Add section on polymorphism.

[matthijs/master-project/dsd-paper.git] / cλash.lhs

diff --git a/cλash.lhs b/cλash.lhs
index 1b681c6430fe0114bf9d83b84c490741a559a3b5..5819c83dd48d7da7398a0c20748dd62278d876d2 100644 (file)
--- a/cλash.lhs
+++ b/cλash.lhs
@@ -122,7 +122,7 @@
 % *** GRAPHICS RELATED PACKAGES ***
 %
 \ifCLASSINFOpdf
 % *** GRAPHICS RELATED PACKAGES ***
 %
 \ifCLASSINFOpdf

-  % \usepackage[pdftex]{graphicx}
+  \usepackage[pdftex]{graphicx}

   % declare the path(s) where your graphic files are
   % \graphicspath{{../pdf/}{../jpeg/}}
   % and their extensions so you won't have to specify these with
   % declare the path(s) where your graphic files are
   % \graphicspath{{../pdf/}{../jpeg/}}
   % and their extensions so you won't have to specify these with


@@ -360,7 +360,7 @@
     \setlength{\leftmargin}{\labelwidth}
     \addtolength{\leftmargin}{\labelsep}
     \setlength{\rightmargin}{0pt}
     \setlength{\leftmargin}{\labelwidth}
     \addtolength{\leftmargin}{\labelsep}
     \setlength{\rightmargin}{0pt}

-    \setlength{\parsep}{0.5ex plus 0.2ex minus 0.1ex}
+    \setlength{\listparindent}{\parindent}

     \setlength{\itemsep}{0 ex plus 0.2ex}
     \renewcommand{\makelabel}[1]{##1:\hfil}
     }
     \setlength{\itemsep}{0 ex plus 0.2ex}
     \renewcommand{\makelabel}[1]{##1:\hfil}
     }


@@ -368,6 +368,8 @@
 {\end{list}}
 
 \usepackage{paralist}
 {\end{list}}
 
 \usepackage{paralist}

+\usepackage{xcolor}
+\def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}

 
 %include polycode.fmt
 %include clash.fmt
 
 %include polycode.fmt
 %include clash.fmt


@@ -463,50 +465,62 @@ The abstract goes here.
 \section{Introduction}
 Hardware description languages has allowed the productivity of hardware 
 engineers to keep pace with the development of chip technology. Standard 
 \section{Introduction}
 Hardware description languages has allowed the productivity of hardware 
 engineers to keep pace with the development of chip technology. Standard 

-Hardware description languages, like \VHDL\ and Verilog, allowed an engineer 
-to describe circuits using a programming language. These standard languages 
-are very good at describing detailed hardware properties such as timing 
-behavior, but are generally cumbersome in expressing higher-level 
-abstractions. These languages also tend to have a complex syntax and a lack of 
-formal semantics. To overcome these complexities, and raise the abstraction 
-level, a great number of approaches based on functional languages has been 
-proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,ForSyDe1,Wired,reFLect}. The idea 
-of using functional languages started in the early 1980s \cite{Cardelli1981,
-muFP,DAISY,FHDL}, a time which also saw the birth of the currently popular 
-hardware description languages such as \VHDL. What gives functional languages 
-as hardware description languages their merits is the fact that basic 
-combinatorial circuits are equivalent to mathematical function, and that 
-functional languages lend themselves very well to describe and compose these 
-mathematical functions.
+Hardware description languages, like \VHDL~\cite{VHDL2008} and 
+Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a 
+programming language. These standard languages are very good at describing 
+detailed hardware properties such as timing behavior, but are generally 
+cumbersome in expressing higher-level abstractions. In an attempt to raise the 
+abstraction level of the descriptions, a great number of approaches based on 
+functional languages has been proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,
+ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware 
+descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL}, 
+a time which also saw the birth of the currently popular hardware description 
+languages such as \VHDL. The merit of using a functional language to describe 
+hardware comes from the fact that basic combinatorial circuits are equivalent 
+to mathematical functions and that functional languages are very good at 
+describing and composing mathematical functions.

 
 In an attempt to decrease the amount of work involved with creating all the 
 required tooling, such as parsers and type-checkers, many functional hardware 
 description languages are embedded as a domain specific language inside the 
 
 In an attempt to decrease the amount of work involved with creating all the 
 required tooling, such as parsers and type-checkers, many functional hardware 
 description languages are embedded as a domain specific language inside the 

-functional language Haskell \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}. What this 
-means is that a developer is given a library of Haskell functions and types 
-that together form the language primitives of the domain specific language. 
-Using these functions, the designer does not only describes a circuit, but 
-actually builds a large domain-specific datatype which can be further 
-processed by an embedded compiler. This compiler actually runs in the same 
-environment as the description; as a result compile-time and run-time become 
-hard to define, as the embedded compiler is usually compiled by the same 
-Haskell compiler as the circuit description itself.
+functional language Haskell \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}. This 
+means that a developer is given a library of Haskell~\cite{Haskell} functions 
+and types that together form the language primitives of the domain specific 
+language. As a result of how the signals are modeled and abstracted, the 
+functions used to describe a circuit also build a large domain-specific 
+datatype (hidden from the designer) which can be further processed by an 
+embedded compiler. This compiler actually runs in the same environment as the 
+description; as a result compile-time and run-time become hard to define, as 
+the embedded compiler is usually compiled by the same Haskell compiler as the 
+circuit description itself.

 
 The approach taken in this research is not to make another domain specific 
 
 The approach taken in this research is not to make another domain specific 

-language embedded in Haskell, but to use (a subset) of the Haskell language 
-itself to be used as hardware description language. By taking this approach, 
-we can capture certain language constructs, such as Haskell's choice elements 
-(if-statement, case-statment, etc.), which are not available in the functional 
-hardware description languages that are embedded in Haskell. As far as the 
-authors know, such extensive support for choice-elements is new in the domain 
-of functional hardware description language. As the hardware descriptions are 
-plain Haskell functions, these descriptions can be compiled for simulation 
-using using the optimizing Haskell compiler \GHC.
+language embedded in Haskell, but to use (a subset of) the Haskell language 
+itself for the purpose of describing hardware. By taking this approach, we can 
+capture certain language constructs, such as Haskell's choice elements 
+(if-constructs, case-constructs, pattern matching, etc.), which are not 
+available in the functional hardware description languages that are embedded 
+in Haskell as a domain specific languages. As far as the authors know, such 
+extensive support for choice-elements is new in the domain of functional 
+hardware description language. As the hardware descriptions are plain Haskell 
+functions, these descriptions can be compiled for simulation using using the 
+optimizing Haskell compiler \GHC.
+
+Where descriptions in a conventional hardware description language have an 
+explicit clock for the purpose state and synchronicity, the clock is implied 
+in this research. The functions describe the behavior of the hardware between 
+clock cycles, as such, only synchronous systems can be described. Many 
+functional hardware description models signals as a stream of all values over 
+time; state is then modeled as a delay on this stream of values. The approach 
+taken in this research is to make the current state of a circuit part of the 
+input of the function and the updated state part of the output.

 
 Like the standard hardware description languages, descriptions made in a 
 
 Like the standard hardware description languages, descriptions made in a 

-functional hardware description languages must eventually be converted into a 
-netlist. This research also features an a prototype translater 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 optimizing \VHDL\ synthesis tools.
+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 an optimizing \VHDL\ synthesis tools.

 
 \section{Hardware description in Haskell}
 
 
 \section{Hardware description in Haskell}
 


@@ -519,14 +533,14 @@ netlist. This research also features an a prototype translater called \CLaSH\
     as a tuple), so having just a single output port does not create a
     limitation.
 
     as a tuple), so having just a single output port does not create a
     limitation.
 

-    Each function application in turn becomes component instantiation.
+    Each function application in turn becomes a component instantiation.

     Here, the result of each argument expression is assigned to a
     signal, which is mapped to the corresponding input port. The output
     port of the function is also mapped to a signal, which is used as
     the result of the application itself.
 
     Since every top level function generates its own component, the
     Here, the result of each argument expression is assigned to a
     signal, which is mapped to the corresponding input port. The output
     port of the function is also mapped to a signal, which is used as
     the result of the application itself.
 
     Since every top level function generates its own component, the

-    hierarchy of of function calls is reflected in the final \VHDL\
+    hierarchy of function calls is reflected in the final \VHDL\

     output as well, creating a hierarchical \VHDL\ description of the
     hardware.  This separation in different components makes the
     resulting \VHDL\ output easier to read and debug.
     output as well, creating a hierarchical \VHDL\ description of the
     hardware.  This separation in different components makes the
     resulting \VHDL\ output easier to read and debug.


@@ -538,7 +552,17 @@ netlist. This research also features an a prototype translater called \CLaSH\
 mac a b c = add (mul a b) c
 \end{code}
 
 mac a b c = add (mul a b) c
 \end{code}
 

-    TODO: Pretty picture
+\begin{figure}
+\centerline{\includegraphics{mac}}
+\caption{Combinatorial Multiply-Accumulate (curried)}
+\label{img:mac-comb}
+\end{figure}
+
+\begin{figure}
+\centerline{\includegraphics{mac-nocurry}}
+\caption{Combinatorial Multiply-Accumulate (uncurried)}
+\label{img:mac-comb-nocurry}
+\end{figure}

 
   \subsection{Choices}
     Although describing components and connections allows describing a
 
   \subsection{Choices}
     Although describing components and connections allows describing a


@@ -570,26 +594,26 @@ mac a b c = add (mul a b) c
     expression, one using only case expressions and one using pattern
     matching and guards.
 
     expression, one using only case expressions and one using pattern
     matching and guards.
 

-\begin{code}
-sumif pred a b =  if  pred == Eq && a == b ||
-                      pred == Neq && a != b
-                  then  a + b
-                  else  0
-
-sumif pred a b = case pred of
-  Eq ->   case a == b of
-    True    -> a + b
-    False   -> 0
-  Neq ->  case a != b of
-    True    -> a + b
-    False   -> 0
-
-sumif Eq a b    | a == b = a + b
-sumif Neq a b   | a != b = a + b
-sumif _ _ _     = 0
-\end{code}
+    \begin{code}
+    sumif pred a b =  if  pred == Eq && a == b ||
+                          pred == Neq && a != b
+                      then  a + b
+                      else  0
+
+    sumif pred a b = case pred of
+      Eq ->   case a == b of
+        True    -> a + b
+        False   -> 0
+      Neq ->  case a != b of
+        True    -> a + b
+        False   -> 0
+
+    sumif Eq a b    | a == b = a + b
+    sumif Neq a b   | a != b = a + b
+    sumif _ _ _     = 0
+    \end{code}

 
 

-  TODO: Pretty picture
+  \comment{TODO: Pretty picture}

 
   \subsection{Types}
     Translation of two most basic functional concepts has been
 
   \subsection{Types}
     Translation of two most basic functional concepts has been


@@ -603,7 +627,7 @@ sumif _ _ _     = 0
     every \emph{type} used in a hardware description is needed.
 
     The following types are \emph{built-in}, meaning that their hardware
     every \emph{type} used in a hardware description is needed.
 
     The following types are \emph{built-in}, meaning that their hardware

-    translation is fixed into the \CLaSH compiler. A designer can also
+    translation is fixed into the \CLaSH\ compiler. A designer can also

     define his own types, which will be translated into hardware types
     using translation rules that are discussed later on.
 
     define his own types, which will be translated into hardware types
     using translation rules that are discussed later on.
 


@@ -627,61 +651,54 @@ sumif _ _ _     = 0
         length type, so you can define an unsigned word of 32 bits wide as
         follows:
 
         length type, so you can define an unsigned word of 32 bits wide as
         follows:
 

-\begin{code}
-type Word32 = SizedWord D32
-\end{code}
+        \begin{code}
+        type Word32 = SizedWord D32
+        \end{code}

 
         Here, a type synonym \hs{Word32} is defined that is equal to the
         \hs{SizedWord} type constructor applied to the type \hs{D32}. \hs{D32}
         is the \emph{type level representation} of the decimal number 32,
 
         Here, a type synonym \hs{Word32} is defined that is equal to the
         \hs{SizedWord} type constructor applied to the type \hs{D32}. \hs{D32}
         is the \emph{type level representation} of the decimal number 32,

-        making the \hs{Word32} type a 32-bit unsigned word.
-
-        These types are translated to the \VHDL\ \texttt{unsigned} and
-        \texttt{signed} respectively.
+        making the \hs{Word32} type a 32-bit unsigned word. These types are 
+        translated to the \VHDL\ \texttt{unsigned} and \texttt{signed} 
+        respectively.

       \item[\hs{Vector}]
         This is a vector type, that can contain elements of any other type and
       \item[\hs{Vector}]
         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. The state
-        type of an 8 element register bank would then for example be:
+        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. The state type of an 8 element register bank would 
+        then for example be:

 
 

-\begin{code}
-type RegisterState = Vector D8 Word32
-\end{code}
+        \begin{code}
+        type RegisterState = Vector D8 Word32
+        \end{code}

 
         Here, a type synonym \hs{RegisterState} is defined that is equal to
 
         Here, a type synonym \hs{RegisterState} is defined that is equal to

-        the \hs{Vector} type constructor applied to the types \hs{D8} (The type
-        level representation of the decimal number 8) and \hs{Word32} (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.
+        the \hs{Vector} type constructor applied to the types \hs{D8} (The 
+        type level representation of the decimal number 8) and \hs{Word32} 
+        (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[\hs{RangedWord}]
         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
       \item[\hs{RangedWord}]
         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.
+        implicitly zero. The main purpose of the \hs{RangedWord} type is to be 
+        used as an index to a \hs{Vector}.

 
 

-        The main purpose of the \hs{RangedWord} type is to be used as an
-        index to a \hs{Vector}.
+        \comment{TODO: Perhaps remove this example?} To define an index for 
+        the 8 element vector above, we would do:

 
 

-        TODO: Perhaps remove this example?
-
-        To define an index for the 8 element vector above, we would do:
-
-\begin{code}
-type RegisterIndex = RangedWord D7
-\end{code}
+        \begin{code}
+        type RegisterIndex = RangedWord D7
+        \end{code}

 
         Here, a type synonym \hs{RegisterIndex} is defined that is equal to
         the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
         other words, this defines an unsigned word with values from
         0 to 7 (inclusive). This word can be be used to index the
 
         Here, a type synonym \hs{RegisterIndex} is defined that is equal to
         the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
         other words, this defines an unsigned word with values from
         0 to 7 (inclusive). This word can be be used to index the

-        8 element vector \hs{RegisterState} above.
-
-        This type is translated to the \texttt{unsigned} \VHDL type.
+        8 element vector \hs{RegisterState} above. This type is translated to 
+        the \texttt{unsigned} \VHDL type.

     \end{xlist}
 
   \subsection{User-defined types}
     \end{xlist}
 
   \subsection{User-defined types}


@@ -708,9 +725,8 @@ type RegisterIndex = RangedWord D7
       \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
       \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. An example of such a type is the following pair 
+        of integers:

 
 \begin{code}
 data IntPair = IntPair Int Int
 
 \begin{code}
 data IntPair = IntPair Int Int


@@ -718,27 +734,82 @@ data IntPair = IntPair Int Int
 
         Haskell's builtin tuple types are also defined as single
         constructor algebraic types and are translated according to this
 
         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.
+        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}]
         Algebraic datatypes with multiple constructors, but without any
         fields are essentially a way to get an enumeration-like type
       \item[\bf{No fields}]
         Algebraic datatypes with multiple constructors, but without any
         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.
-
-        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 value.
+        containing alternatives. Note that Haskell's \hs{Bool} type is also 
+        defined as an enumeration type, but we have a fixed translation for 
+        that. 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 value.

       \item[\bf{Multiple constructors with fields}]
         Algebraic datatypes with multiple constructors, where at least
         one of these constructors has one or more fields are not
         currently supported.
     \end{xlist}
 
       \item[\bf{Multiple constructors with fields}]
         Algebraic datatypes with multiple constructors, where at least
         one of these constructors has one or more fields are not
         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:
+    
+    TODO: Use vectors instead of lists?
+
+    \begin{code}
+    append :: [a] -> a -> [a]
+    \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 (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:
+
+    \begin{code}
+    (+) :: Num a => a -> a -> 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}
+    class, so we can use the addition operator on \hs{SizedWords} as
+    well as on {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).
+
+    \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}).
+

   \subsection{State}
     A very important concept in hardware it the concept of state. In a 
     stateful design, the outputs depend on the history of the inputs, or the 
   \subsection{State}
     A very important concept in hardware it the concept of state. In a 
     stateful design, the outputs depend on the history of the inputs, or the 


@@ -822,7 +893,7 @@ section.
 
 The merits of polymorphic typing, combined with higher-order functions, are 
 now also recognized in the `main-stream' hardware description languages, 
 
 The merits of polymorphic typing, combined with higher-order functions, are 
 now also recognized in the `main-stream' hardware description languages, 

-exemplified by the new \VHDL\-2008 standard~\cite{VHDL2008}. \VHDL-2008 has 
+exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 has 

 support to specify types as generics, thus allowing a developer to describe 
 polymorphic components. Note that those types still require an explicit 
 generic map, whereas type-inference and type-specialization are implicit in 
 support to specify types as generics, thus allowing a developer to describe 
 polymorphic components. Note that those types still require an explicit 
 generic map, whereas type-inference and type-specialization are implicit in