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337 % There should be no need to do such things with IEEEtran.cls V1.6 and later.
338 % (Unless specifically asked to do so by the journal or conference you plan
339 % to submit to, of course. )
341 % correct bad hyphenation here
342 \hyphenation{op-tical net-works semi-conduc-tor}
344 % Macro for certain acronyms in small caps. Doesn't work with the
345 % default font, though (it contains no smallcaps it seems).
346 \def\VHDL{{\small{VHDL}}}
347 \def\GHC{{\small{GHC}}}
348 \def\CLaSH{\textsc{C$\lambda$aSH}}
350 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
351 % we'll get something more complex later on.
352 \def\hs#1{\texttt{#1}}
353 \def\quote#1{``{#1}"}
355 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
357 \settowidth{\labelwidth}{#1:}
358 \setlength{\labelsep}{0.5cm}
359 \setlength{\leftmargin}{\labelwidth}
360 \addtolength{\leftmargin}{\labelsep}
361 \setlength{\rightmargin}{0pt}
362 \setlength{\parsep}{0.5ex plus 0.2ex minus 0.1ex}
363 \setlength{\itemsep}{0 ex plus 0.2ex}
364 \renewcommand{\makelabel}[1]{##1:\hfil}
369 %include polycode.fmt
374 % can use linebreaks \\ within to get better formatting as desired
375 \title{\CLaSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
378 % author names and affiliations
379 % use a multiple column layout for up to three different
381 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards, Bert Molenkamp, Sabih H. Gerez}
382 \IEEEauthorblockA{University of Twente, Department of EEMCS\\
383 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
384 c.p.r.baaij@utwente.nl, matthijs@stdin.nl}}
386 % \IEEEauthorblockN{Homer Simpson}
387 % \IEEEauthorblockA{Twentieth Century Fox\\
389 % Email: homer@thesimpsons.com}
391 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
392 % \IEEEauthorblockA{Starfleet Academy\\
393 % San Francisco, California 96678-2391\\
394 % Telephone: (800) 555--1212\\
395 % Fax: (888) 555--1212}}
397 % conference papers do not typically use \thanks and this command
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400 % after \documentclass
402 % for over three affiliations, or if they all won't fit within the width
403 % of the page, use this alternative format:
405 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
406 %Homer Simpson\IEEEauthorrefmark{2},
407 %James Kirk\IEEEauthorrefmark{3},
408 %Montgomery Scott\IEEEauthorrefmark{3} and
409 %Eldon Tyrell\IEEEauthorrefmark{4}}
410 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
411 %Georgia Institute of Technology,
412 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
413 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
414 %Email: homer@thesimpsons.com}
415 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
416 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
417 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
422 % use for special paper notices
423 %\IEEEspecialpapernotice{(Invited Paper)}
428 % make the title area
434 The abstract goes here.
436 % IEEEtran.cls defaults to using nonbold math in the Abstract.
437 % This preserves the distinction between vectors and scalars. However,
438 % if the conference you are submitting to favors bold math in the abstract,
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441 % math in the abstract anyway.
448 % For peer review papers, you can put extra information on the cover
450 % \ifCLASSOPTIONpeerreview
451 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
454 % For peerreview papers, this IEEEtran command inserts a page break and
455 % creates the second title. It will be ignored for other modes.
456 \IEEEpeerreviewmaketitle
459 \section{Introduction}
460 Hardware description languages has allowed the productivity of hardware
461 engineers to keep pace with the development of chip technology. Standard
462 Hardware description languages, like \VHDL\ and Verilog, allowed an engineer
463 to describe circuits using a programming language. These standard languages
464 are very good at describing detailed hardware properties such as timing
465 behavior, but are generally cumbersome in expressing higher-level
466 abstractions. These languages also tend to have a complex syntax and a lack of
467 formal semantics. To overcome these complexities, and raise the abstraction
468 level, a great number of approaches based on functional languages has been
469 proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,ForSyDe1,Wired,reFLect}. The idea
470 of using functional languages started in the early 1980s \cite{Cardelli1981,
471 muFP,DAISY,FHDL}, a time which also saw the birth of the currently popular
472 hardware description languages such as \VHDL.
474 What gives functional languages as hardware description languages their merits
475 is the fact that basic combinatorial circuits are equivalent to mathematical
476 function, and that functional languages lend themselves very well to describe
477 and compose these mathematical functions.
478 \section{Hardware description in Haskell}
480 \subsection{Function application}
481 The basic syntactic elements of a functional program are functions
482 and function application. These have a single obvious \VHDL\
483 translation: each top level function becomes a hardware component,
484 where each argument is an input port and the result value is the
485 (single) output port. This output port can have a complex type (such
486 as a tuple), so having just a single output port does not create a
489 Each function application in turn becomes component instantiation.
490 Here, the result of each argument expression is assigned to a
491 signal, which is mapped to the corresponding input port. The output
492 port of the function is also mapped to a signal, which is used as
493 the result of the application itself.
495 Since every top level function generates its own component, the
496 hierarchy of of function calls is reflected in the final \VHDL\
497 output as well, creating a hierarchical \VHDL\ description of the
498 hardware. This separation in different components makes the
499 resulting \VHDL\ output easier to read and debug.
501 Example that defines the \texttt{mac} function by applying the
502 \texttt{add} and \texttt{mul} functions to calculate $a * b + c$:
505 mac a b c = add (mul a b) c
510 \subsection{Choices }
511 Although describing components and connections allows describing a
512 lot of hardware designs already, there is an obvious thing missing:
513 choice. We need some way to be able to choose between values based
514 on another value. In Haskell, choice is achieved by \hs{case}
515 expressions, \hs{if} expressions, pattern matching and guards.
517 The easiest of these are of course case expressions (and \hs{if}
518 expressions, which can be very directly translated to \hs{case}
519 expressions). A \hs{case} expression can in turn simply be
520 translated to a conditional assignment in \VHDL, where the
521 conditions use equality comparisons against the constructors in the
522 \hs{case} expressions.
524 A slightly more complex (but very powerful) form of choice is
525 pattern matching. A function can be defined in multiple clauses,
526 where each clause specifies a pattern. When the arguments match the
527 pattern, the corresponding clause will be used.
529 A pattern match (with optional guards) can also be implemented using
530 conditional assignments in \VHDL, where the condition is the logical
531 and of comparison results of each part of the pattern as well as the
534 Contrived example that sums two values when they are equal or
535 non-equal (depending on the predicate given) and returns 0
536 otherwise. This shows three implementations, one using and if
537 expression, one using only case expressions and one using pattern
541 sumif cmp a b = if cmp == Eq && a == b
542 || cmp == Neq && a != b
548 sumif cmp a b = case cmp of
552 Neq -> case a != b of
558 sumif Eq a b | a == b = a + b
559 sumif Neq a b | a != b = a + b
566 Translation of two most basic functional concepts has been
567 discussed: function application and choice. Before looking further
568 into less obvious concepts like higher-order expressions and
569 polymorphism, the possible types that can be used in hardware
570 descriptions will be discussed.
572 Some way is needed to translate every value used to its hardware
573 equivalents. In particular, this means a hardware equivalent for
574 every \emph{type} used in a hardware description is needed.
576 The following types are \emph{built-in}, meaning that their hardware
577 translation is fixed into the \CLaSH compiler. A designer can also
578 define his own types, which will be translated into hardware types
579 using translation rules that are discussed later on.
581 \subsection{Built-in types}
584 This is the most basic type available. It can have two values:
585 \hs{Low} and \hs{High}. It is mapped directly onto the
586 \texttt{std\_logic} \VHDL\ type.
588 This is a basic logic type. It can have two values: \hs{True}
589 and \hs{False}. It is translated to \texttt{std\_logic} exactly
590 like the \hs{Bit} type (where a value of \hs{True} corresponds
591 to a value of \hs{High}). Supporting the Bool type is
592 particularly useful to support \hs{if ... then ... else ...}
593 expressions, which always have a \hs{Bool} value for the
595 \item[\hs{SizedWord}, \hs{SizedInt}]
596 These are types to represent integers. A \hs{SizedWord} is unsigned,
597 while a \hs{SizedInt} is signed. These types are parametrized by a
598 length type, so you can define an unsigned word of 32 bits wide as
602 type Word32 = SizedWord D32
605 Here, a type synonym \hs{Word32} is defined that is equal to the
606 \hs{SizedWord} type constructor applied to the type \hs{D32}. \hs{D32}
607 is the \emph{type level representation} of the decimal number 32,
608 making the \hs{Word32} type a 32-bit unsigned word.
610 These types are translated to the \VHDL\ \texttt{unsigned} and
611 \texttt{signed} respectively.
613 This is a vector type, that can contain elements of any other type and
616 The \hs{Vector} type constructor takes two type arguments: the length
617 of the vector and the type of the elements contained in it. The state
618 type of an 8 element register bank would then for example be:
621 type RegisterState = Vector D8 Word32
624 Here, a type synonym \hs{RegisterState} is defined that is equal to
625 the \hs{Vector} type constructor applied to the types \hs{D8} (The type
626 level representation of the decimal number 8) and \hs{Word32} (The 32
627 bit word type as defined above). In other words, the
628 \hs{RegisterState} type is a vector of 8 32-bit words.
630 A fixed size vector is translated to a \VHDL\ array type.
631 \item[\hs{RangedWord}]
632 This is another type to describe integers, but unlike the previous
633 two it has no specific bit-width, but an upper bound. This means that
634 its range is not limited to powers of two, but can be any number.
635 A \hs{RangedWord} only has an upper bound, its lower bound is
638 The main purpose of the \hs{RangedWord} type is to be used as an
639 index to a \hs{Vector}.
641 TODO: Perhaps remove this example?
643 To define an index for the 8 element vector above, we would do:
646 type RegisterIndex = RangedWord D7
649 Here, a type synonym \hs{RegisterIndex} is defined that is equal to
650 the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
651 other words, this defines an unsigned word with values from
652 0 to 7 (inclusive). This word can be be used to index the
653 8 element vector \hs{RegisterState} above.
655 This type is translated to the \texttt{unsigned} \VHDL type.
658 \subsection{User-defined types}
659 There are three ways to define new types in Haskell: algebraic
660 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
661 keyword and type renamings with the \hs{newtype} keyword. \GHC\
662 offers a few more advanced ways to introduce types (type families,
663 existential typing, {\small{GADT}}s, etc.) which are not standard
664 Haskell. These are not currently supported.
666 Only an algebraic datatype declaration actually introduces a
667 completely new type, for which we provide the \VHDL\ translation
668 below. Type synonyms and renamings only define new names for
669 existing types (where synonyms are completely interchangeable and
670 renamings need explicit conversion). Therefore, these do not need
671 any particular \VHDL\ translation, a synonym or renamed type will
672 just use the same representation as the original type. The
673 distinction between a renaming and a synonym does no longer matter
674 in hardware and can be disregarded in the generated \VHDL.
676 For algebraic types, we can make the following distinction:
679 \item[\bf{Single constructor}]
680 Algebraic datatypes with a single constructor with one or more
681 fields, are essentially a way to pack a few values together in a
682 record-like structure.
684 An example of such a type is the following pair of integers:
687 data IntPair = IntPair Int Int
690 Haskell's builtin tuple types are also defined as single
691 constructor algebraic types and are translated according to this
692 rule by the \CLaSH compiler.
694 These types are translated to \VHDL\ record types, with one field for
695 every field in the constructor.
696 \item[\bf{No fields}]
697 Algebraic datatypes with multiple constructors, but without any
698 fields are essentially a way to get an enumeration-like type
699 containing alternatives.
701 Note that Haskell's \hs{Bool} type is also defined as an
702 enumeration type, but we have a fixed translation for that.
704 These types are translated to \VHDL\ enumerations, with one value for
705 each constructor. This allows references to these constructors to be
706 translated to the corresponding enumeration value.
707 \item[\bf{Multiple constructors with fields}]
708 Algebraic datatypes with multiple constructors, where at least
709 one of these constructors has one or more fields are not
714 \section{\CLaSH\ prototype}
718 \section{Related work}
719 Many functional hardware description languages have been developed over the
720 years. Early work includes such languages as \textsc{$\mu$fp}~\cite{muFP}, an
721 extension of Backus' \textsc{fp} language to synchronous streams, designed
722 particularly for describing and reasoning about regular circuits. The
723 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
724 circuits, and has a particular focus on layout. \textsc{hml}~\cite{HML2} is a
725 hardware modeling language based on the strict functional language
726 \textsc{ml}, and has support for polymorphic types and higher-order functions.
727 Published work suggests that there is no direct simulation support for
728 \textsc{hml}, and that the translation to \VHDL\ is only partial.
730 Like this work, many functional hardware description languages have some sort
731 of foundation in the functional programming language Haskell.
732 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
733 specifications used to model the behavior of superscalar microprocessors. Hawk
734 specifications can be simulated, but there seems to be no support for
735 automated circuit synthesis. The ForSyDe~\cite{ForSyDe2} system uses Haskell
736 to specify abstract system models, which can (manually) be transformed into an
737 implementation model using semantic preserving transformations. ForSyDe has
738 several simulation and synthesis backends, though synthesis is restricted to
739 the synchronous subset of the ForSyDe language.
741 Lava~\cite{Lava} is a hardware description language that focuses on the
742 structural representation of hardware. Besides support for simulation and
743 circuit synthesis, Lava descriptions can be interfaced with formal method
744 tools for formal verification. Lava descriptions are actually circuit
745 generators when viewed from a synthesis viewpoint, in that the language
746 elements of Haskell, such as choice, can be used to guide the circuit
747 generation. If a developer wants to insert a choice element inside an actual
748 circuit he will have to specify this explicitly as a component. In this
749 respect \CLaSH\ differs from Lava, in that all the choice elements, such as
750 case-statements and patter matching, are synthesized to choice elements in the
751 eventual circuit. As such, richer control structures can both be specified and
752 synthesized in \CLaSH\ compared to any of the languages mentioned in this
755 The merits of polymorphic typing, combined with higher-order functions, are
756 now also recognized in the `main-stream' hardware description languages,
757 exemplified by the new \VHDL\ 2008 standard~\cite{VHDL2008}. \VHDL-2008 has
758 support to specify types as generics, thus allowing a developer to describe
759 polymorphic components. Note that those types still require an explicit
760 generic map, whereas type-inference and type-specialization are implicit in
763 Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
765 A functional language designed specifically for hardware design is
766 $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
767 language called \textsc{fl}~\cite{FL} to la
769 % An example of a floating figure using the graphicx package.
770 % Note that \label must occur AFTER (or within) \caption.
771 % For figures, \caption should occur after the \includegraphics.
772 % Note that IEEEtran v1.7 and later has special internal code that
773 % is designed to preserve the operation of \label within \caption
774 % even when the captionsoff option is in effect. However, because
775 % of issues like this, it may be the safest practice to put all your
776 % \label just after \caption rather than within \caption{}.
778 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
779 % option should be used if it is desired that the figures are to be
780 % displayed while in draft mode.
784 %\includegraphics[width=2.5in]{myfigure}
785 % where an .eps filename suffix will be assumed under latex,
786 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
787 % via \DeclareGraphicsExtensions.
788 %\caption{Simulation Results}
792 % Note that IEEE typically puts floats only at the top, even when this
793 % results in a large percentage of a column being occupied by floats.
796 % An example of a double column floating figure using two subfigures.
797 % (The subfig.sty package must be loaded for this to work.)
798 % The subfigure \label commands are set within each subfloat command, the
799 % \label for the overall figure must come after \caption.
800 % \hfil must be used as a separator to get equal spacing.
801 % The subfigure.sty package works much the same way, except \subfigure is
802 % used instead of \subfloat.
805 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
806 %\label{fig_first_case}}
808 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
809 %\label{fig_second_case}}}
810 %\caption{Simulation results}
814 % Note that often IEEE papers with subfigures do not employ subfigure
815 % captions (using the optional argument to \subfloat), but instead will
816 % reference/describe all of them (a), (b), etc., within the main caption.
819 % An example of a floating table. Note that, for IEEE style tables, the
820 % \caption command should come BEFORE the table. Table text will default to
821 % \footnotesize as IEEE normally uses this smaller font for tables.
822 % The \label must come after \caption as always.
825 %% increase table row spacing, adjust to taste
826 %\renewcommand{\arraystretch}{1.3}
827 % if using array.sty, it might be a good idea to tweak the value of
828 % \extrarowheight as needed to properly center the text within the cells
829 %\caption{An Example of a Table}
830 %\label{table_example}
832 %% Some packages, such as MDW tools, offer better commands for making tables
833 %% than the plain LaTeX2e tabular which is used here.
834 %\begin{tabular}{|c||c|}
844 % Note that IEEE does not put floats in the very first column - or typically
845 % anywhere on the first page for that matter. Also, in-text middle ("here")
846 % positioning is not used. Most IEEE journals/conferences use top floats
847 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
848 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
849 % command of the stfloats package.
854 The conclusion goes here.
859 % conference papers do not normally have an appendix
862 % use section* for acknowledgement
863 \section*{Acknowledgment}
866 The authors would like to thank...
872 % trigger a \newpage just before the given reference
873 % number - used to balance the columns on the last page
874 % adjust value as needed - may need to be readjusted if
875 % the document is modified later
876 %\IEEEtriggeratref{8}
877 % The "triggered" command can be changed if desired:
878 %\IEEEtriggercmd{\enlargethispage{-5in}}
882 % can use a bibliography generated by BibTeX as a .bbl file
883 % BibTeX documentation can be easily obtained at:
884 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
885 % The IEEEtran BibTeX style support page is at:
886 % http://www.michaelshell.org/tex/ieeetran/bibtex/
887 \bibliographystyle{IEEEtran}
888 % argument is your BibTeX string definitions and bibliography database(s)
889 \bibliography{IEEEabrv,clash.bib}
891 % <OR> manually copy in the resultant .bbl file
892 % set second argument of \begin to the number of references
893 % (used to reserve space for the reference number labels box)
894 % \begin{thebibliography}{1}
896 % \bibitem{IEEEhowto:kopka}
897 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
898 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
900 % \end{thebibliography}
908 % vim: set ai sw=2 sts=2 expandtab: