methods.dsl.tex

   1 There are several techniques available for creating \glspl{EDSL}. Each of
   2 them have their own advantages and disadvantages such as extendability,
   3 typedness and view support. In the following subsections each of the main
   4 techniques are briefly explained.
   5
   6 \section{Deep embedding}
   7 A deep \gls{EDSL} means that the language is represented as an \gls{ADT}. Views
   8 are functions that transform something to the datatype or the other way around.
   9 As an example we have the simple arithmetic \gls{EDSL} shown in
  10 Listing~\ref{lst:exdeep}.
  11
  12 \begin{lstlisting}[language=Clean,label={lst:exdeep},%
  13         caption={A minimal deep \gls{EDSL}}]
  14 :: DSL
  15         = LitI  Int
  16         | LitB  Bool
  17         | Var   String
  18         | Plus  DSL DSL
  19         | Minus DSL DSL
  20         | And   DSL DSL
  21         | Eq    DSL
  22 \end{lstlisting}
  23 Deep embedding has the advantage that it is very simple to build and the views
  24 are easy to make and add. However, there are also a few downsides.  The
  25 expressions created with this language are not type-safe. In the given language
  26 it is possible an expression such as \CI{Plus (LitI 4) (LitB True)} which to
  27 add a boolean to an integer. Evermore so, extending the \gls{ADT} is easy and
  28 convenient but extending the views accordingly is tedious and has to be done
  29 individually for all views.
  30
  31 The first downside of the type of \gls{EDSL} can be overcome by using
  32 \glspl{GADT}\cite{cheney_first-class_2003}. Listing~\ref{lst:exdeepgadt} shows
  33 the same language, but type-safe with a \gls{GADT}. \glspl{GADT} are not
  34 supported in the current version of \gls{Clean} and therefore the syntax is
  35 artificial. However, it has been shown that \glspl{GADT} can be simulated using
  36 bimaps or projection pairs\cite{cheney_lightweight_2002}. Unfortunately the
  37 lack of extendability stays a problem. If a language construct is added no
  38 compile time guarantee is given that all views support it.
  39
  40 \begin{lstlisting}[language=Clean,label={lst:exdeepgadt},%
  41         caption={A minimal deep \gls{EDSL} using \glspl{GADT}}]
  42 :: DSL a
  43         =     LitI  Int                   -> DSL Int
  44         |     LitB  Bool                  -> DSL Bool
  45         | E.e: Var   String                -> DSL e
  46         |     Plus  (DSL Int) (DSL Int)   -> DSL Int
  47         |     Minus (DSL Int) (DSL Int)   -> DSL Int
  48         |     And   (DSL Bool) (DSL Bool) -> DSL Bool
  49         | E.e: Eq (DSL e) (DSL e)          -> DSL Bool &  == e
  50 \end{lstlisting}
  51
  52 \section{Shallow embedding}
  53 In a shallowly \gls{EDSL} all language constructs are expressed as functions in
  54 the host language. An evaluator view for our example language then looks
  55 something like the code shown in Listing~\ref{lst:exshallow}. Note that much of
  56 the internals of the language can be hidden using monads.
  57
  58 \begin{lstlisting}[language=Clean,label={lst:exshallow},%
  59         caption={A minimal shallow \gls{EDSL}}]
  60 :: Env   = ...            // Some environment
  61 :: DSL a = DSL (Env -> a)
  62
  63 Lit :: a -> DSL a
  64 Lit x = \e->x
  65
  66 Var :: String -> DSL Int
  67 Var i = \e->retrEnv e i
  68
  69 Plus :: (DSL Int) (DSL Int) -> DSL Int
  70 Plus x y = \e->x e + y e
  71
  72 ...
  73
  74 Eq :: (DSL a) (DSL a) -> DSL Bool | == a
  75 Eq x y = \e->x e + y e
  76 \end{lstlisting}
  77
  78 The advantage of shallowly embedding a language in a host language is the
  79 extendability. It is very easy to add functionality and compile time checks
  80 guarantee that the functionality is available. Moreover, the language is type
  81 safe as it is directly typed in the host language.
  82
  83 The downside of this method is extending the language with views. It is near
  84 impossible to add views to a shallowly embedded language. The only way of
  85 achieving this is by decorating the datatype for the \gls{EDSL} with all the
  86 information for all the views. This will mean that every component will have to
  87 implement all views. This makes it slow for multiple views and complex to
  88 implement.
  89
  90 \section{Class based shallow embedding}
  91 The third type of embedding is called class based shallow embedding and has the
  92 best of both shallow and deep embedding. In class based shallow embedding the
  93 language constructs are defined as type classes. The same language is shown
  94 with the new method in Listing~\ref{lst:exclassshallow}.
  95
  96 This type of embedding inherits the easiness of adding views from shallow
  97 embedding. A view is just a different data type implementing one or more of the
  98 type classes as shown in the aforementioned Listing where an evaluator and a
  99 pretty printer are implemented.
 100
 101 Just as with \glspl{GADT} in deep embedding type safety is guaranteed. Type
 102 constraints are enforced through phantom types. One can add as many phantom
 103 type as is necessary. Lastly, extensions can be added easily, just as in
 104 shallow embedding. When an extension is made in an existing class, all views
 105 must be updated accordingly to prevent possible runtime errors. When an
 106 extension is added in a new class this problem does not arise and views can
 107 choose to implement only parts of the collection of classes.
 108
 109 \begin{lstlisting}[language=Clean,label={lst:exclassshallow},%
 110         caption={A minimal class based shallow \gls{EDSL}}]
 111 :: Env   = ...            // Some environment
 112 :: Evaluator a = Evaluator (Env -> a)
 113 :: PrettyPrinter a = PP String
 114
 115 class intArith where
 116         lit   :: t -> v t             | toString t
 117         add   :: (v t) (v t) -> (v t) | + t
 118         minus :: (v t) (v t) -> (v t) | - t
 119
 120 class boolArith where
 121         and :: (v Bool) (v Bool) -> (v Bool)
 122         eq  :: (v t)    (v t)    -> (v Bool) | == t
 123
 124 instance intArith Evaluator where
 125         lit x = \e->x
 126         add x y = ...
 127
 128 instance intArith PrettyPrinter where
 129         lit x = toString x
 130         add x y = x +++ "+" +++ y
 131         ...
 132 \end{lstlisting}