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.
14 %% http://www.michaelshell.org/tex/ieeetran/
15 %% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
17 %% http://www.ieee.org/
19 %%*************************************************************************
21 %% This code is offered as-is without any warranty either expressed or
22 %% implied; without even the implied warranty of MERCHANTABILITY or
23 %% FITNESS FOR A PARTICULAR PURPOSE!
24 %% User assumes all risk.
25 %% In no event shall IEEE or any contributor to this code be liable for
26 %% any damages or losses, including, but not limited to, incidental,
27 %% consequential, or any other damages, resulting from the use or misuse
28 %% of any information contained here.
30 %% All comments are the opinions of their respective authors and are not
31 %% necessarily endorsed by the IEEE.
33 %% This work is distributed under the LaTeX Project Public License (LPPL)
34 %% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
35 %% distributed and modified. A copy of the LPPL, version 1.3, is included
36 %% in the base LaTeX documentation of all distributions of LaTeX released
37 %% 2003/12/01 or later.
38 %% Retain all contribution notices and credits.
39 %% ** Modified files should be clearly indicated as such, including **
40 %% ** renaming them and changing author support contact information. **
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
57 % look in print - the typesetting of the document will not typically be
58 % affected with changes in paper size (but the bottom and side margins will).
59 % Use the testflow package mentioned above to verify correct handling of
60 % both paper sizes by the user's LaTeX system.
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
80 % compilation based on whether the output is pdf or dvi.
87 % The latest version of ifpdf.sty can be obtained from:
88 % http://www.ctan.org/tex-archive/macros/latex/contrib/oberdiek/
89 % Also, note that IEEEtran.cls V1.7 and later provides a builtin
90 % \ifCLASSINFOpdf conditional that works the same way.
91 % When switching from latex to pdflatex and vice-versa, the compiler may
92 % have to be run twice to clear warning/error messages.
99 % *** CITATION PACKAGES ***
102 % cite.sty was written by Donald Arseneau
103 % V1.6 and later of IEEEtran pre-defines the format of the cite.sty package
104 % \cite{} output to follow that of IEEE. Loading the cite package will
105 % result in citation numbers being automatically sorted and properly
106 % "compressed/ranged". e.g., [1], [9], [2], [7], [5], [6] without using
107 % cite.sty will become [1], [2], [5]--[7], [9] using cite.sty. cite.sty's
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.
110 % cite.sty is already installed on most LaTeX systems. Be sure and use
111 % version 4.0 (2003-05-27) and later if using hyperref.sty. cite.sty does
112 % not currently provide for hyperlinked citations.
113 % The latest version can be obtained at:
114 % http://www.ctan.org/tex-archive/macros/latex/contrib/cite/
115 % The documentation is contained in the cite.sty file itself.
122 % *** GRAPHICS RELATED PACKAGES ***
125 % \usepackage[pdftex]{graphicx}
126 % declare the path(s) where your graphic files are
127 % \graphicspath{{../pdf/}{../jpeg/}}
128 % and their extensions so you won't have to specify these with
129 % every instance of \includegraphics
130 % \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
132 % or other class option (dvipsone, dvipdf, if not using dvips). graphicx
133 % will default to the driver specified in the system graphics.cfg if no
134 % driver is specified.
135 % \usepackage[dvips]{graphicx}
136 % declare the path(s) where your graphic files are
137 % \graphicspath{{../eps/}}
138 % and their extensions so you won't have to specify these with
139 % every instance of \includegraphics
140 % \DeclareGraphicsExtensions{.eps}
142 % graphicx was written by David Carlisle and Sebastian Rahtz. It is
143 % required if you want graphics, photos, etc. graphicx.sty is already
144 % installed on most LaTeX systems. The latest version and documentation can
146 % http://www.ctan.org/tex-archive/macros/latex/required/graphics/
147 % Another good source of documentation is "Using Imported Graphics in
148 % LaTeX2e" by Keith Reckdahl which can be found as epslatex.ps or
149 % epslatex.pdf at: http://www.ctan.org/tex-archive/info/
151 % latex, and pdflatex in dvi mode, support graphics in encapsulated
152 % postscript (.eps) format. pdflatex in pdf mode supports graphics
153 % in .pdf, .jpeg, .png and .mps (metapost) formats. Users should ensure
154 % that all non-photo figures use a vector format (.eps, .pdf, .mps) and
155 % not a bitmapped formats (.jpeg, .png). IEEE frowns on bitmapped formats
156 % which can result in "jaggedy"/blurry rendering of lines and letters as
157 % well as large increases in file sizes.
159 % You can find documentation about the pdfTeX application at:
160 % http://www.tug.org/applications/pdftex
166 % *** MATH PACKAGES ***
168 %\usepackage[cmex10]{amsmath}
169 % A popular package from the American Mathematical Society that provides
170 % many useful and powerful commands for dealing with mathematics. If using
171 % it, be sure to load this package with the cmex10 option to ensure that
172 % only type 1 fonts will utilized at all point sizes. Without this option,
173 % it is possible that some math symbols, particularly those within
174 % footnotes, will be rendered in bitmap form which will result in a
175 % document that can not be IEEE Xplore compliant!
177 % Also, note that the amsmath package sets \interdisplaylinepenalty to 10000
178 % thus preventing page breaks from occurring within multiline equations. Use:
179 %\interdisplaylinepenalty=2500
180 % after loading amsmath to restore such page breaks as IEEEtran.cls normally
181 % does. amsmath.sty is already installed on most LaTeX systems. The latest
182 % version and documentation can be obtained at:
183 % http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/
189 % *** SPECIALIZED LIST PACKAGES ***
191 %\usepackage{algorithmic}
192 % algorithmic.sty was written by Peter Williams and Rogerio Brito.
193 % This package provides an algorithmic environment fo describing algorithms.
194 % You can use the algorithmic environment in-text or within a figure
195 % environment to provide for a floating algorithm. Do NOT use the algorithm
196 % floating environment provided by algorithm.sty (by the same authors) or
197 % algorithm2e.sty (by Christophe Fiorio) as IEEE does not use dedicated
198 % algorithm float types and packages that provide these will not provide
199 % correct IEEE style captions. The latest version and documentation of
200 % algorithmic.sty can be obtained at:
201 % http://www.ctan.org/tex-archive/macros/latex/contrib/algorithms/
202 % There is also a support site at:
203 % http://algorithms.berlios.de/index.html
204 % Also of interest may be the (relatively newer and more customizable)
205 % algorithmicx.sty package by Szasz Janos:
206 % http://www.ctan.org/tex-archive/macros/latex/contrib/algorithmicx/
211 % *** ALIGNMENT PACKAGES ***
214 % Frank Mittelbach's and David Carlisle's array.sty patches and improves
215 % the standard LaTeX2e array and tabular environments to provide better
216 % appearance and additional user controls. As the default LaTeX2e table
217 % generation code is lacking to the point of almost being broken with
218 % respect to the quality of the end results, all users are strongly
219 % advised to use an enhanced (at the very least that provided by array.sty)
220 % set of table tools. array.sty is already installed on most systems. The
221 % latest version and documentation can be obtained at:
222 % http://www.ctan.org/tex-archive/macros/latex/required/tools/
225 %\usepackage{mdwmath}
227 % Also highly recommended is Mark Wooding's extremely powerful MDW tools,
228 % especially mdwmath.sty and mdwtab.sty which are used to format equations
229 % and tables, respectively. The MDWtools set is already installed on most
230 % LaTeX systems. The lastest version and documentation is available at:
231 % http://www.ctan.org/tex-archive/macros/latex/contrib/mdwtools/
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
241 % (automatically sized) equal width boxes - aka "natural width parboxes".
243 % http://www.ctan.org/tex-archive/macros/latex/contrib/eqparbox/
249 % *** SUBFIGURE PACKAGES ***
250 %\usepackage[tight,footnotesize]{subfigure}
251 % subfigure.sty was written by Steven Douglas Cochran. This package makes it
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
254 % the amount of white space around the subfigures. subfigure.sty is already
255 % installed on most LaTeX systems. The latest version and documentation can
257 % http://www.ctan.org/tex-archive/obsolete/macros/latex/contrib/subfigure/
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
292 % figure. The latest version and documentation can be found at:
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
305 % which rewrites many portions of the LaTeX2e float routines. It may not work
306 % with other packages that modify the LaTeX2e float routines. The latest
307 % version and documentation can be obtained at:
308 % http://www.ctan.org/tex-archive/macros/latex/contrib/sttools/
309 % Documentation is contained in the stfloats.sty comments as well as in the
310 % presfull.pdf file. Do not use the stfloats baselinefloat ability as IEEE
311 % does not allow \baselineskip to stretch. Authors submitting work to the
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
325 % handling and breaking URLs. url.sty is already installed on most LaTeX
326 % systems. The latest version can be obtained at:
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\acro#1{{\small{#1}}}
347 \def\VHDL{\acro{VHDL}}
349 \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}}
351 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
352 % we'll get something more complex later on.
353 \def\hs#1{\texttt{#1}}
354 \def\quote#1{``{#1}"}
356 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
358 \settowidth{\labelwidth}{#1:}
359 \setlength{\labelsep}{0.5cm}
360 \setlength{\leftmargin}{\labelwidth}
361 \addtolength{\leftmargin}{\labelsep}
362 \setlength{\rightmargin}{0pt}
363 \setlength{\parsep}{0.5ex plus 0.2ex minus 0.1ex}
364 \setlength{\itemsep}{0 ex plus 0.2ex}
365 \renewcommand{\makelabel}[1]{##1:\hfil}
370 \usepackage{paralist}
372 %include polycode.fmt
378 % can use linebreaks \\ within to get better formatting as desired
379 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
382 % author names and affiliations
383 % use a multiple column layout for up to three different
385 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards, Bert Molenkamp, Sabih H. Gerez}
386 \IEEEauthorblockA{University of Twente, Department of EEMCS\\
387 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
388 c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl}}
390 % \IEEEauthorblockN{Homer Simpson}
391 % \IEEEauthorblockA{Twentieth Century Fox\\
393 % Email: homer@thesimpsons.com}
395 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
396 % \IEEEauthorblockA{Starfleet Academy\\
397 % San Francisco, California 96678-2391\\
398 % Telephone: (800) 555--1212\\
399 % Fax: (888) 555--1212}}
401 % conference papers do not typically use \thanks and this command
402 % is locked out in conference mode. If really needed, such as for
403 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
404 % after \documentclass
406 % for over three affiliations, or if they all won't fit within the width
407 % of the page, use this alternative format:
409 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
410 %Homer Simpson\IEEEauthorrefmark{2},
411 %James Kirk\IEEEauthorrefmark{3},
412 %Montgomery Scott\IEEEauthorrefmark{3} and
413 %Eldon Tyrell\IEEEauthorrefmark{4}}
414 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
415 %Georgia Institute of Technology,
416 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
417 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
418 %Email: homer@thesimpsons.com}
419 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
420 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
421 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
426 % use for special paper notices
427 %\IEEEspecialpapernotice{(Invited Paper)}
432 % make the title area
438 The abstract goes here.
440 % IEEEtran.cls defaults to using nonbold math in the Abstract.
441 % This preserves the distinction between vectors and scalars. However,
442 % if the conference you are submitting to favors bold math in the abstract,
443 % then you can use LaTeX's standard command \boldmath at the very start
444 % of the abstract to achieve this. Many IEEE journals/conferences frown on
445 % math in the abstract anyway.
452 % For peer review papers, you can put extra information on the cover
454 % \ifCLASSOPTIONpeerreview
455 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
458 % For peerreview papers, this IEEEtran command inserts a page break and
459 % creates the second title. It will be ignored for other modes.
460 \IEEEpeerreviewmaketitle
463 \section{Introduction}
464 Hardware description languages has allowed the productivity of hardware
465 engineers to keep pace with the development of chip technology. Standard
466 Hardware description languages, like \VHDL\ and Verilog, allowed an engineer
467 to describe circuits using a programming language. These standard languages
468 are very good at describing detailed hardware properties such as timing
469 behavior, but are generally cumbersome in expressing higher-level
470 abstractions. These languages also tend to have a complex syntax and a lack of
471 formal semantics. To overcome these complexities, and raise the abstraction
472 level, a great number of approaches based on functional languages has been
473 proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,ForSyDe1,Wired,reFLect}. The idea
474 of using functional languages started in the early 1980s \cite{Cardelli1981,
475 muFP,DAISY,FHDL}, a time which also saw the birth of the currently popular
476 hardware description languages such as \VHDL. What gives functional languages
477 as hardware description languages their merits is the fact that basic
478 combinatorial circuits are equivalent to mathematical function, and that
479 functional languages lend themselves very well to describe and compose these
480 mathematical functions.
482 In an attempt to decrease the amount of work involved with creating all the
483 required tooling, such as parsers and type-checkers, many functional hardware
484 description languages are embedded as a domain specific language inside the
485 functional language Haskell \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}. What this
486 means is that a developer is given a library of Haskell functions and types
487 that together form the language primitives of the domain specific language.
488 Using these functions, the designer does not only describes a circuit, but
489 actually builds a large domain-specific datatype which can be further
490 processed by an embedded compiler. This compiler actually runs in the same
491 environment as the description; as a result compile-time and run-time become
492 hard to define, as the embedded compiler is usually compiled by the same
493 Haskell compiler as the circuit description itself.
495 The approach taken in this research is not to make another domain specific
496 language embedded in Haskell, but to use (a subset) of the Haskell language
497 itself to be used as hardware description language.
499 \section{Hardware description in Haskell}
501 \subsection{Function application}
502 The basic syntactic elements of a functional program are functions
503 and function application. These have a single obvious \VHDL\
504 translation: each top level function becomes a hardware component,
505 where each argument is an input port and the result value is the
506 (single) output port. This output port can have a complex type (such
507 as a tuple), so having just a single output port does not create a
510 Each function application in turn becomes component instantiation.
511 Here, the result of each argument expression is assigned to a
512 signal, which is mapped to the corresponding input port. The output
513 port of the function is also mapped to a signal, which is used as
514 the result of the application itself.
516 Since every top level function generates its own component, the
517 hierarchy of of function calls is reflected in the final \VHDL\
518 output as well, creating a hierarchical \VHDL\ description of the
519 hardware. This separation in different components makes the
520 resulting \VHDL\ output easier to read and debug.
522 Example that defines the \texttt{mac} function by applying the
523 \texttt{add} and \texttt{mul} functions to calculate $a * b + c$:
526 mac a b c = add (mul a b) c
532 Although describing components and connections allows describing a
533 lot of hardware designs already, there is an obvious thing missing:
534 choice. We need some way to be able to choose between values based
535 on another value. In Haskell, choice is achieved by \hs{case}
536 expressions, \hs{if} expressions, pattern matching and guards.
538 The easiest of these are of course case expressions (and \hs{if}
539 expressions, which can be very directly translated to \hs{case}
540 expressions). A \hs{case} expression can in turn simply be
541 translated to a conditional assignment in \VHDL, where the
542 conditions use equality comparisons against the constructors in the
543 \hs{case} expressions.
545 A slightly more complex (but very powerful) form of choice is
546 pattern matching. A function can be defined in multiple clauses,
547 where each clause specifies a pattern. When the arguments match the
548 pattern, the corresponding clause will be used.
550 A pattern match (with optional guards) can also be implemented using
551 conditional assignments in \VHDL, where the condition is the logical
552 and of comparison results of each part of the pattern as well as the
555 Contrived example that sums two values when they are equal or
556 non-equal (depending on the predicate given) and returns 0
557 otherwise. This shows three implementations, one using and if
558 expression, one using only case expressions and one using pattern
563 if pred == Eq && a == b || pred == Neq && a != b
567 sumif pred a b = case pred of
571 Neq -> case a != b of
575 sumif Eq a b | a == b = a + b
576 sumif Neq a b | a != b = a + b
583 Translation of two most basic functional concepts has been
584 discussed: function application and choice. Before looking further
585 into less obvious concepts like higher-order expressions and
586 polymorphism, the possible types that can be used in hardware
587 descriptions will be discussed.
589 Some way is needed to translate every values used to its hardware
590 equivalents. In particular, this means a hardware equivalent for
591 every \emph{type} used in a hardware description is needed
593 Since most functional languages have a lot of standard types that
594 are hard to translate (integers without a fixed size, lists without
595 a static length, etc.), a number of \quote{built-in} types will be
596 defined first. These types are built-in in the sense that our
597 compiler will have a fixed \VHDL\ type for these. User defined types,
598 on the other hand, will have their hardware type derived directly
599 from their Haskell declaration automatically, according to the rules
602 \subsection{Built-in types}
603 The language currently supports the following built-in types. Of these,
604 only the \hs{Bool} type is supported by Haskell out of the box (the
605 others are defined by the \CLaSH\ package, so they are user-defined types
606 from Haskell's point of view).
610 This is the most basic type available. It is mapped directly onto
611 the \texttt{std\_logic} \VHDL\ type. Mapping this to the
612 \texttt{bit} type might make more sense (since the Haskell version
613 only has two values), but using \texttt{std\_logic} is more standard
614 (and allowed for some experimentation with don't care values)
617 This is the only built-in Haskell type supported and is translated
618 exactly like the Bit type (where a value of \hs{True} corresponds to a
619 value of \hs{High}). Supporting the Bool type is particularly
620 useful to support \hs{if ... then ... else ...} expressions, which
621 always have a \hs{Bool} value for the condition.
623 A \hs{Bool} is translated to a \texttt{std\_logic}, just like \hs{Bit}.
624 \item[\hs{SizedWord}, \hs{SizedInt}]
625 These are types to represent integers. A \hs{SizedWord} is unsigned,
626 while a \hs{SizedInt} is signed. These types are parametrized by a
627 length type, so you can define an unsigned word of 32 bits wide as
631 type Word32 = SizedWord D32
634 Here, a type synonym \hs{Word32} is defined that is equal to the
635 \hs{SizedWord} type constructor applied to the type \hs{D32}. \hs{D32}
636 is the \emph{type level representation} of the decimal number 32,
637 making the \hs{Word32} type a 32-bit unsigned word.
639 These types are translated to the \VHDL\ \texttt{unsigned} and
640 \texttt{signed} respectively.
642 This is a vector type, that can contain elements of any other type and
643 has a fixed length. It has two type parameters: its
644 length and the type of the elements contained in it. By putting the
645 length parameter in the type, the length of a vector can be determined
646 at compile time, instead of only at run-time for conventional lists.
648 The \hs{Vector} type constructor takes two type arguments: the length
649 of the vector and the type of the elements contained in it. The state
650 type of an 8 element register bank would then for example be:
653 type RegisterState = Vector D8 Word32
656 Here, a type synonym \hs{RegisterState} is defined that is equal to
657 the \hs{Vector} type constructor applied to the types \hs{D8} (The type
658 level representation of the decimal number 8) and \hs{Word32} (The 32
659 bit word type as defined above). In other words, the
660 \hs{RegisterState} type is a vector of 8 32-bit words.
662 A fixed size vector is translated to a \VHDL\ array type.
663 \item[\hs{RangedWord}]
664 This is another type to describe integers, but unlike the previous
665 two it has no specific bit-width, but an upper bound. This means that
666 its range is not limited to powers of two, but can be any number.
667 A \hs{RangedWord} only has an upper bound, its lower bound is
668 implicitly zero. There is a lot of added implementation complexity
669 when adding a lower bound and having just an upper bound was enough
670 for the primary purpose of this type: type-safely indexing vectors.
672 To define an index for the 8 element vector above, we would do:
675 type RegisterIndex = RangedWord D7
678 Here, a type synonym \hs{RegisterIndex} is defined that is equal to
679 the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
680 other words, this defines an unsigned word with values from
681 0 to 7 (inclusive). This word can be be used to index the
682 8 element vector \hs{RegisterState} above.
684 This type is translated to the \texttt{unsigned} \VHDL type.
686 \subsection{User-defined types}
687 There are three ways to define new types in Haskell: algebraic
688 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
689 keyword and type renamings with the \hs{newtype} keyword. \GHC\
690 offers a few more advanced ways to introduce types (type families,
691 existential typing, {\small{GADT}}s, etc.) which are not standard
692 Haskell. These will be left outside the scope of this research.
694 Only an algebraic datatype declaration actually introduces a
695 completely new type, for which we provide the \VHDL\ translation
696 below. Type synonyms and renamings only define new names for
697 existing types (where synonyms are completely interchangeable and
698 renamings need explicit conversion). Therefore, these do not need
699 any particular \VHDL\ translation, a synonym or renamed type will
700 just use the same representation as the original type. The
701 distinction between a renaming and a synonym does no longer matter
702 in hardware and can be disregarded in the generated \VHDL.
704 For algebraic types, we can make the following distinction:
707 \item[\textbf{Product types}]
708 A product type is an algebraic datatype with a single constructor with
709 two or more fields, denoted in practice like (a,b), (a,b,c), etc. This
710 is essentially a way to pack a few values together in a record-like
711 structure. In fact, the built-in tuple types are just algebraic product
712 types (and are thus supported in exactly the same way).
714 The \quote{product} in its name refers to the collection of values
715 belonging to this type. The collection for a product type is the
716 Cartesian product of the collections for the types of its fields.
718 These types are translated to \VHDL\ record types, with one field for
719 every field in the constructor. This translation applies to all single
720 constructor algebraic data-types, including those with just one
721 field (which are technically not a product, but generate a VHDL
722 record for implementation simplicity).
723 \item[\textbf{Enumerated types}]
724 An enumerated type is an algebraic datatype with multiple constructors, but
725 none of them have fields. This is essentially a way to get an
726 enumeration-like type containing alternatives.
728 Note that Haskell's \hs{Bool} type is also defined as an
729 enumeration type, but we have a fixed translation for that.
731 These types are translated to \VHDL\ enumerations, with one value for
732 each constructor. This allows references to these constructors to be
733 translated to the corresponding enumeration value.
734 \item[\textbf{Sum types}]
735 A sum type is an algebraic datatype with multiple constructors, where
736 the constructors have one or more fields. Technically, a type with
737 more than one field per constructor is a sum of products type, but
738 for our purposes this distinction does not really make a
739 difference, so this distinction is note made.
741 The \quote{sum} in its name refers again to the collection of values
742 belonging to this type. The collection for a sum type is the
743 union of the the collections for each of the constructors.
745 Sum types are currently not supported by the prototype, since there is
746 no obvious \VHDL\ alternative. They can easily be emulated, however, as
747 we will see from an example:
750 data Sum = A Bit Word | B Word
753 An obvious way to translate this would be to create an enumeration to
754 distinguish the constructors and then create a big record that
755 contains all the fields of all the constructors. This is the same
756 translation that would result from the following enumeration and
757 product type (using a tuple for clarity):
761 type Sum = (SumC, Bit, Word, Word)
764 Here, the \hs{SumC} type effectively signals which of the latter three
765 fields of the \hs{Sum} type are valid (the first two if \hs{A}, the
766 last one if \hs{B}), all the other ones have no useful value.
768 An obvious problem with this naive approach is the space usage: the
769 example above generates a fairly big \VHDL\ type. Since we can be
770 sure that the two \hs{Word}s in the \hs{Sum} type will never be valid
771 at the same time, this is a waste of space.
773 Obviously, duplication detection could be used to reuse a
774 particular field for another constructor, but this would only
775 partially solve the problem. If two fields would be, for
776 example, an array of 8 bits and an 8 bit unsigned word, these are
777 different types and could not be shared. However, in the final
778 hardware, both of these types would simply be 8 bit connections,
779 so we have a 100\% size increase by not sharing these.
783 A very important concept in hardware it the concept of state. In a
784 stateful design, the outputs depend on the history of the inputs, or the
785 state. State is usually stored in registers, which retain their value
786 during a clock cycle. As we want to describe more than simple
787 combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
789 An important property in Haskell, and in most other functional languages,
790 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
793 \item given the same arguments twice, it should return the same value in
795 \item when the function is called, it should not have observable
798 This purity property is important for functional languages, since it
799 enables all kinds of mathematical reasoning that could not be guaranteed
800 correct for impure functions. Pure functions are as such a perfect match
801 for a combinatorial circuit, where the output solely depends on the
802 inputs. When a circuit has state however, it can no longer be simply
803 described by a pure function. Simply removing the purity property is not a
804 valid option, as the language would then lose many of it mathematical
805 properties. In an effort to include the concept of state in pure
806 functions, the current value of the state is made an argument of the
807 function; the updated state becomes part of the result.
809 A simple example is the description of an accumulator circuit:
811 acc :: Word -> State Word -> (State Word, Word)
812 acc inp (State s) = (State s', outp)
817 This approach makes the state of a function very explicit: which variables
818 are part of the state is completely determined by the type signature. This
819 approach to state is well suited to be used in combination with the
820 existing code and language features, such as all the choice constructs, as
821 state values are just normal values.
822 \section{\CLaSH\ prototype}
826 \section{Related work}
827 Many functional hardware description languages have been developed over the
828 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
829 extension of Backus' \acro{FP} language to synchronous streams, designed
830 particularly for describing and reasoning about regular circuits. The
831 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
832 circuits, and has a particular focus on layout. \acro{HML}~\cite{HML2} is a
833 hardware modeling language based on the strict functional language
834 \acro{ML}, and has support for polymorphic types and higher-order functions.
835 Published work suggests that there is no direct simulation support for
836 \acro{HML}, and that the translation to \VHDL\ is only partial.
838 Like this work, many functional hardware description languages have some sort
839 of foundation in the functional programming language Haskell.
840 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
841 specifications used to model the behavior of superscalar microprocessors. Hawk
842 specifications can be simulated, but there seems to be no support for
843 automated circuit synthesis. The ForSyDe~\cite{ForSyDe2} system uses Haskell
844 to specify abstract system models, which can (manually) be transformed into an
845 implementation model using semantic preserving transformations. ForSyDe has
846 several simulation and synthesis backends, though synthesis is restricted to
847 the synchronous subset of the ForSyDe language.
849 Lava~\cite{Lava} is a hardware description language that focuses on the
850 structural representation of hardware. Besides support for simulation and
851 circuit synthesis, Lava descriptions can be interfaced with formal method
852 tools for formal verification. Lava descriptions are actually circuit
853 generators when viewed from a synthesis viewpoint, in that the language
854 elements of Haskell, such as choice, can be used to guide the circuit
855 generation. If a developer wants to insert a choice element inside an actual
856 circuit he will have to specify this explicitly as a component. In this
857 respect \CLaSH\ differs from Lava, in that all the choice elements, such as
858 case-statements and patter matching, are synthesized to choice elements in the
859 eventual circuit. As such, richer control structures can both be specified and
860 synthesized in \CLaSH\ compared to any of the languages mentioned in this
863 The merits of polymorphic typing, combined with higher-order functions, are
864 now also recognized in the `main-stream' hardware description languages,
865 exemplified by the new \VHDL\ 2008 standard~\cite{VHDL2008}. \VHDL-2008 has
866 support to specify types as generics, thus allowing a developer to describe
867 polymorphic components. Note that those types still require an explicit
868 generic map, whereas type-inference and type-specialization are implicit in
871 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
873 % A functional language designed specifically for hardware design is
874 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
875 % language called \acro{FL}~\cite{FL} to la
877 % An example of a floating figure using the graphicx package.
878 % Note that \label must occur AFTER (or within) \caption.
879 % For figures, \caption should occur after the \includegraphics.
880 % Note that IEEEtran v1.7 and later has special internal code that
881 % is designed to preserve the operation of \label within \caption
882 % even when the captionsoff option is in effect. However, because
883 % of issues like this, it may be the safest practice to put all your
884 % \label just after \caption rather than within \caption{}.
886 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
887 % option should be used if it is desired that the figures are to be
888 % displayed while in draft mode.
892 %\includegraphics[width=2.5in]{myfigure}
893 % where an .eps filename suffix will be assumed under latex,
894 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
895 % via \DeclareGraphicsExtensions.
896 %\caption{Simulation Results}
900 % Note that IEEE typically puts floats only at the top, even when this
901 % results in a large percentage of a column being occupied by floats.
904 % An example of a double column floating figure using two subfigures.
905 % (The subfig.sty package must be loaded for this to work.)
906 % The subfigure \label commands are set within each subfloat command, the
907 % \label for the overall figure must come after \caption.
908 % \hfil must be used as a separator to get equal spacing.
909 % The subfigure.sty package works much the same way, except \subfigure is
910 % used instead of \subfloat.
913 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
914 %\label{fig_first_case}}
916 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
917 %\label{fig_second_case}}}
918 %\caption{Simulation results}
922 % Note that often IEEE papers with subfigures do not employ subfigure
923 % captions (using the optional argument to \subfloat), but instead will
924 % reference/describe all of them (a), (b), etc., within the main caption.
927 % An example of a floating table. Note that, for IEEE style tables, the
928 % \caption command should come BEFORE the table. Table text will default to
929 % \footnotesize as IEEE normally uses this smaller font for tables.
930 % The \label must come after \caption as always.
933 %% increase table row spacing, adjust to taste
934 %\renewcommand{\arraystretch}{1.3}
935 % if using array.sty, it might be a good idea to tweak the value of
936 % \extrarowheight as needed to properly center the text within the cells
937 %\caption{An Example of a Table}
938 %\label{table_example}
940 %% Some packages, such as MDW tools, offer better commands for making tables
941 %% than the plain LaTeX2e tabular which is used here.
942 %\begin{tabular}{|c||c|}
952 % Note that IEEE does not put floats in the very first column - or typically
953 % anywhere on the first page for that matter. Also, in-text middle ("here")
954 % positioning is not used. Most IEEE journals/conferences use top floats
955 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
956 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
957 % command of the stfloats package.
962 The conclusion goes here.
967 % conference papers do not normally have an appendix
970 % use section* for acknowledgement
971 \section*{Acknowledgment}
974 The authors would like to thank...
980 % trigger a \newpage just before the given reference
981 % number - used to balance the columns on the last page
982 % adjust value as needed - may need to be readjusted if
983 % the document is modified later
984 %\IEEEtriggeratref{8}
985 % The "triggered" command can be changed if desired:
986 %\IEEEtriggercmd{\enlargethispage{-5in}}
990 % can use a bibliography generated by BibTeX as a .bbl file
991 % BibTeX documentation can be easily obtained at:
992 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
993 % The IEEEtran BibTeX style support page is at:
994 % http://www.michaelshell.org/tex/ieeetran/bibtex/
995 \bibliographystyle{IEEEtran}
996 % argument is your BibTeX string definitions and bibliography database(s)
997 \bibliography{IEEEabrv,clash.bib}
999 % <OR> manually copy in the resultant .bbl file
1000 % set second argument of \begin to the number of references
1001 % (used to reserve space for the reference number labels box)
1002 % \begin{thebibliography}{1}
1004 % \bibitem{IEEEhowto:kopka}
1005 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1006 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1008 % \end{thebibliography}
1016 % vim: set ai sw=2 sts=2 expandtab: