From 35bacc40c098f8fe9b46a8ce5352780997fd99a0 Mon Sep 17 00:00:00 2001 From: Rocco Jiang Date: Tue, 2 Jul 2024 01:48:58 +0100 Subject: [PATCH] Update up to end of impl chapter --- main.pdf | Bin 681398 -> 681625 bytes main.sty | 4 ++-- src/background/parsers.pdf | Bin 50357 -> 50396 bytes src/background/parsers.tex | 15 +++++-------- src/background/tools.pdf | Bin 262475 -> 262476 bytes src/background/tools.tex | 2 +- src/body/body.pdf | Bin 184530 -> 223885 bytes src/body/body.tex | 4 ---- src/body/impl.pdf | Bin 123548 -> 125781 bytes src/body/impl.tex | 12 +--------- src/body/impl/expr.pdf | Bin 106041 -> 106115 bytes src/body/impl/expr.tex | 35 ++++++------------------------ src/body/impl/parser.pdf | Bin 49498 -> 49545 bytes src/body/impl/parser.tex | 3 +-- src/body/leftrec.pdf | Bin 92539 -> 92497 bytes src/body/leftrec.tex | 33 ++++++++-------------------- src/body/simple-rules.pdf | Bin 60489 -> 60567 bytes src/body/simple-rules.tex | 20 +++++------------ src/conclusion/conclusion.pdf | Bin 52471 -> 52471 bytes src/conclusion/conclusion.tex | 13 ----------- src/evaluation/evaluation.pdf | Bin 162598 -> 162610 bytes src/evaluation/evaluation.tex | 6 ++--- src/introduction/introduction.pdf | Bin 50917 -> 50929 bytes src/introduction/introduction.tex | 2 +- 24 files changed, 35 insertions(+), 114 deletions(-) diff --git a/main.pdf b/main.pdf index 636dca861c4070931b737a386a87ac7136ef65bc..09eebb6059d0e8ed62d53b96391fc833bb9542a7 100644 GIT binary patch delta 146816 zcmV)9K*hhd%PE=7DWFLLGBuZhSOgV+S;>wgHw?Y|E9wWjMhmq8Mg#WP4lt)IeGBH4 zAaltaf*kVu(Lzy_N@cr&oP-hTaAF5mt=h~?WNmY)vix5KAf(2HNC zT;BdV$oNz&a&c;L!LQou7yHQc8*B50(`~;VDaQwTW5;p$V^s6f> zwkLT_GQiez?Zzca%GC?~ykG8`pdd;yW+P3;-72Y8Bo2yK-(Jg^)x^BRj7E_Ybdgu& zzP?D44k}@}z8(JQgAS_+Zu#SX`{DPm@!_BG@5>@q9sKfNUiN(fBUj~Y{QURw+u@f1 zOFo8l)exh@t#u-9QHzm&wGjvuu-%A{mStR$ zHd#gEt8inv{iCqBysq=;^HWU|S~vA%=bLOcnWN}=z~6lNoZONXwXZe_cCY?eKFmtlhX>0 z4JKqHgHbZ6tOC#Ad~GIwMmaVmr%0~TAtgb`A+aTb#W}^A=Bl(yrd^k6P?iOxlV?E; 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basicstyle=\ttfamily, flexiblecolumns=false, escapechar=\%, % char to escape out of listings and back to LaTeX - % literate={\\}{{$\lambda$}}1 % the lambda looks pretty bad so I've disabled this + % literate={\\}{{$\lambda$}}1 % the lambda looks pretty bad so I have disabled this } \fi @@ -142,7 +142,7 @@ \pgfplotsset{compat=1.18} \usepgfplotslibrary{fillbetween} -% \setstretch{1.15} % adjust as needed, I like it when there's a bit more vertical space +% \setstretch{1.15} % adjust as needed, I like it when there is a bit more vertical space \setcounter{secnumdepth}{3} % number subsubsections diff --git a/src/background/parsers.pdf b/src/background/parsers.pdf index 83491d13a6ee30c7a25a7e67de975b90b774d4c4..500da68c167f53ffa12f9a967d6ee504f60c74b7 100644 GIT binary patch delta 14486 zcmai)Q*19xwDxP;wr$(CZM)rd`>%~%+qSJ;+qP}H{oa#&7w7I=O(vPlTA7tuS@}Ir zOC;!4BxrpDG$;oXdy=v(8lZ)L+<}bO<@G1(BXDNF7bpm*LLJA*w_(%|cWONB)Tl4` zIvB9q&rdR@C$sEV?m(RaH!@;mXZC%5YWSHPWF_L{f*^Mt)kZ>O^3 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Firstly, compiler plugins are tightly coupled with the compiler itself, and therefore not portable across major compiler versions. % https://github.com/mattmoore/scala-compiler-plugins is a good reference, in case I need to revisit this -For instance, plugins written for the Scala 3 compiler, known as \texttt{dotty}, are completely incompatible with Scala 2 plugins~\cite{lampepfl_changes_2022}. +For instance, plugins written for the Scala 3 compiler, known as \emph{Dotty}, are completely incompatible with Scala 2 plugins~\cite{lampepfl_changes_2022}. Additionally, developing compiler plugins requires a deep understanding of arcane and poorly documented compiler internals. Exposing the full compiler \textsc{api} permits unsafe operations that may violate undocumented invariants assumed by the compiler, leading to exceptions during compilation or even malformed bytecode~\cite{sherwany_refactoring_2015}. 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structures and operations that allow to write metaprograms, i.e. programs that manipulate other programs as data. For example, scala.reflect which is developed and described in this dissertation is a metaprogramming framework, because it contains classes like Tree, Symbol, Type and others that represent Scala programs as data and exposes operations like prettyprinting, name resolution, typechecking and others that can manipulate this data. -% We say that metaprogramming frameworks provide the ability to reflect programs, i.e. reify program elements as data structures that can be introspected by metaprograms. For instance, scala.reflect provides facilities to reflect Scala programs. These facilities include the ability to reify definitions written in the source code as instances of class Symbol. Metaprograms can call methods like Symbol.info to introspect these definitions. - \subfile{simple-rules}% \subfile{leftrec}% \subfile{impl}% diff --git a/src/body/impl.pdf b/src/body/impl.pdf index ff0a22bfcf124cddd6caf04d74044c90665423e9..918f967b15d5767cb2d5e802d2f3b666e0acd6ec 100644 GIT binary patch delta 82706 zcmV(-K-|Ba#Rt{a2e7mW0XCQ61OXJ2$q5aAM*9L33dpL=GBCb)>DypVHarJ=4z>^e zeN&;0q!f`+%OSh7BDGKymq&_a;Sz;XmmmN5 zrr@c(s7uh7kfJcrTz>q1`Q=GUr=_$8{z}I<|v=dLXQX)!oo-v1O&=y8KNZ=Go?BQnYxbMIx&w#Kc8$v~;_HQb^RyYvszy1F0mtW!G-{JG~MG6DE z@xQIv?-%Qo(80s^e_j6i?ay5)sB##PQDH2I8`F;f;t+KgK3hddmrb0-PU$9p5ayyc z0d~`vKv8l5al35by$VL#&@5h8wEb~#dnG>kdlw2_`#8jD=~AWIJjbWn&DJ5VRp#Ed zVOByT1#q=4LJ9BkTD)*!FlUobn9v5SZP!Ye&2x7B$ppqt7ZW^|x87hVX??Qs1LP!A zF7F%l;i)w6OgZpMZ_Qdt(^ryt}GYBu6SZzn4oU6m0}sMF=i#+WLfTg&US z&tyuN&zL-_q1&DX2@4KLKPZ}4UHa{jMyYPL^SrN!pM^P@pGsk|%D=0B{<|3)Z(m#6 zZ9|I&6f4`CbAN*6qmW`M8*Z2s#T8Bs|MUDkU>UW%Uzeb|+e7Y}Oj9bhxzaZBwucdO z>7nTQN{%DE<lXViZXke=-_2%xITr??meW%N} 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The following ideas are explored: \begin{itemize} - \item First, \cref{sec:simplify-parsers} discusses how parser terms can be simplified via domain-specific optimisations based on parser laws. + \item First, \cref{sec:simplify-parsers} discusses how parsers can be simplified via domain-specific optimisations based on parser laws. \item Afterwards, \cref{sec:simplify-exprs} discusses how expressions can be partially evaluated to some extent. This is achieved using another intermediate \textsc{ast}, this time based on the $\lambda$-calculus, which unlocks the idea of $\beta$-reduction and normalisation as tools to reduce the complexity of these terms. \end{itemize} -% Core embedded dsl with shallow embeddings as smart constructors https://link.springer.com/chapter/10.1007/978-3-642-40447-4_2 (folding dsls paper by gibbons and wu cites this as the originator of the "core" language idea) - -% DSL optimisation = for speed, linter optimisation = for readability - -% The idea is that we're linting and rewriting for the PARSLEY DSL, so really its better to work on a parsley ast -% Since it's embedded it also has access to host language features, which is why we still work on top of the scala ast -% And some of the stuff e.g. expressions can also be treated as a dsl and lifted into an intermediate ast - -% https://okmij.org/ftp/Denotational.html % Parser: syntactic approach to optimisation/simplification, focusing on term 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\section{Representing and Normalising Expressions}\label{sec:simplify-exprs} -% \Cref{sec:parser-representation} showed that it is useful to lift Scala \textsc{ast} nodes to a specialised \scala{Parser} \textsc{ast}, making it easier to manipulate and inspect parsers. -% Crucially, this allowed us to simplify parsers via term-rewriting rules based on parser laws. -% \Cref{sec:simplify-parsers} demonstrated why this is necessary for \texttt{parsley-garnish}: transformations such as left-recursion factoring~\cref{sec:factor-leftrec} result in complex parser terms that must be simplified to be readable. - The previous \namecref{sec:simplify-parsers} demonstrated the process of simplifying the \scala{Parser} \textsc{ast}, but this is not the only syntactic structure that requires simplification. So far, parsers such as \scala{pure} and \scala{map} still treat expressions as black boxes in the form of raw \scala{scala.meta.Term} \textsc{ast} nodes. This is evident from where the example in \cref{sec:simplify-example} left off, where the parser itself is in a simplified form, but the function passed to \scala{map} is not: @@ -18,7 +14,7 @@ \section{Representing and Normalising Expressions}\label{sec:simplify-exprs} Therefore, this \namecref{sec:simplify-exprs} explores the following: \begin{itemize} \item How expressions can be represented as another intermediate \textsc{ast}, so that they are statically inspectable enough to be simplified. - \item The idea of \emph{normalisation} to reduce expressions into a semantically equivalent but syntactically simpler form. + \item The notion of \emph{normalisation}, in order to reduce expressions into a semantically equivalent but syntactically simpler form. \end{itemize} \subsection{The $n$-ary Lambda Calculus} @@ -29,7 +25,7 @@ \subsection{The $n$-ary Lambda Calculus} In the standard $\lambda$-calculus, each function only takes one argument, and multi-argument functions are represented as a chain of single-argument functions: this is known as \emph{currying}. Scala supports curried functions using multiple parameter lists, but uncurried functions are preferred for performance reasons. Since these functions will be transformed from Scala code and back, it is desirable to maintain a high-level equivalence between these two representations. -Thus, the expression \textsc{ast} will be based on \cref{fig:lambda-calculus}, which extends the $\lambda$-calculus to support proper multi-argument functions using $n$-ary abstraction and application. +As a result, the expression \textsc{ast} will be based on \cref{fig:lambda-calculus}, which extends the $\lambda$-calculus to support proper multi-argument functions using $n$-ary abstraction and application. \begin{figure} % annoying \enspace hack to get operators aligned along the centre @@ -65,10 +61,10 @@ \subsubsection{$\beta$-Reduction and $\alpha$-Conversion} (\lamabs{x} \lamabs{y} x\ y)\ y &\betastep& (\lamabs{y} x\ y)\ [y / x] \\ &\lameq& \lamabs{y} y\ y \end{lambdacalc} -The $y$ that was substituted was originally a free variable, distinct from the $y$ bound in the lambda $\lambda y. x y$. % some weird spacing hacks because $y$ is weirdly slanted -However, after substitution, it became captured under the lambda, where the two $y\ $ terms are now indistinguishable in the incorrect expression $\lambda y. y y$. -The correct $\beta$-reduction with capture-avoiding substitution would instead proceed as follows: +The $y\ $ that was substituted was originally a free variable, distinct from the $y\ $ bound in the lambda $\lambda y. x y$. +However, after substitution, it became captured under the lambda, where the two $y\ $ terms have become indistinguishable in the incorrect expression $\lambda y. y y$. +Instead, the correct $\beta$-reduction using capture-avoiding substitution would proceed as follows: \begin{lambdacalc} (\lamabs{x} \lamabs{y} x\ y)\ y &\betastep& (\lamabs{y} x\ y)\ [y / x] \\ &\alphaequiv& (\lamabs{z} x\ z)\ [y/x] \\ @@ -153,8 +149,6 @@ \subsection{Representing Names} Therefore, this representation performs substitution through Scala's function application, which makes it extremely fast compared to the other approaches. However, since lambda abstractions are represented as closures within Scala itself, the function body becomes wrapped under Scala's variable bindings, making them difficult to inspect and work with. -% \scala{Expr} has one binding construct -- the n-ary abstraction. This introduces variables and the need for capture-avoiding substitution. - \subsection{Normalisation Strategies}\label{sec:normalisation-approach} One remaining hurdle stands before deciding on an \textsc{adt} representation: how normalisation will be implemented. The ideas of partial evaluation and normalisation are related concepts -- it is useful to view normalisation as statically evaluating as many terms as possible, but since not all terms have known values, the expression cannot be fully evaluated to a result value. @@ -205,18 +199,6 @@ \subsection{The Expression \textsc{adt}} \item Reifying \scala{Sem} terms back into syntactic \scala{Expr} terms automatically $\alpha$-converts names, granting $\alpha$-equivalence for free. \end{itemize} % -% \subsubsection{Defunctionalisation} -% In the same way that representing parsers as datatypes allows them to be statically inspectable, the aforementioned higher-order functions can also be rendered as datatypes to allow them to be analysed in a similar manner. -% This is an example of \emph{defunctionalisation}, a technique to eliminate higher-order functions by transforming them into specialised first-order equivalents~\cite{reynolds_defunc_1972,danvy_defunctionalization_2001}. -% -% Ideally for type safety, this could be represented as a generalised algebraic data type (\textsc{gadt})~\cite{cheney_gadt_2003} with a type parameter documenting the type that the function term represents: -% \begin{minted}{scala} -% trait Defunc[+T] -% case class Identity[A]() extends Defunc[A => A] -% case class Flip[A, B, C]() extends Defunc[(A => B => C) => B => A => C] -% case class Compose[A, B, C]() extends Defunc[(B => C) => (A => B) => A => C] -% \end{minted} -% \Cref{fig:expr-adt} shows the implementation of the untyped \scala{Expr} \textsc{adt} representing the abstract syntax of $n$-ary $\lambda$-terms, extended with the following: \begin{itemize} \item Optional explicit type annotations for variables -- these are not used for type-checking, but are there to preserve Scala type annotations originally written by the user. @@ -302,21 +284,18 @@ \subsection{The Expression \textsc{adt}} \label{fig:higher-order-funcs} \end{figure} -% Ideally for type safety, this could be represented as a generalised algebraic data type (\textsc{gadt})~\cite{cheney_gadt_2003} with a type parameter documenting the type that the function term represents: - \paragraph{Improved type safety} The originally intended design was to represent \scala{Expr} as a type-parameterised \textsc{gadt} for improved type safety, where it would be based on a \emph{typed} variant of the $\lambda$-calculus. This would have also allowed \scala{Parser} to be represented as a \textsc{gadt} parameterised by the result type of the parser. However, attempting to implement this ran into two main hurdles: \begin{itemize} \item \scala{Var} and \scala{Translucent} terms would need to be created with concrete type parameters of their inferred types. Scalafix's semantic \textsc{api} is not powerful enough to guarantee that all terms can be queried for their inferred types -- in fact, the built-in Scalafix rule \emph{Explicit Result Types} calls the Scala 2 presentation compiler to extract information like this\footnote{\url{https://github.com/scalacenter/scalafix/issues/1583}}. This solution is complex and brittle due to its reliance on unstable compiler internals, which undermines Scalafix's goal of being a cross-compatible, higher-level abstraction over compiler details. - \item Scala 2's type inference for \textsc{gadt}s is less than ideal, requiring extra type annotations and unsafe casts which ultimately defeat the original purpose of type safety. This situation is improved, although not completely solved, in Dotty~\cite{parreaux_towards_2019} -- but Scalafix does not yet support Scala 3. + \item Scala 2's type inference for \textsc{gadt}s is less than ideal, requiring extra type annotations and unsafe casts which ultimately defeat the original purpose of type safety. This situation is improved, although not completely solved, in \emph{Dotty}~\cite{parreaux_towards_2019} -- but Scalafix does not yet support Scala 3. \end{itemize} \subsection{Lifting to the Intermediate Expression \textsc{ast}}\label{sec:lifting-expr} The \scala{Parser} \textsc{ast} is amended to take \scala{Expr} arguments where they used to take \scala{scala.meta.Term} values. Take the \scala{Pure} parser as an example: -% TODO: if time, highlight changes with tcolorbox? \begin{minted}{scala} case class Pure(x: Expr) extends Parser object Pure { @@ -486,7 +465,7 @@ \subsection*{Discussion} \paragraph{Normalisation strategy} \texttt{parsley} normalises terms to full $\eta\beta$-\textsc{nf}, whereas \texttt{parsley-garnish} only normalises to $\beta$-\textsc{nf}. This is because $\eta$-reduction in Scala 2 is not as straightforward as in Haskell, and is not always possible -- in most cases the appropriate reduction is instead to convert lambdas to placeholder syntax. -This is left as future work. +Implementing this is left as future work. In \texttt{parsley}, normalisation is implemented as a reduction-based approach over the \textsc{hoas} \haskell{Lambda} datatype. 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z1J_#q@8Xwp-hGuuwdRZBGrac9qQ2-T4d1Y zQK>n!sCkb`E%Z(Aaet{TwAcsl38^!*_^kJ&C3-zmmiXgYWyx=z)lwJdcB2Owzh4aw z1*%k$Y1E>db&9M*J#ws*WCM1f5j)Y0UD%Blv|kjE&V_`CLEANHdi2XN9- zZ~bl^ydw(lb9jJ*xQ9-3p$EMc4SiizDRyn8e@7OR$lx@tp@=bD z#;Em`{JD#`gaU43!ZN>Q*`h4}&-d@(E~c!oDJu@irpi8_#tiP;^iSDLzijTW&mZCu zX05a(D;H!-Z!&!T7$uZ#`G;(U`TDTz>l%9%Lx6~FT+n0B; Z?`!%GEi`DdlVQOh2{17VB_%~qMhY=^#XSH3 diff --git a/src/body/impl/parser.tex b/src/body/impl/parser.tex index aab8651..bb93b91 100644 --- a/src/body/impl/parser.tex +++ b/src/body/impl/parser.tex @@ -52,7 +52,7 @@ \subsection{Parser Laws} \text{\scala{empty <*> u = empty}} \label{eqn:alt-empty-absorb} \\ \text{\scala{empty.map(f) = empty}} \label{eqn:alt-fmap-absorb} \end{gather} -% I've wanted more fine-grained control, so instead of using cleveref I've manually written out the references -- TAKE CARE to keep them in the same order as the equations +% I wanted more fine-grained control, so instead of using \cleveref I have manually written out the references -- TAKE CARE to keep them in the same order as the equations % \caption{Functor~\cref{eqn:functor-comp}, Applicative~\cref{eqn:app-homomorphism,eqn:app-fmap}, and Alternative~\cref{eqn:alt-left-neutral,eqn:alt-right-neutral,eqn:alt-left-biased-choice,eqn:alt-empty-absorb,eqn:alt-fmap-absorb} laws.} \caption{Functor~(\ref{eqn:functor-comp}), Applicative~(\ref{eqn:app-homomorphism}, \ref{eqn:app-fmap}), and Alternative~(\ref{eqn:alt-left-neutral}--\ref{eqn:alt-fmap-absorb}) laws.} \label{fig:parser-laws} @@ -155,7 +155,6 @@ \subsection{Implementing Rewrites on the Parser \textsc{ast}}\label{sec:parser-r \paragraph{Extensibility and Safety} Further design considerations are made to ensure the extensibility of this approach: the \scala{Parser} trait is sealed, which enables compiler warnings if a new \scala{Parser} case is added and the \scala{transform} method is not updated. 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zJ#Z=wszp=TYz+d_Y)1m$^vTKPHz51j)Ws!DLjA++GEQlEvvO=-0s50xlhA4dL>B+&JN z!8n5)r`Gc`$C;RA9Whgb$DkRR!br)6m`vQJTFaED?)SZSmW$_kG^J^@LdwPB+YC2{ z(HqW44uCFN%(3cA^G@#*?r_|qbh`-hv4+l+ckSoMjVG(>sBv=ds|MGY;IcmIml#e= zvM!Ebt;hms5x8Gh_$~r+>!*o9tkA6XQRdvn(TPm%!tt*|U8oZ#ie~0L%pxnI!^$IW uanf)3xiRFvR(UGgsnqqR^a+syp78a*XLlO24Hzyg2NxVArG%0s-2VclV=kEh diff --git a/src/body/leftrec.tex b/src/body/leftrec.tex index 2ed2b7c..ff6569c 100644 --- a/src/body/leftrec.tex +++ b/src/body/leftrec.tex @@ -7,12 +7,12 @@ \emph{Left-recursive} grammar rules are a common pattern to represent left-associativity. Take for example the following definition of a left-associative addition operator: \begin{equation*} -\langle \mathit{expr} \rangle ::= \langle \mathit{expr} \rangle \; \text{`+'} \; \langle \mathit{term} \rangle \enspace | \enspace \langle \mathit{term} \rangle +\nt{expr} ::= \nt{expr} \; \sym{+} \; \nt{term} \alt \nt{term} \end{equation*} % -Since the first production of $\langle \mathit{expr} \rangle$ is itself, this rule is said to be left-recursive. +Since the first production of $\nt{expr}$ is itself, this rule is said to be left-recursive. This poses a problem for recursive-descent parsers, such as those that \texttt{parsley} produces: -it will try to parse $\langle \mathit{expr} \rangle$ by first trying to parse $\langle \mathit{expr} \rangle$, and so on, resulting in an unproductive infinite loop. +it will try to parse $\nt{expr}$ by first trying to parse $\nt{expr}$, and so on, resulting in an unproductive infinite loop. Although it is possible to address the issue by transforming the grammar with algorithms such as Paull's algorithm~\cite{moore_removing_2000}, in the context of parser combinators this is considered an anti-pattern by \textcite{willis_design-haskell_2021}. @@ -24,7 +24,6 @@ Thus, it would be beneficial to provide a linting rule for \texttt{parsley} that can warn users when parsers are left-recursive. In fact, the next major release of \texttt{parsley} 5.0 will introduce a \scala{detectDivergence} combinator, which performs \emph{dynamic} analysis to detect unproductive looping at runtime. Therefore, \texttt{parsley-garnish} could complement this functionality with an auto-fix rule to refactor left-recursive parsers to use \texttt{parsley}'s idiomatic \scala{chain} combinators. -% TODO: could compare what the static vs dynamic analyses can detect? \paragraph{Running example} The following left-recursive parser and its transformation into a non-left-recursive form will be used as an example for this \namecref{sec:factor-leftrec}: @@ -34,20 +33,9 @@ % The \scala{example} parser intends to express the following simple grammar expressed using left-recursion. The goal is to refactor \scala{example} so that it retains the intended semantics, but is transformed into a parser that \texttt{parsley} can handle correctly. \begin{equation*} - \langle \mathit{example} \rangle ::= \langle \mathit{example} \rangle \; \text{``a''} \enspace | \enspace \text{``b''} +\nt{example} ::= \nt{example} \; \sym{a} \alt \sym{b} \end{equation*} -% \begin{minted}{scala} -% def postfix[A](p: Parsley[A], op: =>Parsley[A => A]): Parsley[A] = -% lazy val rest: Parsley[A => A] = (op, rest).zipped(_ andThen _) <|> pure(identity[A]) -% p <**> rest -% \end{minted} -% \begin{minted}{haskell} -% postfix :: Parser a -> Parser (a -> a) -> Parser a -% postfix p op = p <**> rest -% where rest = flip (.) <$> op <*> rest <|> pure id -% \end{minted} - \section{The Left-Recursion Factoring Transformation} \texttt{parsley-garnish} bases its left-recursion factoring transformation on the work of \textcite{baars_leftrec_2004}, adapted to fit the \textsc{peg} semantics of \texttt{parsley}. At a high-level, the transformation involves ``unfolding'' each non-terminal production into three parts: @@ -82,7 +70,7 @@ \section{Necessary Infrastructure}\label{sec:leftrec-infra} Thus, this \namecref{sec:leftrec-infra} discusses the extra infrastructure used to support the left-recursion factoring transformation: \begin{itemize} \item Firstly, \cref{sec:parser-ast-motivation} motivates the idea of using an intermediate \textsc{ast} representation for parsers, distinct from the general-purpose Scala \textsc{ast}. - \item Following this, \cref{sec:lifting-parsers} shows how the \textsc{ast} of a Scala source file is converted into this intermediate representation. + \item Following this, \cref{sec:lifting-parsers} shows how the source Scala \textsc{ast} is converted into this intermediate representation. \item Finally, \cref{sec:lowering-parsers} discusses how the intermediate \textsc{ast} is converted back into Scala code so that it can be applied as a Scalafix patch. \end{itemize} @@ -94,7 +82,7 @@ \subsection{An Intermediate \textsc{ast}}\label{sec:parser-ast-motivation} However, this datatype represents general-purpose abstract Scala syntax, rather than the abstract syntax of a specialised parser combinator \textsc{dsl}. This makes it not well-suited for performing domain-specific operations over the \textsc{ast}. -Take for example the task of combining two \textsc{ast} nodes \scala{Term.Name("p")} and \scala{Term.Name("q")}, representing named parsers \scala{p} and \scala{q}, with the combinator \scala{<*>} (pronunced ``ap''). +Take for example the task of combining two \textsc{ast} nodes \scala{Term.Name("p")} and \scala{Term.Name("q")}, representing named parsers \scala{p} and \scala{q}, with the combinator \scala{<*>} (pronounced ``ap''). This operation can be concisely expressed with Scalameta quasiquotes, rather than manually writing out the full explicit \textsc{ast}: \begin{minted}{scala} q"p <*> q" == @@ -181,8 +169,8 @@ \subsection{Lifting to the Intermediate Parser \textsc{ast}}\label{sec:lifting-p \end{minted} \subsubsection{Identifying Named Parsers} -Finding \textsc{ast} nodes corresponding to the definition sites of named parsers involves pattern matching on \scala{val}, \scala{var}, and \scala{def} definitions with a type inferred to be some \scala{Parsley[_]}. -This type information is accessed by querying the Scalafix semantic \textsc{api} for the node's symbol information. +Finding \textsc{ast} nodes corresponding to the definition sites of named parsers involves pattern matching on \scala{val}, \scala{var}, and \scala{def} nodes with a type inferred as some \scala{Parsley[_]}. +This type information is queried using the Scalafix semantic \textsc{api} on the node's symbol information. Consider the labelled \textsc{ast} structure of the \scala{example} parser: \begin{minted}{scala} // lazy val example: Parsley[String] = (example, string("a")).zipped(_ + _) | string("b") @@ -226,8 +214,6 @@ \subsubsection{Identifying Named Parsers} Seeing that the type of this \textsc{ast} node is \scala{Parsley[String]}, \texttt{parsley-garnish} can then proceed to convert the \scala{rhs} term into a \scala{Parser} \textsc{adt} object. The map entry uses the fully qualified symbol for \scala{example} as the key, and the lifted \scala{Parser} object as the value. -% Thus, a full traversal through the source file builds a map of all named parsers, representing all non-terminals in the grammar defined within that file. - \subsubsection{Converting Scalameta Terms to the Parser \textsc{adt}} Having identified the \textsc{ast} nodes which represent parsers, they need to be transformed into the appropriate \scala{Parser} representation. This involves pattern matching on the \scala{scala.meta.Term} to determine which parser combinator it represents, and then constructing the appropriate \scala{Parser} instance. @@ -408,12 +394,11 @@ \subsection{Unfolding the Core Combinators} \item \scala{p <*> q} can succeed without consuming input only if \emph{both} \scala{p} and \scala{q} can do so. Parser combinators abide by the law that \scala{pure(f) <*> pure(x) = pure(f(x))}, so the resulting semantic action is that of \scala{p} applied as a function to the semantic action of \scala{q}. \item In the \scala{nonLeftRec} and \scala{leftRec} portions, if \scala{p} can succeed without consuming input, then \scala{q} must be subjected to the semantic value corresponding to \scala{p}~\cite{swierstra_deterministic_1996}. This is achieved using the result shown in \cref{eq:ap-leftrec}, which is a special case of grammar right-factoring in reverse. \begin{itemize} - \item The \scala{leftRec} portion requires re-associating semantic actions back to the left, which uses the \scala{flip} higher-order function. Thus, the left branch of the \textsc{rhs} of \cref{eq:ap-leftrec} is reformulated as \scala{p.map(flip) <*> q}. + \item The \scala{leftRec} portion requires re-associating semantic actions back to the left, which necessitates using the \scala{flip} higher-order function. Therefore, the left branch of the \textsc{rhs} in \cref{eq:ap-leftrec} is reformulated as \scala{p.map(flip) <*> q}. \item Since \scala{leftRec} is a parser of a function, the right branch also needs adjusting: the function composition operation must be used in order to apply the function to \scala{q} with the \scala{<*>} combinator. \end{itemize} \end{itemize} -% \text{\scala{(p | pure(f)) <*> q}} \quad \Rightarrow \quad \text{\scala{(p <*> q) | q.map(f)}} \begin{equation} \label{eq:ap-leftrec} \text{\haskell{(p <|> pure f) <*> q}} \quad \Rightarrow \quad \text{\haskell{(p <*> q) <|> (f <$> q)}} \vspace{3ex} % shh... diff --git a/src/body/simple-rules.pdf b/src/body/simple-rules.pdf index 3c903d426b45dbfe45eb18dbe07ec46f44ae7007..528661dddb49e221d21c0ec59f3961b85f0c6658 100644 GIT binary patch delta 28110 zcmZs>Q*bU!8*LjWE4FRhw#^mWw)4ieZQIt0ZQHh;^X)qOZvS1?)z4+$&7Pyj_!?;1 zI%s{v9{?K{8zDbG;s3v&on4$v4Q-)4HhOT!V`)a`2D^<)gMUvg{mWv&!)PS|CLGm 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example to show a diagnostic, and a before and after if it's fixable -% * How it's implemented in the code -% * Proof (if applicable) -% * Limitations - \ourchapter{Idiomatic Implicits Usage}\label{sec:simple-rules} Implicit conversions are a powerful feature in Scala, allowing users to supply an argument of one type when another is expected, to reduce boilerplate. When the Scala compiler encounters a type mismatch, it will search for any implicit methods that are in scope to convert the argument to the expected type. @@ -41,13 +33,13 @@ \section{Ambiguous Implicit Conversions}\label{sec:ambiguous-implicits} \texttt{parsley} has first-class support for both design patterns, defining separate implicit methods for each: \begin{itemize} \item \emph{Implicit Conversions}: the \scala{parsley.syntax.character} package includes implicit methods \scala{stringLift} and \scala{charLift} to lift string and character literals into parsers, respectively. - \item \emph{Implicit Lexer}: the \scala{Lexer} class exposes \scala{implicitSymbol} to allow string and character literals to parse as proper tokens. + \item \emph{Implicit Lexer}: the \scala{Lexer} class exposes the \scala{implicitSymbol} method to allow string and character literals to parse as proper tokens. \end{itemize} % The two implicit conversions cannot be used in conjunction: the \emph{Implicit Lexer} pattern is a specialisation of the former, so \scala{implicitSymbol} is meant to be a \emph{replacement} for \scala{stringLift}. For novice users, this may not be immediately apparent and it is easy to accidentally bring both sets of these implicits into scope. Anecdotally, this issue has been encountered by a number of \textsc{Wacc} students at Imperial. -For example, consider the following code snippet: +Consider the following code snippet: \begin{minted}{scala} val p = 'g' ~> "arnish" p.parse("garnish") @@ -132,8 +124,8 @@ \section{Ambiguous Implicit Conversions}\label{sec:ambiguous-implicits} \subsection{Implementation as a Syntactic Lint Rule} The rule uses the following heuristics to determine if an import clause brings an implicit into scope: \begin{itemize} - \item An import clause of the form \scala{import parsley.syntax.character.xxx}, where \scala{xxx} is either a wildcard import or specifically contains the importee \scala{stringLift}, indicates the \emph{Implicit Conversions} pattern on strings. - \item The import path for the \emph{Implicit Lexer} pattern is subject to how the user names their lexer object, so determining this is much more heuristic-based. The following cases are considered indicative of this pattern: + \item An import clause of the form \scala{import parsley.syntax.character.xxx}, where \scala{xxx} is either a wildcard import or specifically contains the importee \scala{stringLift}, indicates the \emph{Implicit Conversions} pattern on string values. + \item The import path for the \emph{Implicit Lexer} pattern is subject to how the user names their lexer object, so determining this is more heuristic-based. The following cases are considered indicative of this pattern: \begin{itemize} \item An import containing the keyword \scala{lexer}, as well as either \scala{implicit} or \scala{implicits}. \item An import clause that brings in an importee called \scala{implicitSymbol}. @@ -150,8 +142,7 @@ \subsection{Implementation as a Syntactic Lint Rule} This behaviour presents extra challenges for this lint rule, as it must be aware of the exact scope of each import to determine which implicits are in scope at any given point. The lexically ordered management of scope can be respected by visiting all import clauses in the order they appear in the source file. -By treating the parent of an \textsc{ast} node as its enclosing scope, it is possible to use ancestor information to determine the scoping relation between two nodes. -Scoping rules can then be respected by using this information to determine which previously visited imports are still in scope at any given point in the traversal. +By treating the parent of an \textsc{ast} node as its enclosing scope, it is possible to use ancestor information to determine the scoping relation between two nodes: \begin{minted}{scala} extension (tree: Tree) { def isWithinScope(scope: Tree): Boolean = @@ -159,6 +150,7 @@ \subsection{Implementation as a Syntactic Lint Rule} } \end{minted} % +Scoping rules can then be respected by using this information to determine which previously visited imports are still in scope at any given point in the traversal. With this, \cref{fig:ambiguous-implicits-impl} shows the core logic of the rule, implemented as a \emph{tail-recursive} visit over the list of imports, which allows the Scala compiler to optimise the recursion into an efficient iterative loop. The \scala{getClashingImports} method uses the heuristic rules described above to determine which implicits are brought into scope by an import. 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z^_pac()Ef`HoD02aG}eZV1fDJ=;C{=VMo_q(-jY7{tp}^Pym47<;3V+Kul28#|8+Ezb!d;2RT|M)lP7;x49#{&*Qov%~j~x2O9~(CZu>jOs%E|3=KX zzvG@=%GA2fEs!aI&OFEC!n5jWMR#ka4MVrPS6Q+AEpWrSsF{V>RX z=JR{qRWSmX3g16>d#%_JQ}|i+#^PO!N|D+Ubx`2*#G)?I!BHwk3|?UBe_Bkk14m5s zQ3^?xpXEA})g|H{r~T|{lA;{q>>v@_vn#7h&5cg4+~$0yf*E_7iK#OAqL!|3_EBt1 xF<29l>4DRXwSz?bdFp7Vd9n`-33HZ4vv4$bb9c?a@q;5n;X-3zkXDgF`!DF38FBys diff --git a/src/evaluation/evaluation.tex b/src/evaluation/evaluation.tex index 26025e2..0f21e75 100644 --- a/src/evaluation/evaluation.tex +++ b/src/evaluation/evaluation.tex @@ -15,8 +15,6 @@ Then, it evaluates the success of the left-recursion transformation by examining its ability to handle different forms of left-recursion. \section{Performance of Expression Normalisation}\label{sec:eval-exprs} -% TODO: move this to evaluation chapter? -% TODO: tbh could've just stopped at HOAS, but in our case, NbE was an easily attainable logical next step to more aggressively use meta-language constructs Originally, the implementation of \scala{Expr} used a named approach with Barendregt's convention, generating fresh variable names using an atomic counter. Normalisation proceeded by manually substituting variable objects following the $\beta$-reduction rules. However, this required an extra $\alpha$-conversion pass to clean up variable names before pretty-printing the expression, as fresh name generation resulted in undesirably long names like \scala{x4657476}. @@ -55,7 +53,7 @@ \section{Performance of Expression Normalisation}\label{sec:eval-exprs} \subsubsection*{Summary} The performance benchmarks show that the final implementation of expression normalisation is extremely performant, even for unrealistically large $\lambda$-terms. -Although the original named substitution approach would've likely been sufficient for the standard use case of normalising parser terms, the cheap operational cost of \textsc{nbe} allows expression normalisation to be used frequently and liberally throughout the system, without worrying about performance bottlenecks. +Although the original named substitution approach would have likely been sufficient for the standard use case of normalising parser terms, the cheap operational cost of \textsc{nbe} allows expression normalisation to be used frequently and liberally throughout the system, without worrying about performance bottlenecks. \section{Removing Left-Recursion}\label{sec:eval-leftrec} Broadly speaking, left-recursive grammars can be classified into three categories: direct, indirect, and hidden. @@ -141,7 +139,7 @@ \subsubsection{Arithmetic Expression Language} % This also manages to successfully compile, and is relatively clear to read. However, it does highlight a current shortcoming of the left-recursion rule: left-recursive parsers can only be transformed into the most generalised \scala{postfix} form, which may not always be the most optimal choice of combinator. -In this case, the \scala{chain.left1} combinator would've been a more appropriate choice; even better would be the \scala{precedence} combinator, since the grammar forms multiple layers of expression operators. +In this case, the \scala{chain.left1} combinator would have been a more appropriate choice; even better would be the \scala{precedence} combinator, since the grammar forms multiple layers of expression operators. 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From there, \Cref{sec:simple-rules} dives into the first set of linting rules that \texttt{parsley-garnish} implements. -These relatively simple rules focus on enforcing idiomatic design patterns relating to \emph{implicit conversions} in Scala, and were largely inspired by common issues I've seen in my experiences as a teaching assistant for the second-year undergraduate \textsc{Wacc} compilers project at Imperial. +These relatively simple rules focus on enforcing idiomatic design patterns relating to \emph{implicit conversions} in Scala, and were largely inspired by common issues I have seen in my experiences as a teaching assistant for the second-year undergraduate \textsc{Wacc} compilers project at Imperial. \Cref{sec:factor-leftrec} tackles a more ambitious rule to automatically refactor left-recursive parsers into a form that \texttt{parsley} can handle. This chapter introduces the idea of utilising intermediate \textsc{ast} representations to perform higher-level domain-specific transformations.