7 %% http://www.michaelshell.org/
8 %% for current contact information.
10 %% This is a skeleton file demonstrating the use of IEEEtran.cls
11 %% (requires IEEEtran.cls version 1.7 or later) with an IEEE conference paper.
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42 %% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
43 %% bare_conf.tex, bare_jrnl.tex, bare_jrnl_compsoc.tex
44 %%*************************************************************************
46 % *** Authors should verify (and, if needed, correct) their LaTeX system ***
47 % *** with the testflow diagnostic prior to trusting their LaTeX platform ***
48 % *** with production work. IEEE's font choices can trigger bugs that do ***
49 % *** not appear when using other class files. ***
50 % The testflow support page is at:
51 % http://www.michaelshell.org/tex/testflow/
55 % Note that the a4paper option is mainly intended so that authors in
56 % countries using A4 can easily print to A4 and see how their papers will
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58 % affected with changes in paper size (but the bottom and side margins will).
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62 % Also note that the "draftcls" or "draftclsnofoot", not "draft", option
63 % should be used if it is desired that the figures are to be displayed in
66 \documentclass[conference,pdf,a4paper,10pt,final,twoside,twocolumn]{IEEEtran}
67 % Add the compsoc option for Computer Society conferences.
69 % If IEEEtran.cls has not been installed into the LaTeX system files,
70 % manually specify the path to it like:
71 % \documentclass[conference]{../sty/IEEEtran}
73 % Some very useful LaTeX packages include:
74 % (uncomment the ones you want to load)
76 % *** MISC UTILITY PACKAGES ***
79 % Heiko Oberdiek's ifpdf.sty is very useful if you need conditional
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104 % \cite{} output to follow that of IEEE. Loading the cite package will
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108 % \cite will automatically add leading space, if needed. Use cite.sty's
109 % noadjust option (cite.sty V3.8 and later) if you want to turn this off.
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159 % You can find documentation about the pdfTeX application at:
160 % http://www.tug.org/applications/pdftex
166 % *** MATH PACKAGES ***
168 %\usepackage[cmex10]{amsmath}
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189 % *** SPECIALIZED LIST PACKAGES ***
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194 % You can use the algorithmic environment in-text or within a figure
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211 % *** ALIGNMENT PACKAGES ***
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218 % respect to the quality of the end results, all users are strongly
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225 %\usepackage{mdwmath}
227 % Also highly recommended is Mark Wooding's extremely powerful MDW tools,
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234 % IEEEtran contains the IEEEeqnarray family of commands that can be used to
235 % generate multiline equations as well as matrices, tables, etc., of high
239 %\usepackage{eqparbox}
240 % Also of notable interest is Scott Pakin's eqparbox package for creating
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243 % http://www.ctan.org/tex-archive/macros/latex/contrib/eqparbox/
249 % *** SUBFIGURE PACKAGES ***
250 %\usepackage[tight,footnotesize]{subfigure}
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252 % easy to put subfigures in your figures. e.g., "Figure 1a and 1b". For IEEE
253 % work, it is a good idea to load it with the tight package option to reduce
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258 % subfigure.sty has been superceeded by subfig.sty.
262 %\usepackage[caption=false]{caption}
263 %\usepackage[font=footnotesize]{subfig}
264 % subfig.sty, also written by Steven Douglas Cochran, is the modern
265 % replacement for subfigure.sty. However, subfig.sty requires and
266 % automatically loads Axel Sommerfeldt's caption.sty which will override
267 % IEEEtran.cls handling of captions and this will result in nonIEEE style
268 % figure/table captions. To prevent this problem, be sure and preload
269 % caption.sty with its "caption=false" package option. This is will preserve
270 % IEEEtran.cls handing of captions. Version 1.3 (2005/06/28) and later
271 % (recommended due to many improvements over 1.2) of subfig.sty supports
272 % the caption=false option directly:
273 %\usepackage[caption=false,font=footnotesize]{subfig}
275 % The latest version and documentation can be obtained at:
276 % http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/
277 % The latest version and documentation of caption.sty can be obtained at:
278 % http://www.ctan.org/tex-archive/macros/latex/contrib/caption/
283 % *** FLOAT PACKAGES ***
285 %\usepackage{fixltx2e}
286 % fixltx2e, the successor to the earlier fix2col.sty, was written by
287 % Frank Mittelbach and David Carlisle. This package corrects a few problems
288 % in the LaTeX2e kernel, the most notable of which is that in current
289 % LaTeX2e releases, the ordering of single and double column floats is not
290 % guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
291 % single column figure to be placed prior to an earlier double column
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293 % http://www.ctan.org/tex-archive/macros/latex/base/
297 %\usepackage{stfloats}
298 % stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
299 % the ability to do double column floats at the bottom of the page as well
300 % as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
301 % LaTeX2e). It also provides a command:
303 % to enable the placement of footnotes below bottom floats (the standard
304 % LaTeX2e kernel puts them above bottom floats). This is an invasive package
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312 % IEEE should note that IEEE rarely uses double column equations and
313 % that authors should try to avoid such use. Do not be tempted to use the
314 % cuted.sty or midfloat.sty packages (also by Sigitas Tolusis) as IEEE does
315 % not format its papers in such ways.
321 % *** PDF, URL AND HYPERLINK PACKAGES ***
324 % url.sty was written by Donald Arseneau. It provides better support for
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327 % http://www.ctan.org/tex-archive/macros/latex/contrib/misc/
328 % Read the url.sty source comments for usage information. Basically,
335 % *** Do not adjust lengths that control margins, column widths, etc. ***
336 % *** Do not use packages that alter fonts (such as pslatex). ***
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 %include polycode.fmt
360 % can use linebreaks \\ within to get better formatting as desired
361 \title{\CLaSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
364 % author names and affiliations
365 % use a multiple column layout for up to three different
367 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards, Bert Molenkamp, Sabih H. Gerez}
368 \IEEEauthorblockA{University of Twente, Department of EEMCS\\
369 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
370 c.p.r.baaij@utwente.nl, matthijs@stdin.nl}}
372 % \IEEEauthorblockN{Homer Simpson}
373 % \IEEEauthorblockA{Twentieth Century Fox\\
375 % Email: homer@thesimpsons.com}
377 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
378 % \IEEEauthorblockA{Starfleet Academy\\
379 % San Francisco, California 96678-2391\\
380 % Telephone: (800) 555--1212\\
381 % Fax: (888) 555--1212}}
383 % conference papers do not typically use \thanks and this command
384 % is locked out in conference mode. If really needed, such as for
385 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
386 % after \documentclass
388 % for over three affiliations, or if they all won't fit within the width
389 % of the page, use this alternative format:
391 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
392 %Homer Simpson\IEEEauthorrefmark{2},
393 %James Kirk\IEEEauthorrefmark{3},
394 %Montgomery Scott\IEEEauthorrefmark{3} and
395 %Eldon Tyrell\IEEEauthorrefmark{4}}
396 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
397 %Georgia Institute of Technology,
398 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
399 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
400 %Email: homer@thesimpsons.com}
401 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
402 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
403 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
408 % use for special paper notices
409 %\IEEEspecialpapernotice{(Invited Paper)}
414 % make the title area
420 The abstract goes here.
422 % IEEEtran.cls defaults to using nonbold math in the Abstract.
423 % This preserves the distinction between vectors and scalars. However,
424 % if the conference you are submitting to favors bold math in the abstract,
425 % then you can use LaTeX's standard command \boldmath at the very start
426 % of the abstract to achieve this. Many IEEE journals/conferences frown on
427 % math in the abstract anyway.
434 % For peer review papers, you can put extra information on the cover
436 % \ifCLASSOPTIONpeerreview
437 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
440 % For peerreview papers, this IEEEtran command inserts a page break and
441 % creates the second title. It will be ignored for other modes.
442 \IEEEpeerreviewmaketitle
445 \section{Introduction}
446 Hardware description languages has allowed the productivity of hardware
447 engineers to keep pace with the development of chip technology. Standard
448 Hardware description languages, like \VHDL\ and Verilog, allowed an engineer
449 to describe circuits using a programming language. These standard languages
450 are very good at describing detailed hardware properties such as timing
451 behavior, but are generally cumbersome in expressing higher-level
452 abstractions. These languages also tend to have a complex syntax and a lack of
453 formal semantics. To overcome these complexities, and raise the abstraction
454 level, a great number of approaches based on functional languages has been
455 proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,ForSyDe1,Wired,reFLect}. The idea
456 of using functional languages started in the early 1980s \cite{Cardelli1981,
457 muFP,DAISY,FHDL}, a time which also saw the birth of the currently popular
458 hardware description languages such as \VHDL.
460 What gives functional languages as hardware description languages their merits
461 is the fact that basic combinatorial circuits are equivalent to mathematical
462 function, and that functional languages lend themselves very well to describe
463 and compose these mathematical functions.
464 \section{Hardware description in Haskell}
466 \subsection{Function application}
467 The basic syntactic elements of a functional program are functions
468 and function application. These have a single obvious \VHDL\
469 translation: each top level function becomes a hardware component,
470 where each argument is an input port and the result value is the
471 (single) output port. This output port can have a complex type (such
472 as a tuple), so having just a single output port does not create a
475 Each function application in turn becomes component instantiation.
476 Here, the result of each argument expression is assigned to a
477 signal, which is mapped to the corresponding input port. The output
478 port of the function is also mapped to a signal, which is used as
479 the result of the application itself.
481 Since every top level function generates its own component, the
482 hierarchy of of function calls is reflected in the final \VHDL\
483 output as well, creating a hierarchical \VHDL\ description of the
484 hardware. This separation in different components makes the
485 resulting \VHDL\ output easier to read and debug.
487 Example that defines the \texttt{mac} function by applying the
488 \texttt{add} and \texttt{mul} functions to calculate $a * b + c$:
491 mac a b c = add (mul a b) c
496 \subsection{Choices }
497 Although describing components and connections allows describing a
498 lot of hardware designs already, there is an obvious thing missing:
499 choice. We need some way to be able to choose between values based
500 on another value. In Haskell, choice is achieved by \hs{case}
501 expressions, \hs{if} expressions, pattern matching and guards.
503 The easiest of these are of course case expressions (and \hs{if}
504 expressions, which can be very directly translated to \hs{case}
505 expressions). A \hs{case} expression can in turn simply be
506 translated to a conditional assignment in \VHDL, where the
507 conditions use equality comparisons against the constructors in the
508 \hs{case} expressions.
510 A slightly more complex (but very powerful) form of choice is
511 pattern matching. A function can be defined in multiple clauses,
512 where each clause specifies a pattern. When the arguments match the
513 pattern, the corresponding clause will be used.
515 A pattern match (with optional guards) can also be implemented using
516 conditional assignments in \VHDL, where the condition is the logical
517 and of comparison results of each part of the pattern as well as the
520 Contrived example that sums two values when they are equal or
521 non-equal (depending on the predicate given) and returns 0
522 otherwise. This shows three implementations, one using and if
523 expression, one using only case expressions and one using pattern
527 sumif pred a b = if pred == Eq && a == b || pred == Neq && a != b
533 sumif pred a b = case pred of
537 Neq -> case a != b of
543 sumif Eq a b | a == b = a + b
544 sumif Neq a b | a != b = a + b
551 Translation of two most basic functional concepts has been
552 discussed: function application and choice. Before looking further
553 into less obvious concepts like higher-order expressions and
554 polymorphism, the possible types that can be used in hardware
555 descriptions will be discussed.
557 Some way is needed to translate every values used to its hardware
558 equivalents. In particular, this means a hardware equivalent for
559 every \emph{type} used in a hardware description is needed
561 Since most functional languages have a lot of standard types that
562 are hard to translate (integers without a fixed size, lists without
563 a static length, etc.), a number of \quote{built-in} types will be
564 defined first. These types are built-in in the sense that our
565 compiler will have a fixed \VHDL\ type for these. User defined types,
566 on the other hand, will have their hardware type derived directly
567 from their Haskell declaration automatically, according to the rules
570 \subsection{Built-in types}
571 The language currently supports the following built-in types. Of these,
572 only the \hs{Bool} type is supported by Haskell out of the box (the
573 others are defined by the \CLaSH\ package, so they are user-defined types
574 from Haskell's point of view).
578 This is the most basic type available. It is mapped directly onto
579 the \texttt{std\_logic} \VHDL\ type. Mapping this to the
580 \texttt{bit} type might make more sense (since the Haskell version
581 only has two values), but using \texttt{std\_logic} is more standard
582 (and allowed for some experimentation with don't care values)
585 This is the only built-in Haskell type supported and is translated
586 exactly like the Bit type (where a value of \hs{True} corresponds to a
587 value of \hs{High}). Supporting the Bool type is particularly
588 useful to support \hs{if ... then ... else ...} expressions, which
589 always have a \hs{Bool} value for the condition.
591 A \hs{Bool} is translated to a \texttt{std\_logic}, just like \hs{Bit}.
592 \item[\hs{SizedWord}, \hs{SizedInt}]
593 These are types to represent integers. A \hs{SizedWord} is unsigned,
594 while a \hs{SizedInt} is signed. These types are parametrized by a
595 length type, so you can define an unsigned word of 32 bits wide as
599 type Word32 = SizedWord D32
602 Here, a type synonym \hs{Word32} is defined that is equal to the
603 \hs{SizedWord} type constructor applied to the type \hs{D32}. \hs{D32}
604 is the \emph{type level representation} of the decimal number 32,
605 making the \hs{Word32} type a 32-bit unsigned word.
607 These types are translated to the \VHDL\ \texttt{unsigned} and
608 \texttt{signed} respectively.
610 This is a vector type, that can contain elements of any other type and
611 has a fixed length. It has two type parameters: its
612 length and the type of the elements contained in it. By putting the
613 length parameter in the type, the length of a vector can be determined
614 at compile time, instead of only at run-time for conventional lists.
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
636 implicitly zero. There is a lot of added implementation complexity
637 when adding a lower bound and having just an upper bound was enough
638 for the primary purpose of this type: type-safely indexing vectors.
640 To define an index for the 8 element vector above, we would do:
643 type RegisterIndex = RangedWord D7
646 Here, a type synonym \hs{RegisterIndex} is defined that is equal to
647 the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
648 other words, this defines an unsigned word with values from
649 0 to 7 (inclusive). This word can be be used to index the
650 8 element vector \hs{RegisterState} above.
652 This type is translated to the \texttt{unsigned} \VHDL type.
654 \subsection{User-defined types}
655 There are three ways to define new types in Haskell: algebraic
656 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
657 keyword and type renamings with the \hs{newtype} keyword. \GHC\
658 offers a few more advanced ways to introduce types (type families,
659 existential typing, {\small{GADT}}s, etc.) which are not standard
660 Haskell. These will be left outside the scope of this research.
662 Only an algebraic datatype declaration actually introduces a
663 completely new type, for which we provide the \VHDL\ translation
664 below. Type synonyms and renamings only define new names for
665 existing types (where synonyms are completely interchangeable and
666 renamings need explicit conversion). Therefore, these do not need
667 any particular \VHDL\ translation, a synonym or renamed type will
668 just use the same representation as the original type. The
669 distinction between a renaming and a synonym does no longer matter
670 in hardware and can be disregarded in the generated \VHDL.
672 For algebraic types, we can make the following distinction:
677 A product type is an algebraic datatype with a single constructor with
678 two or more fields, denoted in practice like (a,b), (a,b,c), etc. This
679 is essentially a way to pack a few values together in a record-like
680 structure. In fact, the built-in tuple types are just algebraic product
681 types (and are thus supported in exactly the same way).
683 The \quote{product} in its name refers to the collection of values
684 belonging to this type. The collection for a product type is the
685 Cartesian product of the collections for the types of its fields.
687 These types are translated to \VHDL\ record types, with one field for
688 every field in the constructor. This translation applies to all single
689 constructor algebraic data-types, including those with just one
690 field (which are technically not a product, but generate a VHDL
691 record for implementation simplicity).
692 \item[Enumerated types]
693 An enumerated type is an algebraic datatype with multiple constructors, but
694 none of them have fields. This is essentially a way to get an
695 enumeration-like type containing alternatives.
697 Note that Haskell's \hs{Bool} type is also defined as an
698 enumeration type, but we have a fixed translation for that.
700 These types are translated to \VHDL\ enumerations, with one value for
701 each constructor. This allows references to these constructors to be
702 translated to the corresponding enumeration value.
704 A sum type is an algebraic datatype with multiple constructors, where
705 the constructors have one or more fields. Technically, a type with
706 more than one field per constructor is a sum of products type, but
707 for our purposes this distinction does not really make a
708 difference, so this distinction is note made.
710 The \quote{sum} in its name refers again to the collection of values
711 belonging to this type. The collection for a sum type is the
712 union of the the collections for each of the constructors.
714 Sum types are currently not supported by the prototype, since there is
715 no obvious \VHDL\ alternative. They can easily be emulated, however, as
716 we will see from an example:
719 data Sum = A Bit Word | B Word
722 An obvious way to translate this would be to create an enumeration to
723 distinguish the constructors and then create a big record that
724 contains all the fields of all the constructors. This is the same
725 translation that would result from the following enumeration and
726 product type (using a tuple for clarity):
730 type Sum = (SumC, Bit, Word, Word)
733 Here, the \hs{SumC} type effectively signals which of the latter three
734 fields of the \hs{Sum} type are valid (the first two if \hs{A}, the
735 last one if \hs{B}), all the other ones have no useful value.
737 An obvious problem with this naive approach is the space usage: the
738 example above generates a fairly big \VHDL\ type. Since we can be
739 sure that the two \hs{Word}s in the \hs{Sum} type will never be valid
740 at the same time, this is a waste of space.
742 Obviously, duplication detection could be used to reuse a
743 particular field for another constructor, but this would only
744 partially solve the problem. If two fields would be, for
745 example, an array of 8 bits and an 8 bit unsigned word, these are
746 different types and could not be shared. However, in the final
747 hardware, both of these types would simply be 8 bit connections,
748 so we have a 100\% size increase by not sharing these.
752 \section{\CLaSH\ prototype}
756 \section{Related work}
757 Many functional hardware description languages have been developed over the
758 years. Early work includes such languages as \textsc{$\mu$fp}~\cite{muFP}, an
759 extension of Backus' \textsc{fp} language to synchronous streams, designed
760 particularly for describing and reasoning about regular circuits. The
761 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
762 circuits, and has a particular focus on layout. \textsc{hml}~\cite{HML2} is a
763 hardware modeling language based on the strict functional language
764 \textsc{ml}, and has support for polymorphic types and higher-order functions.
765 Published work suggests that there is no direct simulation support for
766 \textsc{hml}, and that the translation to \VHDL\ is only partial.
768 Like this work, many functional hardware description languages have some sort
769 of foundation in the functional programming language Haskell.
770 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
771 specifications used to model the behavior of superscalar microprocessors. Hawk
772 specifications can be simulated, but there seems to be no support for
773 automated circuit synthesis. The ForSyDe~\cite{ForSyDe2} system uses Haskell
774 to specify abstract system models, which can (manually) be transformed into an
775 implementation model using semantic preserving transformations. ForSyDe has
776 several simulation and synthesis backends, though synthesis is restricted to
777 the synchronous subset of the ForSyDe language.
779 Lava~\cite{Lava} is a hardware description language that focuses on the
780 structural representation of hardware. Besides support for simulation and
781 circuit synthesis, Lava descriptions can be interfaced with formal method
782 tools for formal verification. Lava descriptions are actually circuit
783 generators when viewed from a synthesis viewpoint, in that the language
784 elements of Haskell, such as choice, can be used to guide the circuit
785 generation. If a developer wants to insert a choice element inside an actual
786 circuit he will have to specify this explicitly as a component. In this
787 respect \CLaSH\ differs from Lava, in that all the choice elements, such as
788 case-statements and patter matching, are synthesized to choice elements in the
789 eventual circuit. As such, richer control structures can both be specified and
790 synthesized in \CLaSH\ compared to any of the languages mentioned in this
793 The merits of polymorphic typing, combined with higher-order functions, are
794 now also recognized in the `main-stream' hardware description languages,
795 exemplified by the new \VHDL\ 2008 standard~\cite{VHDL2008}. \VHDL-2008 has
796 support to specify types as generics, thus allowing a developer to describe
797 polymorphic components. Note that those types still require an explicit
798 generic map, whereas type-inference and type-specialization are implicit in
801 Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
803 A functional language designed specifically for hardware design is
804 $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
805 language called \textsc{fl}~\cite{FL} to la
807 % An example of a floating figure using the graphicx package.
808 % Note that \label must occur AFTER (or within) \caption.
809 % For figures, \caption should occur after the \includegraphics.
810 % Note that IEEEtran v1.7 and later has special internal code that
811 % is designed to preserve the operation of \label within \caption
812 % even when the captionsoff option is in effect. However, because
813 % of issues like this, it may be the safest practice to put all your
814 % \label just after \caption rather than within \caption{}.
816 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
817 % option should be used if it is desired that the figures are to be
818 % displayed while in draft mode.
822 %\includegraphics[width=2.5in]{myfigure}
823 % where an .eps filename suffix will be assumed under latex,
824 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
825 % via \DeclareGraphicsExtensions.
826 %\caption{Simulation Results}
830 % Note that IEEE typically puts floats only at the top, even when this
831 % results in a large percentage of a column being occupied by floats.
834 % An example of a double column floating figure using two subfigures.
835 % (The subfig.sty package must be loaded for this to work.)
836 % The subfigure \label commands are set within each subfloat command, the
837 % \label for the overall figure must come after \caption.
838 % \hfil must be used as a separator to get equal spacing.
839 % The subfigure.sty package works much the same way, except \subfigure is
840 % used instead of \subfloat.
843 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
844 %\label{fig_first_case}}
846 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
847 %\label{fig_second_case}}}
848 %\caption{Simulation results}
852 % Note that often IEEE papers with subfigures do not employ subfigure
853 % captions (using the optional argument to \subfloat), but instead will
854 % reference/describe all of them (a), (b), etc., within the main caption.
857 % An example of a floating table. Note that, for IEEE style tables, the
858 % \caption command should come BEFORE the table. Table text will default to
859 % \footnotesize as IEEE normally uses this smaller font for tables.
860 % The \label must come after \caption as always.
863 %% increase table row spacing, adjust to taste
864 %\renewcommand{\arraystretch}{1.3}
865 % if using array.sty, it might be a good idea to tweak the value of
866 % \extrarowheight as needed to properly center the text within the cells
867 %\caption{An Example of a Table}
868 %\label{table_example}
870 %% Some packages, such as MDW tools, offer better commands for making tables
871 %% than the plain LaTeX2e tabular which is used here.
872 %\begin{tabular}{|c||c|}
882 % Note that IEEE does not put floats in the very first column - or typically
883 % anywhere on the first page for that matter. Also, in-text middle ("here")
884 % positioning is not used. Most IEEE journals/conferences use top floats
885 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
886 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
887 % command of the stfloats package.
892 The conclusion goes here.
897 % conference papers do not normally have an appendix
900 % use section* for acknowledgement
901 \section*{Acknowledgment}
904 The authors would like to thank...
910 % trigger a \newpage just before the given reference
911 % number - used to balance the columns on the last page
912 % adjust value as needed - may need to be readjusted if
913 % the document is modified later
914 %\IEEEtriggeratref{8}
915 % The "triggered" command can be changed if desired:
916 %\IEEEtriggercmd{\enlargethispage{-5in}}
920 % can use a bibliography generated by BibTeX as a .bbl file
921 % BibTeX documentation can be easily obtained at:
922 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
923 % The IEEEtran BibTeX style support page is at:
924 % http://www.michaelshell.org/tex/ieeetran/bibtex/
925 \bibliographystyle{IEEEtran}
926 % argument is your BibTeX string definitions and bibliography database(s)
927 \bibliography{IEEEabrv,clash.bib}
929 % <OR> manually copy in the resultant .bbl file
930 % set second argument of \begin to the number of references
931 % (used to reserve space for the reference number labels box)
932 % \begin{thebibliography}{1}
934 % \bibitem{IEEEhowto:kopka}
935 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
936 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
938 % \end{thebibliography}
946 % vim: set ai sw=2 sts=2 expandtab: