X-Git-Url: https://git.stderr.nl/gitweb?p=matthijs%2Fmaster-project%2Fdsd-paper.git;a=blobdiff_plain;f=c%CE%BBash.lhs;h=1dd21ce530709fccda16e1fc74af67c2d0ccf7fc;hp=5668e326ec6b9038eed9796396c118f6883af8cf;hb=6835a7a214399baa57eec06aa5698932c4184d42;hpb=2e44f3b1a27636bcf3d878359d8cb317b2b57d45 diff --git "a/c\316\273ash.lhs" "b/c\316\273ash.lhs" index 5668e32..1dd21ce 100644 --- "a/c\316\273ash.lhs" +++ "b/c\316\273ash.lhs" @@ -354,9 +354,10 @@ \newenvironment{xlist}[1][\rule{0em}{0em}]{% \begin{list}{}{% \settowidth{\labelwidth}{#1:} - \setlength{\labelsep}{\parindent} + \setlength{\labelsep}{0.5em} \setlength{\leftmargin}{\labelwidth} \addtolength{\leftmargin}{\labelsep} + \addtolength{\leftmargin}{\parindent} \setlength{\rightmargin}{0pt} \setlength{\listparindent}{\parindent} \setlength{\itemsep}{0 ex plus 0.2ex} @@ -524,7 +525,7 @@ functional hardware description language must eventually be converted into a netlist. This research also features a prototype translator called \CLaSH\ (pronounced: clash), which converts the Haskell code to equivalently behaving synthesizable \VHDL\ code, ready to be converted to an actual netlist format -by any (optimizing) \VHDL\ synthesis tool. +by an (optimizing) \VHDL\ synthesis tool. \section{Hardware description in Haskell} @@ -585,15 +586,19 @@ by any (optimizing) \VHDL\ synthesis tool. consisting of: \hs{case} constructs, \hs{if-then-else} constructs, pattern matching, and guards. The easiest of these are the \hs{case} constructs (\hs{if} expressions can be very directly translated to - \hs{case} expressions). % Choice elements are translated to multiplexers + \hs{case} expressions). A \hs{case} construct is translated to a + multiplexer, where the control value is linked to the selection port and + the output of each case is linked to the corresponding input port on the + multiplexer. % A \hs{case} expression can in turn simply be translated to a conditional % assignment in \VHDL, where the conditions use equality comparisons % against the constructors in the \hs{case} expressions. - We can see two versions of a contrived example, the first + We can see two versions of a contrived example below, the first using a \hs{case} construct and the other using a \hs{if-then-else} constructs, in the code below. The example sums two values when they are equal or non-equal (depending on the predicate given) and returns 0 - otherwise. + otherwise. Both versions of the example roughly correspond to the same + netlist, which is depicted in \Cref{img:choice}. \begin{code} sumif pred a b = case pred of @@ -613,9 +618,6 @@ by any (optimizing) \VHDL\ synthesis tool. if a != b then a + b else 0 \end{code} - Both versions of the example correspond to the same netlist, which is - depicted in \Cref{img:choice}. - \begin{figure} \centerline{\includegraphics{choice-case}} \caption{Choice - sumif} @@ -626,22 +628,19 @@ by any (optimizing) \VHDL\ synthesis tool. matching. A function can be defined in multiple clauses, where each clause specifies a pattern. When the arguments match the pattern, the corresponding clause will be used. Expressions can also contain guards, - where the expression is only executed if the guard evaluates to true. A - pattern match (with optional guards) can be to a conditional assignments - in \VHDL, where the conditions are an equality test of the argument and - one of the patterns (combined with the guard if was present). A third - version of the earlier example, using both pattern matching and guards, - can be seen below: + where the expression is only executed if the guard evaluates to true. Like + \hs{if-then-else} constructs, pattern matching and guards have a + (straightforward) translation to \hs{case} constructs and can as such be + mapped to multiplexers. A third version of the earlier example, using both + pattern matching and guards, can be seen below. The version using pattern + matching and guards also has roughly the same netlist representation + (\Cref{img:choice}) as the earlier two versions of the example. \begin{code} sumif Eq a b | a == b = a + b sumif Neq a b | a != b = a + b sumif _ _ _ = 0 \end{code} - - The version using pattern matching and guards has the same netlist - representation (\Cref{img:choice}) as the earlier two versions of the - example. % \begin{figure} % \centerline{\includegraphics{choice-ifthenelse}} @@ -650,14 +649,17 @@ by any (optimizing) \VHDL\ synthesis tool. % \end{figure} \subsection{Types} - Haskell is a strongly-typed language, meaning that the type of a variable - or function is determined at compile-time. Not all of Haskell's typing - constructs have a clear translation to hardware, as such this section will - only deal with the types that do have a clear correspondence to hardware. - The translatable types are divided into two categories: \emph{built-in} - types and \emph{user-defined} types. Built-in types are those types for - which a direct translation is defined within the \CLaSH\ compiler; the - term user-defined types should not require any further elaboration. + Haskell is a statically-typed language, meaning that the type of a + variable or function is determined at compile-time. Not all of Haskell's + typing constructs have a clear translation to hardware, as such this + section will only deal with the types that do have a clear correspondence + to hardware. The translatable types are divided into two categories: + \emph{built-in} types and \emph{user-defined} types. Built-in types are + those types for which a direct translation is defined within the \CLaSH\ + compiler; the term user-defined types should not require any further + elaboration. The translatable types are also inferable by the compiler, + meaning that a developer does not have to annotate every function with a + type signature. % Translation of two most basic functional concepts has been % discussed: function application and choice. Before looking further @@ -675,6 +677,8 @@ by any (optimizing) \VHDL\ synthesis tool. % using translation rules that are discussed later on. \subsubsection{Built-in types} + The following types have direct translation defined within the \CLaSH\ + compiler: \begin{xlist} \item[\bf{Bit}] This is the most basic type available. It can have two values: @@ -709,7 +713,9 @@ by any (optimizing) \VHDL\ synthesis tool. This is a vector type that can contain elements of any other type and has a fixed length. The \hs{Vector} type constructor takes two type arguments: the length of the vector and the type of the elements - contained in it. + contained in it. The short-hand notation used for the vector type in + the rest of paper is: \hs{[a|n]}. Where the \hs{a} is the element + type, and \hs{n} is the length of the vector. % The state type of an 8 element register bank would then for example % be: @@ -723,12 +729,12 @@ by any (optimizing) \VHDL\ synthesis tool. % (The 32 bit word type as defined above). In other words, the % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size % vector is translated to a \VHDL\ array type. - \item[\bf{RangedWord}] + \item[\bf{Index}] This is another type to describe integers, but unlike the previous two it has no specific bit-width, but an upper bound. This means that its range is not limited to powers of two, but can be any number. - A \hs{RangedWord} only has an upper bound, its lower bound is - implicitly zero. The main purpose of the \hs{RangedWord} type is to be + An \hs{Index} only has an upper bound, its lower bound is + implicitly zero. The main purpose of the \hs{Index} type is to be used as an index to a \hs{Vector}. % \comment{TODO: Perhaps remove this example?} To define an index for @@ -749,36 +755,30 @@ by any (optimizing) \VHDL\ synthesis tool. \subsubsection{User-defined types} There are three ways to define new types in Haskell: algebraic data-types with the \hs{data} keyword, type synonyms with the \hs{type} - keyword and datatype renamings with the \hs{newtype} keyword. \GHC\ - offers a few more advanced ways to introduce types (type families, - existential typing, {\small{GADT}}s, etc.) which are not standard - Haskell. These are not currently supported. + keyword and datatype renaming constructs with the \hs{newtype} keyword. + \GHC\ offers a few more advanced ways to introduce types (type families, + existential typing, {\small{GADT}}s, etc.) which are not standard Haskell. + As it is currently unclear how these advanced type constructs correspond + with hardware, they are for now unsupported by the \CLaSH\ compiler Only an algebraic datatype declaration actually introduces a - completely new type, for which we provide the \VHDL\ translation - below. Type synonyms and renamings only define new names for - existing types, where synonyms are completely interchangeable and - renamings need explicit conversiona. Therefore, these do not need - any particular \VHDL\ translation, a synonym or renamed type will - just use the same representation as the original type. The - distinction between a renaming and a synonym does no longer matter - in hardware and can be disregarded in the generated \VHDL. For algebraic - types, we can make the following distinction: + completely new type. Type synonyms and renaming constructs only define new + names for existing types, where synonyms are completely interchangeable + and renaming constructs need explicit conversions. Therefore, these do not + need any particular translation, a synonym or renamed type will just use + the same representation as the original type. For algebraic types, we can + make the following distinctions: \begin{xlist} \item[\bf{Single constructor}] Algebraic datatypes with a single constructor with one or more fields, are essentially a way to pack a few values together in a - record-like structure. An example of such a type is the following pair - of integers: - + record-like structure. Haskell's built-in tuple types are also defined + as single constructor algebraic types An example of a single + constructor type is the following pair of integers: \begin{code} data IntPair = IntPair Int Int \end{code} - - Haskell's builtin tuple types are also defined as single - constructor algebraic types and are translated according to this - rule by the \CLaSH\ compiler. % These types are translated to \VHDL\ record types, with one field % for every field in the constructor. \item[\bf{No fields}] @@ -786,7 +786,11 @@ by any (optimizing) \VHDL\ synthesis tool. fields are essentially a way to get an enumeration-like type containing alternatives. Note that Haskell's \hs{Bool} type is also defined as an enumeration type, but we have a fixed translation for - that. + that. An example of such an enum type is the type that represents the + colors in a traffic light: + \begin{code} + data TrafficLight = Red | Orange | Green + \end{code} % These types are translated to \VHDL\ enumerations, with one % value for each constructor. This allows references to these % constructors to be translated to the corresponding enumeration @@ -797,96 +801,100 @@ by any (optimizing) \VHDL\ synthesis tool. currently supported. \end{xlist} - \subsection{Polymorphic functions} - A powerful construct in most functional language is polymorphism. - This means the arguments of a function (and consequentially, values - within the function as well) do not need to have a fixed type. - Haskell supports \emph{parametric polymorphism}, meaning a - function's type can be parameterized with another type. - - As an example of a polymorphic function, consider the following - \hs{append} function's type: - - \comment{TODO: Use vectors instead of lists?} + \subsection{Polymorphism} + A powerful construct in most functional languages is polymorphism, it + allows a function to handle values of different data types in a uniform + way. Haskell supports \emph{parametric polymorphism}~\cite{polymorphism}, + meaning functions can be written without mention of any specific type and + can be used transparently with any number of new types. + As an example of a parametric polymorphic function, consider the type of + the following \hs{append} function, which appends an element to a vector: \begin{code} - append :: [a] -> a -> [a] + append :: [a|n] -> a -> [a|n + 1] \end{code} This type is parameterized by \hs{a}, which can contain any type at - all. This means that append can append an element to a list, - regardless of the type of the elements in the list (but the element - added must match the elements in the list, since there is only one - \hs{a}). - - This kind of polymorphism is extremely useful in hardware designs to - make operations work on a vector without knowing exactly what elements - are inside, routing signals without knowing exactly what kinds of - signals these are, or working with a vector without knowing exactly - how long it is. Polymorphism also plays an important role in most - higher order functions, as we will see in the next section. - - The previous example showed unconstrained polymorphism \comment{(TODO: How - is this really called?)}: \hs{a} can have \emph{any} type. - Furthermore,Haskell supports limiting the types of a type parameter to - specific class of types. An example of such a type class is the - \hs{Num} class, which contains all of Haskell's numerical types. - - Now, take the addition operator, which has the following type: - + all. This means that \hs{append} can append an element to a vector, + regardless of the type of the elements in the list (as long as the type of + the value to be added is of the same type as the values in the vector). + This kind of polymorphism is extremely useful in hardware designs to make + operations work on a vector without knowing exactly what elements are + inside, routing signals without knowing exactly what kinds of signals + these are, or working with a vector without knowing exactly how long it + is. Polymorphism also plays an important role in most higher order + functions, as we will see in the next section. + + Another type of polymorphism is \emph{ad-hoc + polymorphism}~\cite{polymorphism}, which refers to polymorphic + functions which can be applied to arguments of different types, but which + behave differently depending on the type of the argument to which they are + applied. In Haskell, ad-hoc polymorphism is achieved through the use of + type classes, where a class definition provides the general interface of a + function, and class instances define the functionality for the specific + types. An example of such a type class is the \hs{Num} class, which + contains all of Haskell's numerical operations. A developer can make use + of this ad-hoc polymorphism by adding a constraint to a parametrically + polymorphic type variable. Such a constraint indicates that the type + variable can only be instantiated to a type whose members supports the + overloaded functions associated with the type class. + + As an example we will take a look at type signature of the function + \hs{sum}, which sums the values in a vector: \begin{code} - (+) :: Num a => a -> a -> a + sum :: Num a => [a|n] -> a \end{code} This type is again parameterized by \hs{a}, but it can only contain - types that are \emph{instances} of the \emph{type class} \hs{Num}. - Our numerical built-in types are also instances of the \hs{Num} + types that are \emph{instances} of the \emph{type class} \hs{Num}, so that + we know that the addition (+) operator is defined for that type. + \CLaSH's built-in numerical types are also instances of the \hs{Num} class, so we can use the addition operator on \hs{SizedWords} as - well as on {SizedInts}. + well as on \hs{SizedInts}. - In \CLaSH, unconstrained polymorphism is completely supported. Any - function defined can have any number of unconstrained type - parameters. The \CLaSH\ compiler will infer the type of every such - argument depending on how the function is applied. There is one - exception to this: The top level function that is translated, can - not have any polymorphic arguments (since it is never applied, so - there is no way to find out the actual types for the type - parameters). + In \CLaSH, parametric polymorphism is completely supported. Any function + defined can have any number of unconstrained type parameters. The \CLaSH\ + compiler will infer the type of every such argument depending on how the + function is applied. There is one exception to this: The top level + function that is translated, can not have any polymorphic arguments (as + they are never applied, so there is no way to find out the actual types + for the type parameters). \CLaSH\ does not support user-defined type classes, but does use some - of the builtin ones for its builtin functions (like \hs{Num} and - \hs{Eq}). + of the built-in type classes for its built-in function, such as: \hs{Num} + for numerical operations, \hs{Eq} for the equality operators, and + \hs{Ord} for the comparison/order operators. - \subsection{Higher order} + \subsection{Higher-order functions} Another powerful abstraction mechanism in functional languages, is - the concept of \emph{higher order functions}, or \emph{functions as + the concept of \emph{higher-order functions}, or \emph{functions as a first class value}. This allows a function to be treated as a value and be passed around, even as the argument of another - function. Let's clarify that with an example: + function. The following example should clarify this concept: \begin{code} - notList xs = map not xs + negVector xs = map not xs \end{code} - This defines a function \hs{notList}, with a single list of booleans - \hs{xs} as an argument, which simply negates all of the booleans in - the list. To do this, it uses the function \hs{map}, which takes - \emph{another function} as its first argument and applies that other - function to each element in the list, returning again a list of the - results. - - As you can see, the \hs{map} function is a higher order function, - since it takes another function as an argument. Also note that - \hs{map} is again a polymorphic function: It does not pose any - constraints on the type of elements in the list passed, other than - that it must be the same as the type of the argument the passed - function accepts. The type of elements in the resulting list is of - course equal to the return type of the function passed (which need - not be the same as the type of elements in the input list). Both of - these can be readily seen from the type of \hs{map}: + The code above defines a function \hs{negVector}, which takes a vector of + booleans, and returns a vector where all the values are negated. It + achieves this by calling the \hs{map} function, and passing it + \emph{another function}, boolean negation, and the vector of booleans, + \hs{xs}. The \hs{map} function applies the negation function to all the + elements in the vector. + + The \hs{map} function is called a higher-order function, since it takes + another function as an argument. Also note that \hs{map} is again a + parametric polymorphic function: It does not pose any constraints on the + type of the vector elements, other than that it must be the same type as + the input type of the function passed to \hs{map}. The element type of the + resulting vector is equal to the return type of the function passed, which + need not necessarily be the same as the element type of the input vector. + All of these characteristics can readily be inferred from the type + signature belonging to \hs{map}: \begin{code} - map :: (a -> b) -> [a] -> [b] + map :: (a -> b) -> [a|n] -> [b|n] \end{code} As an example from a common hardware design, let's look at the @@ -907,7 +915,7 @@ by any (optimizing) \VHDL\ synthesis tool. show in the next section about state. \begin{code} - fir ... = foldl1 (+) (zipwith (*) xs hs) + fir {-"$\ldots$"-} = foldl1 (+) (zipwith (*) xs hs) \end{code} Here, the \hs{zipwith} function is very similar to the \hs{map}