dsl/dsl_techniques.tex

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   5 \begin{document}
   6 \chapter{\texorpdfstring{\Glsxtrshort{DSL}}{DSL} embedding techniques}%
   7 \label{chp:dsl_embedding_techniques}%
   8 An \gls{EDSL} is a language embedded in a host language created for a specific domain\todo{citation needed?}.
   9 Properties such as referential transparency, minimal syntax, powerful type systems and rich data types make \gls{FP} languages excellent candidates for hosting \glspl{EDSL}.
  10
  11 There are two flavours of \gls{DSL} embedding: deep- and shallow embedding~\citep{boulton_experience_1992}.
  12 Shallow embedding---also called tagless embedding---models language constructs as functions in the host language.
  13 As a result, adding new language constructs---extra functions---is easy.
  14 However, the interpretation of the language is embedded in these functions, making it troublesome to add semantics since it requires updating all existing language constructs.
  15
  16 In contrast to shallow embedding, deep embedding---also called tagged embedding---models terms in the language as data types.
  17 Interpretations are functions over these data types.
  18
  19 Consequently, adding new semantics, i.e.\ novel functions, is straightforward.
  20 It can be stated that the language constructs are embedded in the functions that form a semantics.
  21 If one wants to add a language construct, all semantics functions must be revisited and revised to avoid ending up with partial functions.
  22
  23 This juxtaposition has been known for many years~\citep{reynolds_user-defined_1978} and discussed by many others~\citep{krishnamurthi_synthesizing_1998} but most famously dubbed the \emph{expression problem} by Wadler~\citep{wadler_expression_1998}:
  24
  25 \begin{quote}
  26         The \emph{expression problem} is a new name for an old problem.
  27         The goal is to define a data type by cases, where one can add new cases to the data type and new functions over the data type, without recompiling existing code, and while retaining static type safety (e.g., no casts).
  28 \end{quote}
  29
  30 Terms in an \glspl{EDSL} can have multiple interpretations\footnote{Interpretations are also called backends or views}, i.e.\ a term in the \gls{DSL} is just an interface.
  31 Commonly used intepretations are printing, compiling, simulating, optimising, verifying, proving the program\etc.
  32 There are two main flavours of embedding \glspl{DSL}.
  33 Deep embedding---also called shallow--- models terms in the language as data types, interpretations are functions over these terms.
  34 Shallow embedding---also called tagless---models terms in the language as functions, interpretations are embedded in these functions.
  35
  36 Most importantly, the two flavours differ on two axes: extensibility of language constructs and extensibility of interpretations.
  37 \todo{elaborate}
  38
  39 \Cref{sec:deep_embedding} shows the basics of deep embedding.
  40 \Cref{sec:shallow_embedding} shows the basics of shallow embedding including tagless embedding.
  41 \Cref{sec:compare_embedding} compares the embedding technique.
  42
  43 In the following sections the basics of both techniques are explained.
  44 A simple language with integers, booleans and some arithmetic operators is used as a running example.
  45
  46 \section{Deep embedding}\label{sec:deep_embedding}
  47 In a deeply embedded \gls{DSL}, the language terms are represented as data type{(s)} in the host language.
  48 Therefore, interpretations of the terms are functions that operate on these data types.
  49 \Cref{lst:exdeep} shows an implementation for the example \gls{DSL}.
  50
  51 \begin{lstHaskell}[label={lst:exdeep},caption={A deeply embedded expression \gls{DSL}.}]
  52 data Value = I Int | B Bool
  53 data Expr
  54         = Lit  Value
  55         | Plus Expr Expr
  56         | Eq   Expr Expr
  57   deriving Show
  58 \end{lstHaskell}
  59
  60 Implementing a printer for the language is straightforward, we just define a function that transforms the term to a string.
  61
  62 \begin{lstHaskell}[caption={A printer for the deeply embedded expression \gls{DSL}.}]
  63 print :: Expr -> String
  64 print (Lit i)    = show i
  65 print (Plus l r) = "(" ++ print l ++ "+" ++ print r ++ ")"
  66 print (Eq l r)   = "(" ++ print l ++ "==" ++ print r ++ ")"
  67 \end{lstHaskell}
  68
  69 Adding a construct---for example subtraction---reveals the Achilles' heel of deep embedding, namely that we need to revisit the original data type \emph{and} all the existing views.
  70 I.e.\ we need to add \haskellinline{| Sub Expr Expr} to the \haskellinline{Expr} data type.
  71 Furthermore, we need to add \haskellinline{print (Sub l r) = ...} to the \haskellinline{print} view in order to not end up with a partial function.
  72 This limitation can be overcome by lifting the views to classes (See \cref{chp:classy_deep_embedding}).
  73
  74 Implementing an evaluator for the language is possible without touching any original code, we just add a function operating on the \haskellinline{Expr} data type.
  75 To store variables, it has an extra environment argument.
  76 Here another downside of basic deep embedding arises immediately, the expressions are not typed, and therefore there has to be some type checking in the evaluation code.
  77 Luckily this problem can be overcome by switching from regular \glspl{ADT} to \glspl{GADT}, resulting in the following data type and evaluator.
  78
  79 \begin{lstHaskell}[caption={An evaluator for the deeply embedded expression \gls{DSL}.}]
  80 eval :: Expr -> Value
  81 eval (Lit i)    = i
  82 eval (Plus l r) = case (eval l, eval r) of
  83         (Lit (I l), Lit (I r)) -> I (l+r))
  84         (l, r)       -> error ("Can't add " ++ show l ++ " to " ++ show r)
  85 eval (Eq l r) = case (eval l, eval r) of
  86         (Lit (I l), Lit (I r)) -> B (l==r)
  87         (Lit (B l), Lit (B r)) -> B (l==r)
  88         (l, r)       -> error ("Can't compare " ++ show l ++ " to " ++ show r)
  89 \end{lstHaskell}
  90
  91 \subsection{\texorpdfstring{\Glsxtrlongpl{GADT}}{Generalised algebraic data types}}
  92 Deep embedding has the advantage that it is easy to build and views are easy to add.
  93 On the downside, the expressions created with this language are not necessarily type-safe.
  94 In the given language it is possible to create an expression such as \haskellinline{LitI 4 `Plus` LitB True} that adds a boolean to an integer.
  95 Extending the \gls{ADT} is easy and convenient but extending the views accordingly is tedious since it has to be done individually for all views.
  96
  97 The first downside of this type of \gls{EDSL} can be overcome by using \glspl{GADT}~\citep{cheney_first-class_2003}.
  98 \Cref{lst:exdeepgadt} shows the same language, but type-safe with a \gls{GADT}.
  99 \glspl{GADT} are not supported in the current version of \gls{CLEAN} and therefore the syntax is hypothetical (See \todo{insert link to appendix}).
 100 However, it has been shown that \glspl{GADT} can be simulated using bimaps or projection pairs~\citep[\citesection{2.2}]{cheney_lightweight_2002}.
 101 Unfortunately the lack of extendability remains a problem.
 102 If a language construct is added, no compile time guarantee can be given that all views support it.
 103
 104 \begin{lstHaskell}[label={lst:exdeepgadt},caption={A deeply embedded expression \gls{DSL} using \glspl{GADT}.}]
 105 data Expr a where
 106     Lit  :: Show a => a -> Expr a
 107     Plus :: Num a  => Expr a -> Expr a -> Expr a
 108     Eq   :: Eq a   => Expr a -> Expr a -> Expr Bool
 109
 110 eval :: Expr a -> a
 111 eval (Lit i)    = i
 112 eval (Plus l r) = eval l + eval r
 113 eval (Eq l r)   = eval l == eval r
 114 \end{lstHaskell}
 115
 116 \section{Shallow embedding}\label{sec:shallow_embedding}
 117 In a shallowly \gls{EDSL} all language constructs are expressed as functions in the host language.
 118 An evaluator view for the example language then can be implemented as the code shown in \cref{lst:exshallow}.
 119 Note that the internals of the language could have been hidden using a reader monad.
 120
 121 \begin{lstHaskell}[label={lst:exshallow}, caption={A minimal shallow \gls{EDSL}.}]
 122 type Env   = String -> Int
 123 type DSL a = Env -> a
 124
 125 lit :: a -> DSL a
 126 lit x = \e->x
 127
 128 var :: String -> DSL Int
 129 var i = \e->retrEnv e i
 130
 131 plus :: DSL Int -> DSL Int -> DSL Int
 132 plus x y = \e->x e + y e
 133
 134 eq :: Eq a => DSL a -> DSL a -> DSL Bool
 135 eq x y = \e->x e == y e
 136 \end{lstHaskell}
 137
 138 One of the advantages of shallowly embedding a language in a host language is its extendability.
 139 It is very easy to add functionality because the compile time checks of the host language guarantee whether or not the functionality is available when used.
 140 For example, adding a new construct---such as subtraction---is done as follows:
 141
 142 \begin{lstHaskell}[label={lst:exshallowsubst},caption={Adding subtraction to the shallow \gls{EDSL}.}]
 143 sub :: DSL Int -> DSL Int -> DSL Int
 144 sub x y = \e->x e - y e
 145 \end{lstHaskell}
 146
 147 Moreover, the language is type safe as it is directly typed in the host language, i.e.\ \haskellinline{lit True `plus` lit 4} is rejected.
 148 Another advantage is the intimate link with the host language, allowing for a lot more linguistic reuse such as the support of implicit sharing \citep{krishnamurthi_linguistic_2001}.
 149
 150 The downside of this method is extending the language with views.
 151 It is nearly impossible to add views to a shallowly embedded language.
 152 The only way of achieving this is by reimplementing all functions so that they run all backends at the same time or to create a single interpretation that produces a fold function \citep{gibbons_folding_2014}.
 153
 154 \subsection{Tagless-final embedding}\label{ssec:tagless}
 155 By lifting the functions representing the \gls{DSL} terms to type classes, interpretations can be added.
 156 This technique is called tagless-final---or class-based shallow---embedding.
 157 The interface for the \gls{DSL} looks as follows:
 158
 159 \begin{lstHaskell}[label={lst:extagless},caption={A minimal tagless-final \gls{EDSL}.}]
 160 class DSL v where
 161         lit :: a -> v a
 162         var :: String -> v a
 163         plus :: v Int -> v Int -> v Int
 164         eq :: Eq a => v a -> v a -> v Bool
 165 \end{lstHaskell}
 166
 167 An interpretation of this view is a data type that implements the type class.
 168
 169 \begin{lstHaskell}[label={lst:extaglessprint},caption={A pretty printer for the tagless-final \gls{EDSL}.}]
 170 data Print a = P {runPrint :: String}
 171 instance DSL Print where
 172         lit a = P (show a)
 173         var i = P i
 174         plus x y = P ("(" ++ runPrint x ++ "+" ++ runPrint y ++ ")"
 175         eq x y = P ("(" ++ runPrint x ++ "==" ++ runPrint y ++ ")"
 176 \end{lstHaskell}
 177
 178 Adding a language construct---e.g.\ subtraction---is a easy as adding a type class and providing instances for interpretations.
 179
 180 \begin{lstHaskell}[label={lst:extaglesssubt},caption={Adding subtraction to the shallow \gls{EDSL}.}]
 181 class Sub v where
 182         sub :: v Int -> v Int -> v Int
 183
 184 instance Sub Print where
 185         sub x y = P ("(" ++ runPrint x ++ "-" ++ runPrint y ++ ")"
 186 \end{lstHaskell}
 187
 188 Adding an interpretation means adding a data type and providing instances for the language constructs.
 189
 190 \begin{lstHaskell}[label={lst:extaglesseval},caption={An evaluator interpretation of the minimal tagless-final \gls{EDSL}.}]
 191 data Eval a = Eval {runEval :: Env -> a}
 192
 193 instance DSL v where
 194         lit a = Eval (\_->a)
 195         var i = Eval (\e->retrEnv e i)
 196         plus x y = Eval (\e->runEval x e + runEval y e)
 197         eq x y = Eval (\e->runEval x e == runEval y e)
 198
 199 instance Sub Eval where
 200         sub x y = Eval (\e->runEval x e - runEval y e)
 201 \end{lstHaskell}
 202
 203 \section{Comparison}\label{sec:compare_embedding}
 204 Both flavours have their strengths and weaknesses and both flavours can be improved in order to mitigate (some of the) downsides.
 205
 206 \begin{table}[ht]
 207         \begin{threeparttable}[b]
 208                 \caption{Comparison of embedding techniques, adapted from \citet[\citesection{3.6}]{sun_compositional_2022}}%
 209                 \label{tbl:dsl_comparison}
 210                 \begin{tabular}{lllllll}
 211                         \toprule
 212                                                                         & Shallow & Deep  & Hybrid          & Poly           & Comp. & Classy\\
 213                         \midrule
 214                         Transcoding free        & yes     & yes   & no              & yes            & yes            & yes\\
 215                         Linguistic reuse        & yes     & no    & partly\tnote{1} & yes            & yes            & no?\\
 216                         Extend constructs       & yes     & no    & partly\tnote{1} & yes            & yes            & yes\\
 217                         Extend interpretations  & no      & yes   & yes             & yes            & yes            & yes\\
 218                         Transformations         & no      & yes   & yes             & maybe\tnote{2} & maybe\tnote{2} & yes\\
 219                         Modular dependencies    & no      & maybe & maybe           & yes            & yes            & yes\\
 220                         Nested pattern matching & no      & yes   & yes             & no             & maybe          & maybe\tnote{3}\\
 221                         Type safe               & yes     & maybe & no              & yes            & yes            & yes\\
 222                         \bottomrule
 223                 \end{tabular}
 224                 \begin{tablenotes}
 225                         \item [1] Only in the shallowly embedded part.
 226                         \item [2] Transformations require some ingenuity and are sometimes awkward to write.
 227                         \item [3] It requires some---safe---form of dynamic typing.
 228                 \end{tablenotes}
 229         \end{threeparttable}
 230 \end{table}
 231
 232 \input{subfilepostamble}
 233 \end{document}