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333 % *** Do not adjust lengths that control margins, column widths, etc. ***
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335 % There should be no need to do such things with IEEEtran.cls V1.6 and later.
336 % (Unless specifically asked to do so by the journal or conference you plan
337 % to submit to, of course. )
339 % correct bad hyphenation here
340 \hyphenation{op-tical net-works semi-conduc-tor}
342 % Macro for certain acronyms in small caps. Doesn't work with the
343 % default font, though (it contains no smallcaps it seems).
344 \def\acro#1{{\small{#1}}}
345 \def\VHDL{\acro{VHDL}}
347 \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}}
349 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
350 % we'll get something more complex later on.
351 \def\hs#1{\texttt{#1}}
352 \def\quote#1{``{#1}"}
354 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
356 \settowidth{\labelwidth}{#1:}
357 \setlength{\labelsep}{0.5em}
358 \setlength{\leftmargin}{\labelwidth}
359 \addtolength{\leftmargin}{\labelsep}
360 \addtolength{\leftmargin}{\parindent}
361 \setlength{\rightmargin}{0pt}
362 \setlength{\listparindent}{\parindent}
363 \setlength{\itemsep}{0 ex plus 0.2ex}
364 \renewcommand{\makelabel}[1]{##1:\hfil}
369 \usepackage{paralist}
371 \def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}
373 \usepackage{cleveref}
374 \crefname{figure}{figure}{figures}
375 \newcommand{\fref}[1]{\cref{#1}}
376 \newcommand{\Fref}[1]{\Cref{#1}}
379 %include polycode.fmt
385 % can use linebreaks \\ within to get better formatting as desired
386 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
389 % author names and affiliations
390 % use a multiple column layout for up to three different
392 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards, Bert Molenkamp, Sabih H. Gerez}
393 \IEEEauthorblockA{University of Twente, Department of EEMCS\\
394 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
395 c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl, j.kuper@@utwente.nl}}
397 % \IEEEauthorblockN{Homer Simpson}
398 % \IEEEauthorblockA{Twentieth Century Fox\\
400 % Email: homer@thesimpsons.com}
402 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
403 % \IEEEauthorblockA{Starfleet Academy\\
404 % San Francisco, California 96678-2391\\
405 % Telephone: (800) 555--1212\\
406 % Fax: (888) 555--1212}}
408 % conference papers do not typically use \thanks and this command
409 % is locked out in conference mode. If really needed, such as for
410 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
411 % after \documentclass
413 % for over three affiliations, or if they all won't fit within the width
414 % of the page, use this alternative format:
416 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
417 %Homer Simpson\IEEEauthorrefmark{2},
418 %James Kirk\IEEEauthorrefmark{3},
419 %Montgomery Scott\IEEEauthorrefmark{3} and
420 %Eldon Tyrell\IEEEauthorrefmark{4}}
421 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
422 %Georgia Institute of Technology,
423 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
424 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
425 %Email: homer@thesimpsons.com}
426 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
427 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
428 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
433 % use for special paper notices
434 %\IEEEspecialpapernotice{(Invited Paper)}
439 % make the title area
445 \CLaSH\ is a functional hardware description language that borrows both its
446 syntax and semantics from the functional programming language Haskell. The use of polymorphism and higher-order functions allow a circuit designer to describe more abstract and general specifications than are possible in the traditional hardware description languages.
448 Circuit descriptions can be translated to synthesizable VHDL using the prototype \CLaSH\ compiler. As the circuit descriptions are made in plain Haskell, simulations can also be compiled by any Haskell compiler.
450 % IEEEtran.cls defaults to using nonbold math in the Abstract.
451 % This preserves the distinction between vectors and scalars. However,
452 % if the conference you are submitting to favors bold math in the abstract,
453 % then you can use LaTeX's standard command \boldmath at the very start
454 % of the abstract to achieve this. Many IEEE journals/conferences frown on
455 % math in the abstract anyway.
462 % For peer review papers, you can put extra information on the cover
464 % \ifCLASSOPTIONpeerreview
465 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
468 % For peerreview papers, this IEEEtran command inserts a page break and
469 % creates the second title. It will be ignored for other modes.
470 \IEEEpeerreviewmaketitle
473 \section{Introduction}
474 Hardware description languages has allowed the productivity of hardware
475 engineers to keep pace with the development of chip technology. Standard
476 Hardware description languages, like \VHDL~\cite{VHDL2008} and
477 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
478 programming language. These standard languages are very good at describing
479 detailed hardware properties such as timing behavior, but are generally
480 cumbersome in expressing higher-level abstractions. In an attempt to raise the
481 abstraction level of the descriptions, a great number of approaches based on
482 functional languages has been proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,
483 ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware
484 descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL},
485 a time which also saw the birth of the currently popular hardware description
486 languages such as \VHDL. The merit of using a functional language to describe
487 hardware comes from the fact that combinatorial circuits can be directly
488 modeled as mathematical functions and that functional languages are very good
489 at describing and composing mathematical functions.
491 In an attempt to decrease the amount of work involved with creating all the
492 required tooling, such as parsers and type-checkers, many functional hardware
493 description languages are embedded as a domain specific language inside the
494 functional language Haskell \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}. This
495 means that a developer is given a library of Haskell~\cite{Haskell} functions
496 and types that together form the language primitives of the domain specific
497 language. As a result of how the signals are modeled and abstracted, the
498 functions used to describe a circuit also build a large domain-specific
499 datatype (hidden from the designer) which can be further processed by an
500 embedded compiler. This compiler actually runs in the same environment as the
501 description; as a result compile-time and run-time become hard to define, as
502 the embedded compiler is usually compiled by the same Haskell compiler as the
503 circuit description itself.
505 The approach taken in this research is not to make another domain specific
506 language embedded in Haskell, but to use (a subset of) the Haskell language
507 itself for the purpose of describing hardware. By taking this approach, we can
508 capture certain language constructs, such as Haskell's choice elements
509 (if-constructs, case-constructs, pattern matching, etc.), which are not
510 available in the functional hardware description languages that are embedded
511 in Haskell as a domain specific languages. As far as the authors know, such
512 extensive support for choice-elements is new in the domain of functional
513 hardware description languages. As the hardware descriptions are plain Haskell
514 functions, these descriptions can be compiled for simulation using an
515 optimizing Haskell compiler such as the Glasgow Haskell Compiler (\GHC)~\cite{ghc}.
517 Where descriptions in a conventional hardware description language have an
518 explicit clock for the purpose state and synchronicity, the clock is implied
519 in this research. A developer describes the behavior of the hardware between
520 clock cycles, as such, only synchronous systems can be described. Many
521 functional hardware description model signals as a stream of all values over
522 time; state is then modeled as a delay on this stream of values. The approach
523 taken in this research is to make the current state of a circuit part of the
524 input of the function and the updated state part of the output.
526 Like the standard hardware description languages, descriptions made in a
527 functional hardware description language must eventually be converted into a
528 netlist. This research also features a prototype translator called \CLaSH\
529 (pronounced: clash), which converts the Haskell code to equivalently behaving
530 synthesizable \VHDL\ code, ready to be converted to an actual netlist format
531 by an (optimizing) \VHDL\ synthesis tool.
533 \section{Hardware description in Haskell}
535 \subsection{Function application}
536 The basic syntactic elements of a functional program are functions
537 and function application. These have a single obvious translation to a
540 \item every function is translated to a component,
541 \item every function argument is translated to an input port,
542 \item the result value of a function is translated to an output port,
544 \item function applications are translated to component instantiations.
546 The output port can have a complex type (such as a tuple), so having just
547 a single output port does not pose any limitation. The arguments of a
548 function applications are assigned to a signal, which are then mapped to
549 the corresponding input ports of the component. The output port of the
550 function is also mapped to a signal, which is used as the result of the
553 Since every top level function generates its own component, the
554 hierarchy of function calls is reflected in the final netlist,% aswell,
555 creating a hierarchical description of the hardware. This separation in
556 different components makes the resulting \VHDL\ output easier to read and
559 As an example we can see the netlist of the |mac| function in
560 \Cref{img:mac-comb}; the |mac| function applies both the |mul| and |add|
561 function to calculate $a * b + c$:
564 mac a b c = add (mul a b) c
568 \centerline{\includegraphics{mac}}
569 \caption{Combinatorial Multiply-Accumulate}
573 The result of using a complex input type can be seen in
574 \cref{img:mac-comb-nocurry} where the |mac| function now uses a single
575 input tuple for the |a|, |b|, and |c| arguments:
578 mac (a, b, c) = add (mul a b) c
582 \centerline{\includegraphics{mac-nocurry}}
583 \caption{Combinatorial Multiply-Accumulate (complex input)}
584 \label{img:mac-comb-nocurry}
588 In Haskell, choice can be achieved by a large set of language constructs,
589 consisting of: \hs{case} constructs, \hs{if-then-else} constructs,
590 pattern matching, and guards. The easiest of these are the \hs{case}
591 constructs (\hs{if} expressions can be very directly translated to
592 \hs{case} expressions). A \hs{case} construct is translated to a
593 multiplexer, where the control value is linked to the selection port and
594 the output of each case is linked to the corresponding input port on the
596 % A \hs{case} expression can in turn simply be translated to a conditional
597 % assignment in \VHDL, where the conditions use equality comparisons
598 % against the constructors in the \hs{case} expressions.
599 We can see two versions of a contrived example below, the first
600 using a \hs{case} construct and the other using a \hs{if-then-else}
601 constructs, in the code below. The example sums two values when they are
602 equal or non-equal (depending on the predicate given) and returns 0
603 otherwise. Both versions of the example roughly correspond to the same
604 netlist, which is depicted in \Cref{img:choice}.
607 sumif pred a b = case pred of
611 Neq -> case a != b of
619 if a == b then a + b else 0
621 if a != b then a + b else 0
625 \centerline{\includegraphics{choice-case}}
626 \caption{Choice - sumif}
630 A slightly more complex (but very powerful) form of choice is pattern
631 matching. A function can be defined in multiple clauses, where each clause
632 specifies a pattern. When the arguments match the pattern, the
633 corresponding clause will be used. Expressions can also contain guards,
634 where the expression is only executed if the guard evaluates to true. Like
635 \hs{if-then-else} constructs, pattern matching and guards have a
636 (straightforward) translation to \hs{case} constructs and can as such be
637 mapped to multiplexers. A third version of the earlier example, using both
638 pattern matching and guards, can be seen below. The version using pattern
639 matching and guards also has roughly the same netlist representation
640 (\Cref{img:choice}) as the earlier two versions of the example.
643 sumif Eq a b | a == b = a + b
644 sumif Neq a b | a != b = a + b
649 % \centerline{\includegraphics{choice-ifthenelse}}
650 % \caption{Choice - \emph{if-then-else}}
655 Haskell is a statically-typed language, meaning that the type of a
656 variable or function is determined at compile-time. Not all of Haskell's
657 typing constructs have a clear translation to hardware, as such this
658 section will only deal with the types that do have a clear correspondence
659 to hardware. The translatable types are divided into two categories:
660 \emph{built-in} types and \emph{user-defined} types. Built-in types are
661 those types for which a direct translation is defined within the \CLaSH\
662 compiler; the term user-defined types should not require any further
663 elaboration. The translatable types are also inferable by the compiler,
664 meaning that a developer does not have to annotate every function with a
667 % Translation of two most basic functional concepts has been
668 % discussed: function application and choice. Before looking further
669 % into less obvious concepts like higher-order expressions and
670 % polymorphism, the possible types that can be used in hardware
671 % descriptions will be discussed.
673 % Some way is needed to translate every value used to its hardware
674 % equivalents. In particular, this means a hardware equivalent for
675 % every \emph{type} used in a hardware description is needed.
677 % The following types are \emph{built-in}, meaning that their hardware
678 % translation is fixed into the \CLaSH\ compiler. A designer can also
679 % define his own types, which will be translated into hardware types
680 % using translation rules that are discussed later on.
682 \subsubsection{Built-in types}
683 The following types have direct translation defined within the \CLaSH\
687 This is the most basic type available. It can have two values:
688 \hs{Low} and \hs{High}.
689 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
691 This is a basic logic type. It can have two values: \hs{True}
693 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
694 % type (where a value of \hs{True} corresponds to a value of
696 Supporting the Bool type is required in order to support the
697 \hs{if-then-else} construct, which requires a \hs{Bool} value for
699 \item[\bf{SizedWord}, \bf{SizedInt}]
700 These are types to represent integers. A \hs{SizedWord} is unsigned,
701 while a \hs{SizedInt} is signed. Both are parametrizable in their
703 % , so you can define an unsigned word of 32 bits wide as follows:
706 % type Word32 = SizedWord D32
709 % Here, a type synonym \hs{Word32} is defined that is equal to the
710 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
711 % \hs{D32} is the \emph{type level representation} of the decimal
712 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
713 % types are translated to the \VHDL\ \texttt{unsigned} and
714 % \texttt{signed} respectively.
716 This is a vector type that can contain elements of any other type and
717 has a fixed length. The \hs{Vector} type constructor takes two type
718 arguments: the length of the vector and the type of the elements
719 contained in it. The short-hand notation used for the vector type in
720 the rest of paper is: \hs{[a|n]}. Where the \hs{a} is the element
721 type, and \hs{n} is the length of the vector.
722 % The state type of an 8 element register bank would then for example
726 % type RegisterState = Vector D8 Word32
729 % Here, a type synonym \hs{RegisterState} is defined that is equal to
730 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
731 % type level representation of the decimal number 8) and \hs{Word32}
732 % (The 32 bit word type as defined above). In other words, the
733 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
734 % vector is translated to a \VHDL\ array type.
736 This is another type to describe integers, but unlike the previous
737 two it has no specific bit-width, but an upper bound. This means that
738 its range is not limited to powers of two, but can be any number.
739 An \hs{Index} only has an upper bound, its lower bound is
740 implicitly zero. The main purpose of the \hs{Index} type is to be
741 used as an index to a \hs{Vector}.
743 % \comment{TODO: Perhaps remove this example?} To define an index for
744 % the 8 element vector above, we would do:
747 % type RegisterIndex = RangedWord D7
750 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
751 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
752 % other words, this defines an unsigned word with values from
753 % 0 to 7 (inclusive). This word can be be used to index the
754 % 8 element vector \hs{RegisterState} above. This type is translated
755 % to the \texttt{unsigned} \VHDL type.
758 \subsubsection{User-defined types}
759 There are three ways to define new types in Haskell: algebraic
760 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
761 keyword and datatype renaming constructs with the \hs{newtype} keyword.
762 \GHC\ offers a few more advanced ways to introduce types (type families,
763 existential typing, {\small{GADT}}s, etc.) which are not standard Haskell.
764 As it is currently unclear how these advanced type constructs correspond
765 with hardware, they are for now unsupported by the \CLaSH\ compiler
767 Only an algebraic datatype declaration actually introduces a
768 completely new type. Type synonyms and renaming constructs only define new
769 names for existing types, where synonyms are completely interchangeable
770 and renaming constructs need explicit conversions. Therefore, these do not
771 need any particular translation, a synonym or renamed type will just use
772 the same representation as the original type. For algebraic types, we can
773 make the following distinctions:
776 \item[\bf{Single constructor}]
777 Algebraic datatypes with a single constructor with one or more
778 fields, are essentially a way to pack a few values together in a
779 record-like structure. Haskell's built-in tuple types are also defined
780 as single constructor algebraic types An example of a single
781 constructor type is the following pair of integers:
783 data IntPair = IntPair Int Int
785 % These types are translated to \VHDL\ record types, with one field
786 % for every field in the constructor.
787 \item[\bf{No fields}]
788 Algebraic datatypes with multiple constructors, but without any
789 fields are essentially a way to get an enumeration-like type
790 containing alternatives. Note that Haskell's \hs{Bool} type is also
791 defined as an enumeration type, but we have a fixed translation for
792 that. An example of such an enum type is the type that represents the
793 colors in a traffic light:
795 data TrafficLight = Red | Orange | Green
797 % These types are translated to \VHDL\ enumerations, with one
798 % value for each constructor. This allows references to these
799 % constructors to be translated to the corresponding enumeration
801 \item[\bf{Multiple constructors with fields}]
802 Algebraic datatypes with multiple constructors, where at least
803 one of these constructors has one or more fields are not
807 \subsection{Polymorphism}
808 A powerful construct in most functional languages is polymorphism, it
809 allows a function to handle values of different data types in a uniform
810 way. Haskell supports \emph{parametric polymorphism}~\cite{polymorphism},
811 meaning functions can be written without mention of any specific type and
812 can be used transparently with any number of new types.
814 As an example of a parametric polymorphic function, consider the type of
815 the following \hs{append} function, which appends an element to a vector:
817 append :: [a|n] -> a -> [a|n + 1]
820 This type is parameterized by \hs{a}, which can contain any type at
821 all. This means that \hs{append} can append an element to a vector,
822 regardless of the type of the elements in the list (as long as the type of
823 the value to be added is of the same type as the values in the vector).
824 This kind of polymorphism is extremely useful in hardware designs to make
825 operations work on a vector without knowing exactly what elements are
826 inside, routing signals without knowing exactly what kinds of signals
827 these are, or working with a vector without knowing exactly how long it
828 is. Polymorphism also plays an important role in most higher order
829 functions, as we will see in the next section.
831 Another type of polymorphism is \emph{ad-hoc
832 polymorphism}~\cite{polymorphism}, which refers to polymorphic
833 functions which can be applied to arguments of different types, but which
834 behave differently depending on the type of the argument to which they are
835 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
836 type classes, where a class definition provides the general interface of a
837 function, and class instances define the functionality for the specific
838 types. An example of such a type class is the \hs{Num} class, which
839 contains all of Haskell's numerical operations. A developer can make use
840 of this ad-hoc polymorphism by adding a constraint to a parametrically
841 polymorphic type variable. Such a constraint indicates that the type
842 variable can only be instantiated to a type whose members supports the
843 overloaded functions associated with the type class.
845 As an example we will take a look at type signature of the function
846 \hs{sum}, which sums the values in a vector:
848 sum :: Num a => [a|n] -> a
851 This type is again parameterized by \hs{a}, but it can only contain
852 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
853 we know that the addition (+) operator is defined for that type.
854 \CLaSH's built-in numerical types are also instances of the \hs{Num}
855 class, so we can use the addition operator on \hs{SizedWords} as
856 well as on \hs{SizedInts}.
858 In \CLaSH, parametric polymorphism is completely supported. Any function
859 defined can have any number of unconstrained type parameters. The \CLaSH\
860 compiler will infer the type of every such argument depending on how the
861 function is applied. There is one exception to this: The top level
862 function that is translated, can not have any polymorphic arguments (as
863 they are never applied, so there is no way to find out the actual types
864 for the type parameters).
866 \CLaSH\ does not support user-defined type classes, but does use some
867 of the built-in type classes for its built-in function, such as: \hs{Num}
868 for numerical operations, \hs{Eq} for the equality operators, and
869 \hs{Ord} for the comparison/order operators.
871 \subsection{Higher-order functions \& values}
872 Another powerful abstraction mechanism in functional languages, is
873 the concept of \emph{higher-order functions}, or \emph{functions as
874 a first class value}. This allows a function to be treated as a
875 value and be passed around, even as the argument of another
876 function. The following example should clarify this concept:
879 negVector xs = map not xs
882 The code above defines a function \hs{negVector}, which takes a vector of
883 booleans, and returns a vector where all the values are negated. It
884 achieves this by calling the \hs{map} function, and passing it
885 \emph{another function}, boolean negation, and the vector of booleans,
886 \hs{xs}. The \hs{map} function applies the negation function to all the
887 elements in the vector.
889 The \hs{map} function is called a higher-order function, since it takes
890 another function as an argument. Also note that \hs{map} is again a
891 parametric polymorphic function: It does not pose any constraints on the
892 type of the vector elements, other than that it must be the same type as
893 the input type of the function passed to \hs{map}. The element type of the
894 resulting vector is equal to the return type of the function passed, which
895 need not necessarily be the same as the element type of the input vector.
896 All of these characteristics can readily be inferred from the type
897 signature belonging to \hs{map}:
900 map :: (a -> b) -> [a|n] -> [b|n]
903 So far, only functions have been used as higher-order values. In
904 Haskell, there are two more ways to obtain a function-typed value:
905 partial application and lambda abstraction. Partial application
906 means that a function that takes multiple arguments can be applied
907 to a single argument, and the result will again be a function (but
908 that takes one argument less). As an example, consider the following
909 expression, that adds one to every element of a vector:
915 Here, the expression \hs{(+) 1} is the partial application of the
916 plus operator to the value \hs{1}, which is again a function that
917 adds one to its argument. A lambda expression allows one to introduce an
918 anonymous function in any expression. Consider the following expression,
919 which again adds one to every element of a vector:
925 Finally, higher order arguments are not limited to just built-in
926 functions, but any function defined in \CLaSH\ can have function
927 arguments. This allows the hardware designer to use a powerful
928 abstraction mechanism in his designs and have an optimal amount of
931 \comment{TODO: Describe ALU example (no code)}
934 A very important concept in hardware it the concept of state. In a
935 stateful design, the outputs depend on the history of the inputs, or the
936 state. State is usually stored in registers, which retain their value
937 during a clock cycle. As we want to describe more than simple
938 combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
940 An important property in Haskell, and in most other functional languages,
941 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
944 \item given the same arguments twice, it should return the same value in
946 \item when the function is called, it should not have observable
949 % This purity property is important for functional languages, since it
950 % enables all kinds of mathematical reasoning that could not be guaranteed
951 % correct for impure functions.
952 Pure functions are as such a perfect match or a combinatorial circuit,
953 where the output solely depends on the inputs. When a circuit has state
954 however, it can no longer be simply described by a pure function.
955 % Simply removing the purity property is not a valid option, as the
956 % language would then lose many of it mathematical properties.
957 In an effort to include the concept of state in pure
958 functions, the current value of the state is made an argument of the
959 function; the updated state becomes part of the result. In this sense the
960 descriptions made in \CLaSH are the describing the combinatorial parts of
963 A simple example is adding an accumulator register to the earlier
964 multiply-accumulate circuit, of which the resulting netlist can be seen in
965 \Cref{img:mac-state}:
968 macS (State c) a b = (State c', outp)
975 \centerline{\includegraphics{mac-state}}
976 \caption{Stateful Multiply-Accumulate}
977 \label{img:mac-state}
980 The \hs{State} keyword indicates which arguments are part of the current
981 state, and what part of the output is part of the updated state. This
982 aspect will also reflected in the type signature of the function.
983 Abstracting the state of a circuit in this way makes it very explicit:
984 which variables are part of the state is completely determined by the
985 type signature. This approach to state is well suited to be used in
986 combination with the existing code and language features, such as all the
987 choice constructs, as state values are just normal values. We can simulate
988 stateful descriptions using the recursive \hs{run} function:
991 run f s (i:inps) = o : (run f s' inps)
996 The \hs{run} function maps a list of inputs over the function that a
997 developer wants to simulate, passing the state to each new iteration. Each
998 value in the input list corresponds to exactly one cycle of the (implicit)
999 clock. The result of the simulation is a list of outputs for every clock
1000 cycle. As both the \hs{run} function and the hardware description are
1001 plain hardware, the complete simulation can be compiled by an optimizing
1004 \section{\CLaSH\ prototype}
1009 As an example of a common hardware design where the use of higher-order
1010 functions leads to a very natural description is a FIR filter, which is
1011 basically the dot-product of two vectors:
1014 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1017 A FIR filter multiplies fixed constants ($h$) with the current
1018 and a few previous input samples ($x$). Each of these multiplications
1019 are summed, to produce the result at time $t$. The equation of a FIR
1020 filter is indeed equivalent to the equation of the dot-product, which is
1024 \mathbf{x}\bullet\mathbf{y} = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot y_i }
1027 We can easily and directly implement the equation for the dot-product
1028 using higher-order functions:
1031 xs *+* ys = foldl1 (+) (zipWith (*) xs hs)
1034 The \hs{zipWith} function is very similar to the \hs{map} function: It
1035 takes a function, two vectors, and then applies the function to each of
1036 the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*) [1,
1037 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]} $\equiv$ \hs{[3,8]}).
1039 The \hs{foldl1} function takes a function, a single vector, and applies
1040 the function to the first two elements of the vector. It then applies the
1041 function to the result of the first application and the next element from
1042 the vector. This continues until the end of the vector is reached. The
1043 result of the \hs{foldl1} function is the result of the last application.
1044 As you can see, the \hs{zipWith (*)} function is just pairwise
1045 multiplication and the \hs{foldl1 (+)} function is just summation.
1047 Returning to the actual FIR filter, we will slightly change the
1048 equation belong to it, so as to make the translation to code more obvious.
1049 What we will do is change the definition of the vector of input samples.
1050 So, instead of having the input sample received at time
1051 $t$ stored in $x_t$, $x_0$ now always stores the current sample, and $x_i$
1052 stores the $ith$ previous sample. This changes the equation to the
1053 following (Note that this is completely equivalent to the original
1054 equation, just with a different definition of $x$ that will better suit
1055 the transformation to code):
1058 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1061 Consider that the vector \hs{hs} contains the FIR coefficients and the
1062 vector \hs{xs} contains the current input sample in front and older
1063 samples behind. The function that shifts the input samples is shown below:
1066 x >> xs = x +> tail xs
1069 Where the \hs{tail} function returns all but the first element of a
1070 vector, and the concatenate operator ($\succ$) adds a new element to the
1071 left of a vector. The complete definition of the FIR filter then becomes:
1074 fir (State (xs,hs)) x = (State (x >> xs,hs), xs *+* hs)
1077 The resulting netlist of a 4-taps FIR filter based on the above definition
1078 is depicted in \Cref{img:4tapfir}.
1081 \centerline{\includegraphics{4tapfir}}
1082 \caption{4-taps FIR Filter}
1086 \section{Related work}
1087 Many functional hardware description languages have been developed over the
1088 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1089 extension of Backus' \acro{FP} language to synchronous streams, designed
1090 particularly for describing and reasoning about regular circuits. The
1091 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1092 circuits, and has a particular focus on layout.
1094 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1095 functional language \acro{ML}, and has support for polymorphic types and
1096 higher-order functions. Published work suggests that there is no direct
1097 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1098 be translated to \VHDL\ and that the translated description can than be
1099 simulated in a \VHDL\ simulator. Also not all of the mentioned language
1100 features of \acro{HML} could be translated to hardware. The \CLaSH\ compiler
1101 on the other hand can correctly translate all of the language constructs
1102 mentioned in this paper to a netlist format.
1104 Like this work, many functional hardware description languages have some sort
1105 of foundation in the functional programming language Haskell.
1106 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1107 specifications used to model the behavior of superscalar microprocessors. Hawk
1108 specifications can be simulated, but there seems to be no support for
1109 automated circuit synthesis.
1111 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1112 models, which can (manually) be transformed into an implementation model using
1113 semantic preserving transformations. ForSyDe has several simulation and
1114 synthesis backends, though synthesis is restricted to the synchronous subset
1115 of the ForSyDe language.
1117 Lava~\cite{Lava} is a hardware description language that focuses on the
1118 structural representation of hardware. Besides support for simulation and
1119 circuit synthesis, Lava descriptions can be interfaced with formal method
1120 tools for formal verification. Lava descriptions are actually circuit
1121 generators when viewed from a synthesis viewpoint, in that the language
1122 elements of Haskell, such as choice, can be used to guide the circuit
1123 generation. If a developer wants to insert a choice element inside an actual
1124 circuit he will have to specify this explicitly as a component. In this
1125 respect \CLaSH\ differs from Lava, in that all the choice elements, such as
1126 case-statements and pattern matching, are synthesized to choice elements in the
1127 eventual circuit. As such, richer control structures can both be specified and
1128 synthesized in \CLaSH\ compared to any of the languages mentioned in this
1131 The merits of polymorphic typing, combined with higher-order functions, are
1132 now also recognized in the `main-stream' hardware description languages,
1133 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 has
1134 support to specify types as generics, thus allowing a developer to describe
1135 polymorphic components. Note that those types still require an explicit
1136 generic map, whereas type-inference and type-specialization are implicit in
1139 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1141 % A functional language designed specifically for hardware design is
1142 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1143 % language called \acro{FL}~\cite{FL} to la
1145 % An example of a floating figure using the graphicx package.
1146 % Note that \label must occur AFTER (or within) \caption.
1147 % For figures, \caption should occur after the \includegraphics.
1148 % Note that IEEEtran v1.7 and later has special internal code that
1149 % is designed to preserve the operation of \label within \caption
1150 % even when the captionsoff option is in effect. However, because
1151 % of issues like this, it may be the safest practice to put all your
1152 % \label just after \caption rather than within \caption{}.
1154 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1155 % option should be used if it is desired that the figures are to be
1156 % displayed while in draft mode.
1160 %\includegraphics[width=2.5in]{myfigure}
1161 % where an .eps filename suffix will be assumed under latex,
1162 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1163 % via \DeclareGraphicsExtensions.
1164 %\caption{Simulation Results}
1168 % Note that IEEE typically puts floats only at the top, even when this
1169 % results in a large percentage of a column being occupied by floats.
1172 % An example of a double column floating figure using two subfigures.
1173 % (The subfig.sty package must be loaded for this to work.)
1174 % The subfigure \label commands are set within each subfloat command, the
1175 % \label for the overall figure must come after \caption.
1176 % \hfil must be used as a separator to get equal spacing.
1177 % The subfigure.sty package works much the same way, except \subfigure is
1178 % used instead of \subfloat.
1180 %\begin{figure*}[!t]
1181 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1182 %\label{fig_first_case}}
1184 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1185 %\label{fig_second_case}}}
1186 %\caption{Simulation results}
1190 % Note that often IEEE papers with subfigures do not employ subfigure
1191 % captions (using the optional argument to \subfloat), but instead will
1192 % reference/describe all of them (a), (b), etc., within the main caption.
1195 % An example of a floating table. Note that, for IEEE style tables, the
1196 % \caption command should come BEFORE the table. Table text will default to
1197 % \footnotesize as IEEE normally uses this smaller font for tables.
1198 % The \label must come after \caption as always.
1201 %% increase table row spacing, adjust to taste
1202 %\renewcommand{\arraystretch}{1.3}
1203 % if using array.sty, it might be a good idea to tweak the value of
1204 % \extrarowheight as needed to properly center the text within the cells
1205 %\caption{An Example of a Table}
1206 %\label{table_example}
1208 %% Some packages, such as MDW tools, offer better commands for making tables
1209 %% than the plain LaTeX2e tabular which is used here.
1210 %\begin{tabular}{|c||c|}
1220 % Note that IEEE does not put floats in the very first column - or typically
1221 % anywhere on the first page for that matter. Also, in-text middle ("here")
1222 % positioning is not used. Most IEEE journals/conferences use top floats
1223 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1224 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1225 % command of the stfloats package.
1229 \section{Conclusion}
1230 The conclusion goes here.
1235 % conference papers do not normally have an appendix
1238 % use section* for acknowledgement
1239 \section*{Acknowledgment}
1242 The authors would like to thank...
1248 % trigger a \newpage just before the given reference
1249 % number - used to balance the columns on the last page
1250 % adjust value as needed - may need to be readjusted if
1251 % the document is modified later
1252 %\IEEEtriggeratref{8}
1253 % The "triggered" command can be changed if desired:
1254 %\IEEEtriggercmd{\enlargethispage{-5in}}
1256 % references section
1258 % can use a bibliography generated by BibTeX as a .bbl file
1259 % BibTeX documentation can be easily obtained at:
1260 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1261 % The IEEEtran BibTeX style support page is at:
1262 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1263 \bibliographystyle{IEEEtran}
1264 % argument is your BibTeX string definitions and bibliography database(s)
1265 \bibliography{IEEEabrv,clash.bib}
1267 % <OR> manually copy in the resultant .bbl file
1268 % set second argument of \begin to the number of references
1269 % (used to reserve space for the reference number labels box)
1270 % \begin{thebibliography}{1}
1272 % \bibitem{IEEEhowto:kopka}
1273 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1274 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1276 % \end{thebibliography}
1284 % vim: set ai sw=2 sts=2 expandtab: