf{SizedInt}]
758 these are types to represent integers. A \hs{SizedWord} is unsigned,
759 while a \hs{SizedInt} is signed. Both are parametrizable in their
761 % , so you can define an unsigned word of 32 bits wide as follows:
764 % type Word32 = SizedWord D32
767 % Here, a type synonym \hs{Word32} is defined that is equal to the
768 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
769 % \hs{D32} is the \emph{type level representation} of the decimal
770 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
771 % types are translated to the \VHDL\ \texttt{unsigned} and
772 % \texttt{signed} respectively.
774 this is a vector type that can contain elements of any other type and
775 has a fixed length. The \hs{Vector} type constructor takes two type
776 arguments: the length of the vector and the type of the elements
777 contained in it. The short-hand notation used for the vector type in
778 the rest of paper is: \hs{[a|n]}, here \hs{a} is the element
779 type, and \hs{n} is the length of the vector. Note that this is
780 a notation used in this paper only, vectors are slightly more
781 verbose in real \CLaSH\ descriptions.
782 % The state type of an 8 element register bank would then for example
786 % type RegisterState = Vector D8 Word32
789 % Here, a type synonym \hs{RegisterState} is defined that is equal to
790 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
791 % type level representation of the decimal number 8) and \hs{Word32}
792 % (The 32 bit word type as defined above). In other words, the
793 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
794 % vector is translated to a \VHDL\ array type.
796 this is another type to describe integers, but unlike the previous
797 two it has no specific bit-width, but an upper bound. This means that
798 its range is not limited to powers of two, but can be any number.
799 An \hs{Index} only has an upper bound, its lower bound is
800 implicitly zero. The main purpose of the \hs{Index} type is to be
801 used as an index to a \hs{Vector}.
803 % \comment{TODO: Perhaps remove this example?} To define an index for
804 % the 8 element vector above, we would do:
807 % type RegisterIndex = RangedWord D7
810 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
811 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
812 % other words, this defines an unsigned word with values from
813 % 0 to 7 (inclusive). This word can be be used to index the
814 % 8 element vector \hs{RegisterState} above. This type is translated
815 % to the \texttt{unsigned} \VHDL type.
818 \subsubsection{User-defined types}
819 There are three ways to define new types in Haskell: algebraic
820 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
821 keyword and datatype renaming constructs with the \hs{newtype} keyword.
822 \GHC\ offers a few more advanced ways to introduce types (type families,
823 existential typing, {\acro{GADT}}s, etc.) which are not standard Haskell.
824 As it is currently unclear how these advanced type constructs correspond
825 to hardware, they are for now unsupported by the \CLaSH\ compiler.
827 Only an algebraic datatype declaration actually introduces a
828 completely new type. Type synonyms and type renaming only define new
829 names for existing types, where synonyms are completely interchangeable
830 and type renaming requires explicit conversions. Therefore, these do not
831 need any particular translation, a synonym or renamed type will just use
832 the same representation as the original type.
834 For algebraic types, we can make the following distinctions:
836 \item[\bf{Single constructor}]
837 Algebraic datatypes with a single constructor with one or more
838 fields, are essentially a way to pack a few values together in a
839 record-like structure. Haskell's built-in tuple types are also defined
840 as single constructor algebraic types (but with a bit of
841 syntactic sugar). An example of a single constructor type is the
842 following pair of integers:
844 data IntPair = IntPair Int Int
846 % These types are translated to \VHDL\ record types, with one field
847 % for every field in the constructor.
848 \item[\bf{No fields}]
849 Algebraic datatypes with multiple constructors, but without any
850 fields are essentially a way to get an enumeration-like type
851 containing alternatives. Note that Haskell's \hs{Bool} type is also
852 defined as an enumeration type, but that there is a fixed translation
853 for that type within the \CLaSH\ compiler. An example of such an
854 enumeration type is the type that represents the colors in a traffic
857 data TrafficLight = Red | Orange | Green
859 % These types are translated to \VHDL\ enumerations, with one
860 % value for each constructor. This allows references to these
861 % constructors to be translated to the corresponding enumeration
863 \item[\bf{Multiple constructors with fields}]
864 Algebraic datatypes with multiple constructors, where at least
865 one of these constructors has one or more fields are currently not
869 \subsection{Polymorphism}\label{sec:polymorhpism}
870 A powerful feature of most (functional) programming languages is
871 polymorphism, it allows a function to handle values of different data
872 types in a uniform way. Haskell supports \emph{parametric
873 polymorphism}~\cite{polymorphism}, meaning functions can be written
874 without mention of any specific type and can be used transparently with
875 any number of new types.
877 As an example of a parametric polymorphic function, consider the type of
878 the following \hs{append} function, which appends an element to a
879 vector:\footnote{The \hs{::} operator is used to annotate a function
883 append :: [a|n] -> a -> [a|n + 1]
886 This type is parameterized by \hs{a}, which can contain any type at
887 all. This means that \hs{append} can append an element to a vector,
888 regardless of the type of the elements in the list (as long as the type of
889 the value to be added is of the same type as the values in the vector).
890 This kind of polymorphism is extremely useful in hardware designs to make
891 operations work on a vector without knowing exactly what elements are
892 inside, routing signals without knowing exactly what kinds of signals
893 these are, or working with a vector without knowing exactly how long it
894 is. Polymorphism also plays an important role in most higher order
895 functions, as we will see in the next section.
897 Another type of polymorphism is \emph{ad-hoc
898 polymorphism}~\cite{polymorphism}, which refers to polymorphic
899 functions which can be applied to arguments of different types, but which
900 behave differently depending on the type of the argument to which they are
901 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
902 type classes, where a class definition provides the general interface of a
903 function, and class instances define the functionality for the specific
904 types. An example of such a type class is the \hs{Num} class, which
905 contains all of Haskell's numerical operations. A designer can make use
906 of this ad-hoc polymorphism by adding a constraint to a parametrically
907 polymorphic type variable. Such a constraint indicates that the type
908 variable can only be instantiated to a type whose members supports the
909 overloaded functions associated with the type class.
911 As an example we will take a look at type signature of the function
912 \hs{sum}, which sums the values in a vector:
914 sum :: Num a => [a|n] -> a
917 This type is again parameterized by \hs{a}, but it can only contain
918 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
919 we know that the addition (+) operator is defined for that type.
920 \CLaSH's built-in numerical types are also instances of the \hs{Num}
921 class, so we can use the addition operator (and thus the \hs{sum}
922 function) with \hs{SizedWords} as well as with \hs{SizedInts}.
924 In \CLaSH, parametric polymorphism is completely supported. Any function
925 defined can have any number of unconstrained type parameters. The \CLaSH\
926 compiler will infer the type of every such argument depending on how the
927 function is applied. There is however one constraint: the top level
928 function that is being translated can not have any polymorphic arguments.
929 The arguments can not be polymorphic as the function is never applied and
930 consequently there is no way to determine the actual types for the type
933 \CLaSH\ does \emph{currently} not support\emph{ user-defined} type
934 classes, but does use some of the standard Haskell type classes for its
935 built-in function, such as: \hs{Num} for numerical operations, \hs{Eq} for
936 the equality operators, and \hs{Ord} for the comparison/order operators.
938 \subsection{Higher-order functions \& values}
939 Another powerful abstraction mechanism in functional languages, is
940 the concept of \emph{higher-order functions}, or \emph{functions as
941 a first class value}. This allows a function to be treated as a
942 value and be passed around, even as the argument of another
943 function. The following example should clarify this concept:
945 %format not = "\mathit{not}"
947 negateVector xs = map not xs
950 The code above defines the \hs{negateVector} function, which takes a
951 vector of booleans, \hs{xs}, and returns a vector where all the values are
952 negated. It achieves this by calling the \hs{map} function, and passing it
953 \emph{another function}, boolean negation, and the vector of booleans,
954 \hs{xs}. The \hs{map} function applies the negation function to all the
955 elements in the vector.
957 The \hs{map} function is called a higher-order function, since it takes
958 another function as an argument. Also note that \hs{map} is again a
959 parametric polymorphic function: it does not pose any constraints on the
960 type of the input vector, other than that its elements must have the same
961 type as the first argument of the function passed to \hs{map}. The element
962 type of the resulting vector is equal to the return type of the function
963 passed, which need not necessarily be the same as the element type of the
964 input vector. All of these characteristics can readily be inferred from
965 the type signature belonging to \hs{map}:
968 map :: (a -> b) -> [a|n] -> [b|n]
971 So far, only functions have been used as higher-order values. In
972 Haskell, there are two more ways to obtain a function-typed value:
973 partial application and lambda abstraction. Partial application
974 means that a function that takes multiple arguments can be applied
975 to a single argument, and the result will again be a function (but
976 that takes one argument less). As an example, consider the following
977 expression, that adds one to every element of a vector:
983 Here, the expression \hs{(add 1)} is the partial application of the
984 addition function to the value \hs{1}, which is again a function that
985 adds one to its (next) argument. A lambda expression allows one to
986 introduce an anonymous function in any expression. Consider the following
987 expression, which again adds one to every element of a vector:
993 Finally, not only built-in functions can have higher order
994 arguments, but any function defined in \CLaSH can have function
995 arguments. This allows the hardware designer to use a powerful
996 abstraction mechanism in his designs and have an optimal amount of
997 code reuse. The only exception is again the top-level function: if a
998 function-typed argument is not applied with an actual function, no
999 hardware can be generated.
1001 % \comment{TODO: Describe ALU example (no code)}
1004 A very important concept in hardware is the concept of state. In a
1005 stateful design, the outputs depend on the history of the inputs, or the
1006 state. State is usually stored in registers, which retain their value
1007 during a clock cycle. As we want to describe more than simple
1008 combinational designs, \CLaSH\ needs an abstraction mechanism for state.
1010 An important property in Haskell, and in most other functional languages,
1011 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
1014 \item given the same arguments twice, it should return the same value in
1016 \item that the function has no observable side-effects.
1018 % This purity property is important for functional languages, since it
1019 % enables all kinds of mathematical reasoning that could not be guaranteed
1020 % correct for impure functions.
1021 Pure functions are as such a perfect match for combinational circuits,
1022 where the output solely depends on the inputs. When a circuit has state
1023 however, it can no longer be simply described by a pure function.
1024 % Simply removing the purity property is not a valid option, as the
1025 % language would then lose many of it mathematical properties.
1026 In \CLaSH\ we deal with the concept of state in pure functions by making
1027 current value of the state an additional argument of the function and the
1028 updated state part of result. In this sense the descriptions made in
1029 \CLaSH\ are the combinational parts of a mealy machine.
1031 A simple example is adding an accumulator register to the earlier
1032 multiply-accumulate circuit, of which the resulting netlist can be seen in
1033 \Cref{img:mac-state}:
1036 macS (State c) a b = (State c', c')
1042 \centerline{\includegraphics{mac-state.svg}}
1043 \caption{Stateful Multiply-Accumulate}
1044 \label{img:mac-state}
1047 Note that the \hs{macS} function returns bot the new state and the value
1048 of the output port. The \hs{State} keyword indicates which arguments are
1049 part of the current state, and what part of the output is part of the
1050 updated state. This aspect will also be reflected in the type signature of
1051 the function. Abstracting the state of a circuit in this way makes it very
1052 explicit: which variables are part of the state is completely determined
1053 by the type signature. This approach to state is well suited to be used in
1054 combination with the existing code and language features, such as all the
1055 choice elements, as state values are just normal values. We can simulate
1056 stateful descriptions using the recursive \hs{run} function:
1059 run f s (i : inps) = o : (run f s' inps)
1064 The \hs{(:)} operator is the list concatenation operator, where the
1065 left-hand side is the head of a list and the right-hand side is the
1066 remainder of the list. The \hs{run} function applies the function the
1067 developer wants to simulate, \hs{f}, to the current state, \hs{s}, and the
1068 first input value, \hs{i}. The result is the first output value, \hs{o},
1069 and the updated state \hs{s'}. The next iteration of the \hs{run} function
1070 is then called with the updated state, \hs{s'}, and the rest of the
1071 inputs, \hs{inps}. For the time being, and in the context of this paper,
1072 It is assumed that there is one input per clock cycle.
1073 Also note how the order of the input, output, and state in the \hs{run}
1074 function corresponds with the order of the input, output and state of the
1075 \hs{macS} function described earlier.
1077 As the \hs{run} function, the hardware description, and the test
1078 inputs are also valid Haskell, the complete simulation can be compiled to
1079 an executable binary by an optimizing Haskell compiler, or executed in an
1080 Haskell interpreter. Both simulation paths are much faster than first
1081 translating the description to \VHDL\ and then running a \VHDL\
1084 \section{The \CLaSH\ compiler}
1085 An important aspect in this research is the creation of the prototype
1086 compiler, which allows us to translate descriptions made in the \CLaSH\
1087 language as described in the previous section to synthesizable \VHDL, allowing
1088 a designer to actually run a \CLaSH\ design on an \acro{FPGA}.
1090 The Glasgow Haskell Compiler (\GHC) is an open-source Haskell compiler that
1091 also provides a high level API to most of its internals. The availability of
1092 this high-level API obviated the need to design many of the tedious parts of
1093 the prototype compiler, such as the parser, semantic checker, and especially
1094 the type-checker. These parts together form the front-end of the prototype compiler pipeline, as seen in \Cref{img:compilerpipeline}.
1097 \centerline{\includegraphics{compilerpipeline.svg}}
1098 \caption{\CLaSHtiny\ compiler pipeline}
1099 \label{img:compilerpipeline}
1102 The output of the \GHC\ front-end consists of the translation of the original Haskell description in \emph{Core}~\cite{Sulzmann2007}, which is a smaller, typed, functional language. This \emph{Core} language is relatively easy to process compared to the larger Haskell language. A description in \emph{Core} can still contain elements which have no direct translation to hardware, such as polymorphic types and function-valued arguments. Such a description needs to be transformed to a \emph{normal form}, which only contains elements that have a direct translation. The second stage of the compiler, the \emph{normalization} phase, exhaustively applies a set of \emph{meaning-preserving} transformations on the \emph{Core} description until this description is in a \emph{normal form}. This set of transformations includes transformations typically found in reduction systems and lambda calculus~\cite{lambdacalculus}, such as $\beta$-reduction and $\eta$-expansion. It also includes self-defined transformations that are responsible for the reduction of higher-order functions to `regular' first-order functions.
1104 The final step in the compiler pipeline is the translation to a \VHDL\
1105 \emph{netlist}, which is a straightforward process due to resemblance of a
1106 normalized description and a set of concurrent signal assignments. We call the
1107 end-product of the \CLaSH\ compiler a \VHDL\ \emph{netlist} as the resulting
1108 \VHDL\ resembles an actual netlist description and not idiomatic \VHDL.
1111 \label{sec:usecases}
1112 \subsection{FIR Filter}
1113 As an example of a common hardware design where the use of higher-order
1114 functions leads to a very natural description is a \acro{FIR} filter, which is
1115 basically the dot-product of two vectors:
1118 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1121 A \acro{FIR} filter multiplies fixed constants ($h$) with the current
1122 and a few previous input samples ($x$). Each of these multiplications
1123 are summed, to produce the result at time $t$. The equation of a \acro{FIR}
1124 filter is indeed equivalent to the equation of the dot-product, which is
1128 \mathbf{a}\bullet\mathbf{b} = \sum\nolimits_{i = 0}^{n - 1} {a_i \cdot b_i }
1131 We can easily and directly implement the equation for the dot-product
1132 using higher-order functions:
1135 as *+* bs = foldl1 (+) (zipWith (*) as bs)
1138 The \hs{zipWith} function is very similar to the \hs{map} function seen
1139 earlier: It takes a function, two vectors, and then applies the function to
1140 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1141 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]}).
1143 The \hs{foldl1} function takes a binary function, a single vector, and applies
1144 the function to the first two elements of the vector. It then applies the
1145 function to the result of the first application and the next element in the
1146 vector. This continues until the end of the vector is reached. The result of
1147 the \hs{foldl1} function is the result of the last application. It is obvious
1148 that the \hs{zipWith (*)} function is pairwise multiplication and that the
1149 \hs{foldl1 (+)} function is summation.
1150 % Returning to the actual \acro{FIR} filter, we will slightly change the
1151 % equation describing it, so as to make the translation to code more obvious and
1152 % concise. What we do is change the definition of the vector of input samples
1153 % and delay the computation by one sample. Instead of having the input sample
1154 % received at time $t$ stored in $x_t$, $x_0$ now always stores the newest
1155 % sample, and $x_i$ stores the $ith$ previous sample. This changes the equation
1156 % to the following (note that this is completely equivalent to the original
1157 % equation, just with a different definition of $x$ that will better suit the
1158 % transformation to code):
1161 % y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1163 The complete definition of the \acro{FIR} filter in code then becomes:
1166 fir (State (xs,hs)) x =
1167 (State (x >> xs,hs), (x +> xs) *+* hs)
1170 Where the vector \hs{xs} contains the previous input samples, the vector \hs{hs} contains the \acro{FIR} coefficients, and \hs{x} is the current input sample. The concatenate operator (\hs{+>}) creates a new vector by placing the current sample (\hs{x}) in front of the previous samples vector (\hs{xs}). The code for the shift (\hs{>>}) operator, that adds the new input sample (\hs{x}) to the list of previous input samples (\hs{xs}) and removes the oldest sample, is shown below:
1173 x >> xs = x +> init xs
1176 Where the \hs{init} function returns all but the last element of a vector.
1177 The resulting netlist of a 4-taps \acro{FIR} filter, created by specializing
1178 the vectors of the \acro{FIR} code to a length of 4, is depicted in
1182 \centerline{\includegraphics{4tapfir.svg}}
1183 \caption{4-taps \acrotiny{FIR} Filter}
1187 \subsection{Higher-order CPU}
1188 The following simple \acro{CPU} is an example of user-defined higher order
1189 functions and pattern matching. The \acro{CPU} consists of four function
1190 units, of which three have a fixed function and one can perform certain less
1193 The \acro{CPU} contains a number of data sources, represented by the
1194 horizontal wires in \Cref{img:highordcpu}. These data sources offer the
1195 previous outputs of each function units, along with the single data input the
1196 \acro{CPU} has and two fixed initialization values.
1198 Each of the function units has both its operands connected to all data
1199 sources, and can be programmed to select any data source for either
1200 operand. In addition, the leftmost function unit has an additional
1201 opcode input to select the operation it performs. The output of the rightmost
1202 function unit is also the output of the entire \acro{CPU}.
1204 Looking at the code, the function unit (\hs{fu}) is the most simple. It
1205 arranges the operand selection for the function unit. Note that it does not
1206 define the actual operation that takes place inside the function unit,
1207 but simply accepts the (higher-order) argument \hs{op} which is a function
1208 of two arguments that defines the operation.
1211 fu op inputs (addr1, addr2) = regIn
1218 The \hs{multiop} function defines the operation that takes place in the
1219 leftmost function unit. It is essentially a simple three operation \acro{ALU}
1220 that makes good use of pattern matching and guards in its description.
1221 The \hs{shift} function used here shifts its first operand by the number
1222 of bits indicated in the second operand, the \hs{xor} function produces
1223 the bitwise xor of its operands.
1226 data Opcode = Shift | Xor | Equal
1228 multiop :: Opcode -> Word -> Word -> Word
1229 multiop Shift a b = shift a b
1230 multiop Xor a b = xor a b
1231 multiop Equal a b | a == b = 1
1235 The \acro{CPU} function ties everything together. It applies the \hs{fu}
1236 function four times, to create a different function unit each time. The
1237 first application is interesting, because it does not just pass a
1238 function to \hs{fu}, but a partial application of \hs{multiop}. This
1239 shows how the first function unit effectively gets an extra input,
1240 compared to the others.
1242 The vector \hs{inputs} is the set of data sources, which is passed to
1243 each function unit as a set of possible operants. The \acro{CPU} also receives
1244 a vector of address pairs, which are used by each function unit to select
1245 their operand. The application of the function units to the \hs{inputs} and
1246 \hs{addrs} arguments seems quite repetitive and could be rewritten to use
1247 a combination of the \hs{map} and \hs{zipwith} functions instead.
1248 However, the prototype compiler does not currently support working with lists of functions, so a more explicit version of the code is given instead.
1251 type CpuState = State [Word | 4]
1253 cpu :: CpuState -> Word -> [(Index 6, Index 6) | 4]
1254 -> Opcode -> (CpuState, Word)
1255 cpu (State s) input addrs opc = (State s', out)
1257 s' = [ fu (multiop opc) inputs (addrs!0)
1258 , fu add inputs (addrs!1)
1259 , fu sub inputs (addrs!2)
1260 , fu mul inputs (addrs!3)
1262 inputs = 0 +> (1 +> (input +> s))
1267 \centerline{\includegraphics{highordcpu.svg}}
1268 \caption{CPU with higher-order Function Units}
1269 \label{img:highordcpu}
1272 This is still a simple example, but it could form the basis
1273 of an actual design, in which the same techniques can be reused.
1275 \section{Related work}
1276 This section describes the features of existing (functional) hardware
1277 description languages and highlights the advantages that this research has
1280 Many functional hardware description languages have been developed over the
1281 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1282 extension of Backus' \acro{FP} language to synchronous streams, designed
1283 particularly for describing and reasoning about regular circuits. The
1284 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1285 circuits, and has a particular focus on layout.
1287 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1288 functional language \acro{ML}, and has support for polymorphic types and
1289 higher-order functions. Published work suggests that there is no direct
1290 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1291 be translated to \VHDL\ and that the translated description can then be
1292 simulated in a \VHDL\ simulator. Also not all of the mentioned language
1293 features of \acro{HML} could be translated to hardware. The \CLaSH\ compiler
1294 on the other hand can correctly translate all of the language constructs
1295 mentioned in this paper to a netlist format.
1297 Like the work presented in this paper, many functional hardware description languages have some sort of foundation in the functional programming language Haskell. Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1298 specifications used to model the behavior of superscalar microprocessors. Hawk
1299 specifications can be simulated; to the best knowledge of the authors there is however no support for automated circuit synthesis.
1301 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1302 models, which can (manually) be transformed into an implementation model using
1303 semantic preserving transformations. A designer can model systems using
1304 heterogeneous models of computation, which include continuous time,
1305 synchronous and untimed models of computation. Using so-called domain
1306 interfaces a designer can simulate electronic systems which have both analog
1307 as digital parts. ForSyDe has several backends including simulation and
1308 automated synthesis, though automated synthesis is restricted to the
1309 synchronous model of computation within ForSyDe. Unlike \CLaSH\ there is no
1310 support for the automated synthesis of descriptions that contain polymorphism
1311 or higher-order functions.
1313 Lava~\cite{Lava} is a hardware description language that focuses on the
1314 structural representation of hardware. Besides support for simulation and
1315 circuit synthesis, Lava descriptions can be interfaced with formal method
1316 tools for formal verification. Lava descriptions are actually circuit
1317 generators when viewed from a synthesis viewpoint, in that the language
1318 elements of Haskell, such as choice, can be used to guide the circuit
1319 generation. If a developer wants to insert a choice element inside an actual
1320 circuit he will have to explicitly instantiate a multiplexer-like component.
1321 In this respect \CLaSH\ differs from Lava, in that all the choice elements,
1322 such as case-statements and pattern matching, are synthesized to choice
1323 elements in the eventual circuit. As such, richer control structures can both
1324 be specified and synthesized in \CLaSH\ compared to any of the embedded
1325 languages such as Hawk, ForSyDe and Lava.
1327 The merits of polymorphic typing, combined with higher-order functions, are
1328 now also recognized in the `main-stream' hardware description languages,
1329 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 support
1330 for generics has been extended to types and subprograms, allowing a developer
1331 to describe components with polymorphic ports and function-valued arguments.
1332 Note that the types and subprograms still require an explicit generic map,
1333 whereas types can be automatically inferred, and function-values can be
1334 automatically propagated by the \CLaSH\ compiler. There are also no (generally
1335 available) \VHDL\ synthesis tools that currently support the \VHDL-2008
1336 standard, and thus the synthesis of polymorphic types and function-valued
1339 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1341 % A functional language designed specifically for hardware design is
1342 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1343 % language called \acro{FL}~\cite{FL} to la
1345 % An example of a floating figure using the graphicx package.
1346 % Note that \label must occur AFTER (or within) \caption.
1347 % For figures, \caption should occur after the \includegraphics.
1348 % Note that IEEEtran v1.7 and later has special internal code that
1349 % is designed to preserve the operation of \label within \caption
1350 % even when the captionsoff option is in effect. However, because
1351 % of issues like this, it may be the safest practice to put all your
1352 % \label just after \caption rather than within \caption{}.
1354 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1355 % option should be used if it is desired that the figures are to be
1356 % displayed while in draft mode.
1360 %\includegraphics[width=2.5in]{myfigure}
1361 % where an .eps filename suffix will be assumed under latex,
1362 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1363 % via \DeclareGraphicsExtensions.
1364 %\caption{Simulation Results}
1368 % Note that IEEE typically puts floats only at the top, even when this
1369 % results in a large percentage of a column being occupied by floats.
1372 % An example of a double column floating figure using two subfigures.
1373 % (The subfig.sty package must be loaded for this to work.)
1374 % The subfigure \label commands are set within each subfloat command, the
1375 % \label for the overall figure must come after \caption.
1376 % \hfil must be used as a separator to get equal spacing.
1377 % The subfigure.sty package works much the same way, except \subfigure is
1378 % used instead of \subfloat.
1380 %\begin{figure*}[!t]
1381 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1382 %\label{fig_first_case}}
1384 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1385 %\label{fig_second_case}}}
1386 %\caption{Simulation results}
1390 % Note that often IEEE papers with subfigures do not employ subfigure
1391 % captions (using the optional argument to \subfloat), but instead will
1392 % reference/describe all of them (a), (b), etc., within the main caption.
1395 % An example of a floating table. Note that, for IEEE style tables, the
1396 % \caption command should come BEFORE the table. Table text will default to
1397 % \footnotesize as IEEE normally uses this smaller font for tables.
1398 % The \label must come after \caption as always.
1401 %% increase table row spacing, adjust to taste
1402 %\renewcommand{\arraystretch}{1.3}
1403 % if using array.sty, it might be a good idea to tweak the value of
1404 % \extrarowheight as needed to properly center the text within the cells
1405 %\caption{An Example of a Table}
1406 %\label{table_example}
1408 %% Some packages, such as MDW tools, offer better commands for making tables
1409 %% than the plain LaTeX2e tabular which is used here.
1410 %\begin{tabular}{|c||c|}
1420 % Note that IEEE does not put floats in the very first column - or typically
1421 % anywhere on the first page for that matter. Also, in-text middle ("here")
1422 % positioning is not used. Most IEEE journals/conferences use top floats
1423 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1424 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1425 % command of the stfloats package.
1429 \section{Conclusion}
1430 This research demonstrates once more that functional languages are well suited
1431 for hardware descriptions: function applications provide an elegant notation
1432 for component instantiation. Where this research goes beyond the existing
1433 (functional) hardware descriptions languages is the inclusion of various
1434 choice elements, such as patter matching, that are well suited to describe the
1435 conditional assignments in control-oriented hardware. Besides being able to
1436 translate these basic constructs to synthesizable \VHDL, the prototype
1437 compiler can also correctly translate descriptions that contain both
1438 polymorphic types and function-valued arguments.
1440 Where recent functional hardware description languages have mostly opted to
1441 embed themselves in an existing functional language, this research features a
1442 `true' compiler. As a result there is a clear distinction between compile-time
1443 and run-time, which allows a myriad of choice constructs to be part of the
1444 actual circuit description; a feature the embedded hardware description
1445 languages do not offer.
1447 \section{Future Work}
1448 The choice of describing state explicitly as extra arguments and results can
1449 be seen as a mixed blessing. Even though the description that use state are
1450 usually very clear, one finds that dealing with unpacking, passing, receiving
1451 and repacking can become tedious and even error-prone, especially in the case
1452 of sub-states. Removing this boilerplate, or finding a more suitable
1453 abstraction mechanism would make \CLaSH\ easier to use.
1455 The transformations in normalization phase of the prototype compiler were
1456 developed in an ad-hoc manner, which makes the existence of many desirable
1457 properties unclear. Such properties include whether the complete set of
1458 transformations will always lead to a normal form or if the normalization
1459 process always terminates. Though various use cases suggests that these
1460 properties usually hold, they have not been formally proven. A systematic
1461 approach to defining the set of transformations allows one to proof that the
1462 earlier mentioned properties do indeed exist.
1464 % conference papers do not normally have an appendix
1467 % use section* for acknowledgement
1468 % \section*{Acknowledgment}
1470 % The authors would like to thank...
1472 % trigger a \newpage just before the given reference
1473 % number - used to balance the columns on the last page
1474 % adjust value as needed - may need to be readjusted if
1475 % the document is modified later
1476 % \IEEEtriggeratref{14}
1477 % The "triggered" command can be changed if desired:
1478 %\IEEEtriggercmd{\enlargethispage{-5in}}
1480 % references section
1482 % can use a bibliography generated by BibTeX as a .bbl file
1483 % BibTeX documentation can be easily obtained at:
1484 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1485 % The IEEEtran BibTeX style support page is at:
1486 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1487 \bibliographystyle{IEEEtran}
1488 % argument is your BibTeX string definitions and bibliography database(s)
1489 \bibliography{clash}
1491 % <OR> manually copy in the resultant .bbl file
1492 % set second argument of \begin to the number of references
1493 % (used to reserve space for the reference number labels box)
1494 % \begin{thebibliography}{1}
1496 % \bibitem{IEEEhowto:kopka}
1497 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1498 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1500 % \end{thebibliography}
1508 % vim: set ai sw=2 sts=2 expandtab: