Simplify.lhs 20.8 KB
 Bjoern Peemoeller committed May 06, 2011 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 % $Id: Simplify.lhs,v 1.10 2004/02/13 14:02:58 wlux Exp$ % % Copyright (c) 2003, Wolfgang Lux % See LICENSE for the full license. % % Modified by Martin Engelke (men@informatik.uni-kiel.de) % \nwfilename{Simplify.lhs} \section{Optimizing the Desugared Code}\label{sec:simplify} After desugaring the source code, but before lifting local declarations, the compiler performs a few simple optimizations to improve the efficiency of the generated code. In addition, the optimizer replaces pattern bindings with simple variable bindings and selector functions. Currently, the following optimizations are implemented: \begin{itemize} \item Remove unused declarations. \item Inline simple constants. \item Compute minimal binding groups. \item Under certain conditions, inline local function definitions. \end{itemize} \begin{verbatim} > module Transform.Simplify (simplify) where > import Control.Monad.Reader as R > import Control.Monad.State as S > import qualified Data.Map as Map > import Curry.Base.Position > import Curry.Base.Ident > import Curry.Syntax  Björn Peemöller committed May 17, 2011 35 > import Base.Eval (EvalEnv)  Björn Peemöller committed Jun 24, 2011 36 > import Base.Expr  Bjoern Peemoeller committed May 06, 2011 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 > import Base.Value (ValueEnv, ValueInfo (..), bindFun, qualLookupValue) > import Messages (internalError) > import SCC > import Types > import Typing > type SimplifyState a = S.StateT ValueEnv (ReaderT EvalEnv (S.State Int)) a > type InlineEnv = Map.Map Ident Expression > type SimplifyFlags = Bool > flatFlag :: SimplifyFlags -> Bool > flatFlag x = x > simplify :: SimplifyFlags -> ValueEnv -> EvalEnv -> Module -> (Module,ValueEnv) > simplify flags tyEnv evEnv m > = S.evalState (R.runReaderT (S.evalStateT (simplifyModule flags m) tyEnv) evEnv) 1 > simplifyModule :: SimplifyFlags -> Module -> SimplifyState (Module,ValueEnv) > simplifyModule flat (Module m es ds) = > do > ds' <- mapM (simplifyDecl flat m Map.empty) ds > tyEnv <- S.get > return (Module m es ds',tyEnv) > simplifyDecl :: SimplifyFlags -> ModuleIdent -> InlineEnv -> Decl -> SimplifyState Decl > simplifyDecl flat m env (FunctionDecl p f eqs) = > liftM (FunctionDecl p f . concat) (mapM (simplifyEquation flat m env) eqs) > simplifyDecl flat m env (PatternDecl p t rhs) = > liftM (PatternDecl p t) (simplifyRhs flat m env rhs) > simplifyDecl _ _ _ d = return d \end{verbatim} After simplifying the right hand side of an equation, the compiler transforms declarations of the form \begin{quote}\tt $f\;t_1\dots t_{k-k'}\;x_{k-k'+1}\dots x_{k}$ = let $f'\;t'_1\dots t'_{k'}$ = $e$ in $f'\;x_1\dots x_{k'}$ \end{quote} into the equivalent definition \begin{quote}\tt $f\;t_1\dots t_{k-k'}\;(x_{k-k'+1}$@$t'_1)\dots(x_k$@$t'_{k'})$ = $e$ \end{quote} where the arities of $f$ and $f'$ are $k$ and $k'$, respectively, and $x_{k-k'+1},\dots,x_{k}$ are variables. This optimization was introduced in order to avoid an auxiliary function being generated for definitions whose right-hand side is a $\lambda$-expression, e.g., \verb|f . g = \x -> f (g x)|. This declaration is transformed into \verb|(.) f g x = let lambda x = f (g x) in lambda x| by desugaring and in turn is optimized into \verb|(.) f g x = f (g x)|, here. The transformation can obviously be generalized to the case where $f'$ is defined by more than one equation. However, we must be careful not to change the evaluation mode of arguments. Therefore, the transformation is applied only if $f$ and $f'$ use them same evaluation mode or all of the arguments $t'_1,\dots,t'_k$ are variables. Actually, the transformation could be applied to the case where the arguments $t_1,\dots,t_{k-k'}$ are all variables as well, but in this case the evaluation mode of $f$ may have to be changed to match that of $f'$. We have to be careful with this optimization in conjunction with newtype constructors. It is possible that the local function is applied only partially, e.g., for \begin{verbatim} newtype ST s a = ST (s -> (a,s)) returnST x = ST (\s -> (x,s)) \end{verbatim} the desugared code is equivalent to \begin{verbatim} returnST x = let lambda1 s = (x,s) in lambda1 \end{verbatim} We must not optimize'' this into \texttt{returnST x s = (x,s)} because the compiler assumes that \texttt{returnST} is a unary function. Note that this transformation is not strictly semantic preserving as the evaluation order of arguments can be changed. This happens if $f$ is defined by more than one rule with overlapping patterns and the local functions of each rule have disjoint patterns. As an example, consider the function \begin{verbatim} f (Just x) _ = let g (Left z) = x + z in g f _ (Just y) = let h (Right z) = y + z in h \end{verbatim} The definition of \texttt{f} is non-deterministic because of the overlapping patterns in the first and second argument. However, the optimized definition \begin{verbatim} f (Just x) _ (Left z) = x + z f _ (Just y) (Right z) = y + z \end{verbatim} is deterministic. It will evaluate and match the third argument first, whereas the original definition is going to evaluate the first or the second argument first, depending on the non-deterministic branch chosen. As such definitions are presumably rare, and the optimization avoids a non-deterministic split of the computation, we put up with the change of evaluation order. This transformation is actually just a special case of inlining a (local) function definition. We are unable to handle the general case because it would require to represent the pattern matching code explicitly in a Curry expression. \begin{verbatim} > simplifyEquation :: SimplifyFlags -> ModuleIdent -> InlineEnv -> Equation > -> SimplifyState [Equation] > simplifyEquation flat m env (Equation p lhs rhs) = > do > rhs' <- simplifyRhs flat m env rhs > tyEnv <- S.get > evEnv <- S.lift R.ask > return (inlineFun flat m tyEnv evEnv p lhs rhs') > inlineFun :: SimplifyFlags -> ModuleIdent -> ValueEnv -> EvalEnv -> Position -> Lhs -> Rhs > -> [Equation] > inlineFun _ m tyEnv evEnv p (FunLhs f ts) > (SimpleRhs _ (Let [FunctionDecl _ f' eqs'] e) _) > | True -- False -- inlining of functions is deactivated (hsi) > && f' notElem qfv m eqs' && e' == Variable (qualify f') && > n == arrowArity (funType m tyEnv (qualify f')) && > (evMode evEnv f == evMode evEnv f' || > and [all isVarPattern ts1 | Equation _ (FunLhs _ ts1) _ <- eqs']) = > map (mergeEqns p f ts' vs') eqs' > where n :: Int -- type signature necessary for nhc > (n,vs',ts',e') = etaReduce 0 [] (reverse ts) e > mergeEqns p1 f1 ts1 vs (Equation _ (FunLhs _ ts2) rhs) = > Equation p1 (FunLhs f1 (ts1 ++ zipWith AsPattern vs ts2)) rhs > mergeEqns _ _ _ _ _ = error "Simplify.inlineFun.mergeEqns: no pattern match" > etaReduce n1 vs (VariablePattern v : ts1) (Apply e1 (Variable v')) > | qualify v == v' = etaReduce (n1+1) (v:vs) ts1 e1 > etaReduce n1 vs ts1 e1 = (n1,vs,reverse ts1,e1) > inlineFun _ _ _ _ p lhs rhs = [Equation p lhs rhs] > simplifyRhs :: SimplifyFlags -> ModuleIdent -> InlineEnv -> Rhs -> SimplifyState Rhs > simplifyRhs flat m env (SimpleRhs p e _) = > do > e' <- simplifyExpr flat m env e > return (SimpleRhs p e' []) > simplifyRhs _ _ _ (GuardedRhs _ _) = error "Simplify.simplifyRhs: guarded rhs" \end{verbatim} Variables that are bound to (simple) constants and aliases to other variables are substituted. In terms of conventional compiler technology these optimizations correspond to constant folding and copy propagation, respectively. The transformation is applied recursively to a substituted variable in order to handle chains of variable definitions. The bindings of a let expression are sorted topologically in order to split them into minimal binding groups. In addition, local declarations occurring on the right hand side of a pattern declaration are lifted into the enclosing binding group using the equivalence (modulo $\alpha$-conversion) of \texttt{let} $x$~=~\texttt{let} \emph{decls} \texttt{in} $e_1$ \texttt{in} $e_2$ and \texttt{let} \emph{decls}\texttt{;} $x$~=~$e_1$ \texttt{in} $e_2$. This transformation avoids the creation of some redundant lifted functions in later phases of the compiler. \begin{verbatim} > simplifyExpr :: SimplifyFlags -> ModuleIdent -> InlineEnv -> Expression > -> SimplifyState Expression > simplifyExpr _ _ _ (Literal l) = return (Literal l) > simplifyExpr flat m env (Variable v) > | isQualified v = return (Variable v) > | otherwise = maybe (return (Variable v)) (simplifyExpr flat m env) > (Map.lookup (unqualify v) env) > simplifyExpr _ _ _ (Constructor c) = return (Constructor c) > simplifyExpr flags m env (Apply (Let ds e1) e2) > = simplifyExpr flags m env (Let ds (Apply e1 e2)) > simplifyExpr flags m env (Apply (Case r e1 alts) e2) > = simplifyExpr flags m env (Case r e1 (map (applyToAlt e2) alts)) > where applyToAlt e (Alt p t rhs) = Alt p t (applyRhs rhs e) > applyRhs (SimpleRhs p e1' _) e2' = SimpleRhs p (Apply e1' e2') [] > applyRhs (GuardedRhs _ _) _ = error "Simplify.simplifyExpr.applyRhs: Guarded rhs" > simplifyExpr flat m env (Apply e1 e2) = > do > e1' <- simplifyExpr flat m env e1 > e2' <- simplifyExpr flat m env e2 > return (Apply e1' e2') > simplifyExpr flags m env (Let ds e) = > do > tyEnv <- S.get > dss' <- mapM (sharePatternRhs m tyEnv) ds > simplifyLet flags m env > (scc bv (qfv m) (foldr (hoistDecls flags) [] (concat dss'))) e > simplifyExpr flat m env (Case r e alts) = > do > e' <- simplifyExpr flat m env e > alts' <- mapM (simplifyAlt flat m env) alts > return (Case r e' alts') > simplifyExpr _ _ _ _ = error "Simplify.simplifyExpr: no pattern match" > simplifyAlt :: SimplifyFlags -> ModuleIdent -> InlineEnv -> Alt -> SimplifyState Alt > simplifyAlt flat m env (Alt p t rhs) = > liftM (Alt p t) (simplifyRhs flat m env rhs) > hoistDecls :: SimplifyFlags -> Decl -> [Decl] -> [Decl] > hoistDecls flags (PatternDecl p t (SimpleRhs p' (Let ds e) _)) ds' > = foldr (hoistDecls flags) ds' (PatternDecl p t (SimpleRhs p' e []) : ds) > hoistDecls _ d ds = d : ds \end{verbatim} The declaration groups of a let expression are first processed from outside to inside, simplifying the right hand sides and collecting inlineable expressions on the fly. At present, only simple constants and aliases to other variables are inlined. A constant is considered simple if it is either a literal, a constructor, or a non-nullary function. Note that it is not possible to define nullary functions in local declarations in Curry. Thus, an unqualified name always refers to either a variable or a non-nullary function. Applications of constructors and partial applications of functions to at least one argument are not inlined because the compiler has to allocate space for them, anyway. In order to prevent non-termination, recursive binding groups are not processed. With the list of inlineable expressions, the body of the let is simplified and then the declaration groups are processed from inside to outside to construct the simplified, nested let expression. In doing so unused bindings are discarded. In addition, all pattern bindings are replaced by simple variable declarations using selector functions to access the pattern variables. \begin{verbatim} > simplifyLet :: SimplifyFlags -> ModuleIdent -> InlineEnv -> [[Decl]] -> Expression > -> SimplifyState Expression > simplifyLet flat m env [] e = simplifyExpr flat m env e > simplifyLet flags m env (ds:dss) e = > do > ds' <- mapM (simplifyDecl flags m env) ds > tyEnv <- S.get > e' <- simplifyLet flags m (inlineVars flags m tyEnv ds' env) dss e > dss'' <- > mapM (expandPatternBindings flags m tyEnv (qfv m ds' ++ qfv m e')) ds' > return (foldr (mkLet flags m) e' > (scc bv (qfv m) (concat dss''))) > inlineVars :: SimplifyFlags -> ModuleIdent -> ValueEnv -> [Decl] -> InlineEnv -> InlineEnv > inlineVars _ _ _ [PatternDecl _ (VariablePattern v) (SimpleRhs _ e _)] env > | canInline e = Map.insert v e env > where > canInline (Literal _) = True > canInline (Constructor _) = True > canInline _ = False -- inlining of variables is deactivated (hsi) > -- canInline (Variable v') > -- | isQualified v' = arrowArity (funType m tyEnv v') > 0 > -- | otherwise = v /= unqualify v' > -- canInline _ = False > inlineVars _ _ _ _ env = env > mkLet :: SimplifyFlags -> ModuleIdent -> [Decl] -> Expression -> Expression > mkLet _ m [ExtraVariables p vs] e > | null vs' = e > | otherwise = Let [ExtraVariables p vs'] e > where vs' = filter (elem qfv m e) vs > mkLet _ m [PatternDecl _ (VariablePattern v) (SimpleRhs _ e _)] (Variable v') > | v' == qualify v && v notElem qfv m e = e > mkLet _ m ds e > | null (filter (elem qfv m e) (bv ds)) = e > | otherwise = Let ds e \end{verbatim} \label{pattern-binding} In order to implement lazy pattern matching in local declarations, pattern declarations $t$~\texttt{=}~$e$ where $t$ is not a variable are transformed into a list of declarations $v_0$~\texttt{=}~$e$\texttt{;} $v_1$~\texttt{=}~$f_1$~$v_0$\texttt{;} \dots{} $v_n$~\texttt{=}~$f_n$~$v_0$ where $v_0$ is a fresh variable, $v_1,\dots,v_n$ are the variables occurring in $t$ and the auxiliary functions $f_i$ are defined by $f_i$~$t$~\texttt{=}~$v_i$ (see also appendix D.8 of the Curry report~\cite{Hanus:Report}). The bindings $v_0$~\texttt{=}~$e$ are introduced before splitting the declaration groups of the enclosing let expression (cf. the \texttt{Let} case in \texttt{simplifyExpr} above) so that they are placed in their own declaration group whenever possible. In particular, this ensures that the new binding is discarded when the expression $e$ is itself a variable. Unfortunately, this transformation introduces a well-known space leak~\cite{Wadler87:Leaks,Sparud93:Leaks} because the matched expression cannot be garbage collected until all of the matched variables have been evaluated. Consider the following function: \begin{verbatim} f x | all (' ' ==) cs = c where (c:cs) = x \end{verbatim} One might expect the call \verb|f (replicate 10000 ' ')| to execute in constant space because (the tail of) the long list of blanks is consumed and discarded immediately by \texttt{all}. However, the application of the selector function that extracts the head of the list is not evaluated until after the guard has succeeded and thus prevents the list from being garbage collected. In order to avoid this space leak we use the approach from~\cite{Sparud93:Leaks} and update all pattern variables when one of the selector functions has been evaluated. Therefore all pattern variables except for the matched one are passed as additional arguments to each of the selector functions. Thus, each of these variables occurs twice in the argument list of a selector function, once in the first argument and also as one of the remaining arguments. This duplication of names is used by the compiler to insert the code that updates the variables when generating abstract machine code. By its very nature, this transformation introduces cyclic variable bindings. Since cyclic bindings are not supported by PAKCS, we revert to a simpler translation when generating FlatCurry output. We will add only those pattern variables as additional arguments which are actually used in the code. This reduces the number of auxiliary variables and can prevent the introduction of a recursive binding group when only a single variable is used. It is also the reason for performing this transformation here instead of in the \texttt{Desugar} module. The selector functions are defined in a local declaration on the right hand side of a projection declaration so that there is exactly one declaration for each used variable. Another problem of the translation scheme is the handling of pattern variables with higher-order types, e.g., \begin{verbatim} strange :: [a->a] -> Maybe (a->a) strange xs = Just x where (x:_) = xs \end{verbatim} By reusing the types of the pattern variables, the selector function \verb|f (x:_) = x| has type \texttt{[a->a] -> a -> a} and therefore seems to be binary function. Thus, in the goal \verb|strange []| the selector is only applied partially and not evaluated. Note that this goal will fail without the type annotation. In order to ensure that a selector function is always evaluated when the corresponding variable is used, we assume that the projection declarations -- ignoring the additional arguments to prevent the space leak -- are actually defined by $f_i$~$t$~\texttt{= I}~$v_i$, using a private renaming type \begin{verbatim} newtype Identity a = I a \end{verbatim} As newtype constructors are completely transparent to the compiler, this does not change the generated code, but only the types of the selector functions. \begin{verbatim} > sharePatternRhs :: ModuleIdent -> ValueEnv -> Decl -> SimplifyState [Decl] > sharePatternRhs m tyEnv (PatternDecl p t rhs) = > case t of > VariablePattern _ -> return [PatternDecl p t rhs] > _ -> > do > v0 <- freshIdent m patternId (monoType (typeOf tyEnv t)) > let v = addRefId (srcRefOf p) v0 > return [PatternDecl p t (SimpleRhs p (mkVar v) []), > PatternDecl p (VariablePattern v) rhs] > where patternId n = mkIdent ("_#pat" ++ show n) > sharePatternRhs _ _ d = return [d] > expandPatternBindings :: SimplifyFlags -> ModuleIdent -> ValueEnv -> [Ident] > -> Decl -> SimplifyState [Decl] > > expandPatternBindings flags m tyEnv fvs (PatternDecl p t (SimpleRhs p' e _)) = > case t of > VariablePattern _ -> return [PatternDecl p t (SimpleRhs p' e [])] > _ > | flatFlag flags -> > do > fs <- sequence (zipWith getId tys vs) > return (zipWith (flatProjectionDecl p t e) fs vs) > | otherwise -> > do > fs <- mapM (freshIdent m fpSelectorId . selectorType ty) > (shuffle tys) > return (zipWith (projectionDecl p t e) fs (shuffle vs)) > > where getId t1 v = freshIdent m > (\ i -> updIdentName ( ++'#':name v) (fpSelectorId i)) > (flatSelectorType ty t1) > > vs = filter (elem fvs) (bv t) > ty = typeOf tyEnv t > tys = map (typeOf tyEnv) vs > selectorType ty0 (ty1:tys1) = > polyType (foldr TypeArrow (identityType ty1) (ty0:tys1)) > selectorType _ [] = error "Simplify.expandPatternBindings.selectorType: empty list" > > selectorDecl p1 f t1 (v:vs1) = > funDecl p1 f (t1 : map VariablePattern vs1) (mkVar v) > selectorDecl _ _ _ [] = error "Simplify.expandPatternBindings.selectorDecl: empty list" > projectionDecl p1 t1 e1 f (v:vs1) = > varDecl p1 v (Let [selectorDecl p1 f t1 (v:vs1)] > (foldl applyVar (Apply (mkVar f) e1) vs1)) > projectionDecl _ _ _ _ [] = error "Simplify.expandPatternBindings.projectionDecl: empty list" > > flatSelectorType ty0 ty1 = > polyType (TypeArrow ty0 (identityType ty1)) > flatSelectorDecl p1 f1 t1 v1 = funDecl p1 f1 [t1] (mkVar v1) > flatProjectionDecl p1 t1 e1 f1 v1 = > varDecl p1 v1 (Let [flatSelectorDecl p1 f1 t1 v1] (Apply (mkVar f1) e1)) > > expandPatternBindings _ _ _ _ d = return [d] \end{verbatim} Auxiliary functions \begin{verbatim} > isVarPattern :: ConstrTerm -> Bool > isVarPattern (VariablePattern _) = True > isVarPattern (AsPattern _ t) = isVarPattern t > isVarPattern (ConstructorPattern _ _) = False > isVarPattern (LiteralPattern _) = False > isVarPattern _ = error "Simplify.isVarPattern: no pattern match" > funType :: ModuleIdent -> ValueEnv -> QualIdent -> Type > funType m tyEnv f = > case (qualLookupValue f tyEnv) of > [Value _ (ForAll _ ty)] -> ty > _ -> case (qualLookupValue (qualQualify m f) tyEnv) of > [Value _ (ForAll _ ty)] -> ty > _ -> internalError ("funType " ++ show f) > evMode :: EvalEnv -> Ident -> Maybe EvalAnnotation > evMode evEnv f = Map.lookup f evEnv > freshIdent :: ModuleIdent -> (Int -> Ident) -> TypeScheme > -> SimplifyState Ident > freshIdent m f ty = > do > x <- liftM f (S.lift (R.lift ( S.modify succ >> S.get))) > S.modify (bindFun m x ty) > return x > shuffle :: [a] -> [[a]] > shuffle xs = shuffle' id xs > where shuffle' _ [] = [] > shuffle' f (x1:xs1) = (x1 : f xs1) : shuffle' (f . (x1:)) xs1 > mkVar :: Ident -> Expression > mkVar = Variable . qualify > applyVar :: Expression -> Ident -> Expression > applyVar e v = Apply e (mkVar v) > varDecl :: Position -> Ident -> Expression -> Decl > varDecl p v e = PatternDecl p (VariablePattern v) (SimpleRhs p e []) > funDecl :: Position -> Ident -> [ConstrTerm] -> Expression -> Decl > funDecl p f ts e = > FunctionDecl p f [Equation p (FunLhs f ts) (SimpleRhs p e [])] > identityType :: Type -> Type > identityType = TypeConstructor qIdentityId . return > where qIdentityId = qualify (mkIdent "Identity") \end{verbatim}