From 59720370849c0e15f207f059e54b21e4f8e05d82 Mon Sep 17 00:00:00 2001 From: "Edward Z. Yang" Date: Wed, 13 May 2015 16:16:39 -0700 Subject: [PATCH] Backpack docs: Rewrite type checking section to have a more concrete plan. Signed-off-by: Edward Z. Yang --- docs/backpack/algorithm.pdf | Bin 272423 -> 279771 bytes docs/backpack/algorithm.tex | 425 +++++++++++++++++++----------------- 2 files changed, 225 insertions(+), 200 deletions(-) diff --git a/docs/backpack/algorithm.pdf b/docs/backpack/algorithm.pdf index 05738bc3d91c86cf7dca8c92ef05ac227feb6c2f..557bdf23f4d3d4c4e0a5b5447dccfbafe0f37f53 100644 GIT binary patch delta 145812 zcmV)lK%c*-&=A{+5fLR&L`E$!E;R}z(A34)3OF^95$J!@8+s85S197;+dL{*p@qi% zYo1G%sWe)rn&nz}mFod^rD?qBR%?;R<#AuND|i`^EaOczlzn{%|7CGC5N)*Qggy40 z8Jv&D2mfmS7OJ9_ifA<{ zSP|be9y@w&0)=7b^bO&a~UA>9%g? zr4^HC4W7>hr!C(f`np-IWs$`q2aOeM51T(vS)ORvPy1j`D&nEuwq`u`6@6~1vN63G z>#ik23x@6Jwdp{op570Ahev#@H|P|E}v9W*tvM*%nU0au?aa+8n>_^oO)oWBf zT04c;1VK`p81XFLcVqpyQY!Y!0`0!*>1DK-!Z(tJ)}(KugC9R18aSG%+iF7;P<3f+ zkpR}y)En(xyB^B!fFMUC$UHe8c%W}%kDe8A+l@p)TfzFrdH_X-rC)fFvWypA23xIl zp(%foQRBg4Y8c5TGT}@@IFeB`Z7G3o_32o(CBjoAad!_-UN}48n|;DRR~m|HsVk#`~rV8pz23*Hc`j~8R8O`gA+jcJ<$-A_&fjt 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It has t \begin{verbatim} provides: (nothing) - requires: M -> { exports of renamed M } + requires: M -> { exports of renamed M under HOLE:M } \end{verbatim} \noindent Example: @@ -448,7 +448,7 @@ proceeds as follows: $p$.} For each requirement $M$ of $q$ that is provided by $p$ (in particular, all of its required \verb|Name|s are provided), substitute each \I{Module} occurrence of \verb|HOLE:M| with the - provided $p(M)$, unify the names, and remove the requirement from $q$. + provided $p\verb|(|M\verb|)|$, unify the names, and remove the requirement from $q$. If the names of the provision are not a superset of the required names, error. \item If mutual recursion is supported, \emph{fill every requirement of $p$ with provided modules from $q$.} \item \emph{Merge leftover requirements.} For each requirement $M$ of $q$ that is not @@ -972,9 +972,11 @@ $$ \I{ModIface} & ::= & \verb|module| \; \I{Module} \; \verb|(| \I{mi\_exports} \verb|)| \; \verb|where| \\ & & \qquad \I{mi\_decls} \\ & & \qquad \I{mi\_insts} \\ -\I{mi\_exports} & ::= & \I{AvailInfo}_0 \verb|,|\, \ldots \verb|,|\, \I{AvailInfo}_n \\ -\I{mi\_decls} & ::= & \I{IfaceDecl}_0 \verb|;|\, \ldots \verb|;|\, \I{IfaceDecl}_n \\ -\I{mi\_insts} & ::= & \I{IfaceClsInst}_0 \verb|;|\, \ldots \verb|;|\, \I{IfaceClsInst}_n \\[1em] +& & \qquad \I{dep\_orphs} \\ +\I{mi\_exports} & ::= & \I{AvailInfo}_0 \verb|,|\, \ldots \verb|,|\, \I{AvailInfo}_n & \mbox{Export list} \\ +\I{mi\_decls} & ::= & \I{IfaceDecl}_0 \verb|;|\, \ldots \verb|;|\, \I{IfaceDecl}_n & \mbox{Defined declarations} \\ +\I{mi\_insts} & ::= & \I{IfaceClsInst}_0 \verb|;|\, \ldots \verb|;|\, \I{IfaceClsInst}_n & \mbox{Defined instances} \\ +\I{dep\_orphs} & ::= & \I{Module}_0 \verb|;|\, \ldots \verb|;|\, \I{Module}_n & \mbox{Transitive orphan dependencies} \\[1em] \multicolumn{3}{l}{\mbox{\bf Interface declarations}} \\ \I{IfaceDecl} & ::= & \I{OccName} \; \verb|::| \; \I{IfaceId} \\ & | & \verb|data| \; \I{OccName} \; \verb|=| \;\ \I{IfaceData} \\ @@ -987,7 +989,8 @@ $$ \caption{Module interfaces in GHC} \label{fig:typecheck} \end{figure} -Type checking an indefinite package (a package with holes) involves +In general terms, +type checking an indefinite package (a package with holes) involves calculating, for every module, a \I{ModIface} representing the type/interface of the module in question (which is serialized to disk). The general form of these @@ -1017,33 +1020,16 @@ the \I{PkgType} is: -- where THIS = p(H -> HOLE:H) \end{verbatim} % -However, a \I{PkgType} of \I{ModIface}s is not the whole story: -when a package has holes, a \I{PkgType} specified in this manner -defines a family of possible types, based on how the holes are -shaped and instantiated. A package which writes \verb|include p requires (H as S)| -and has a sharing constraint of \verb|H.T| with \verb|q():B.T| may -end up with this ``type'': - -\begin{verbatim} - module HOLE:S (q():B.T) where - module THIS:A (THIS:A.S, q():B.T) where - data S = S q():B.T - -- where THIS = p(H -> HOLE:S) -\end{verbatim} -% -Furthermore, for ease of implementation, GHC prefers to resolve all -indirect \I{Name} references (which are just strings) into a -\I{ModIface} into direct \I{TyThing} references (which are data -structures that have type information). This resolution is done lazily -with some hackery! - -Thus, given a shaping and a hole instantiation, a \I{ModIface} can be -converted into an in-memory \I{ModDetails}, described in -Figure~\ref{fig:typecheck-more}. (Technically, the \I{Module} does not -have to be recorded as it is recorded in the \I{Name} associated with a -\I{TyThing}; so you can think of a \I{ModDetails} as a big bag of type-checkable -entities which GHC knows about; in the source code this -is referred to as the \emph{external package state (EPT)}). +However, while it is true that the \I{ModIface} is the final result +of type checking, we actually are conflating two distinct concepts: the user-visible +notion of a \I{ModuleName}, which, when imported, brings some \I{Name}s +into scope (or could trigger a deprecation warning, or pull in some +orphan instances\ldots), versus the actual declarations, which, while recorded +in the \I{ModIface}, have an independent existence: even if a declaration +is not visible for an import, we may internally refer to its \I{Name}, and +need to look it up to find out type information. (A simple case when +this can occur is if a module exports a function with type \verb|T -> T|, +but doesn't export \verb|T|). \begin{figure}[htpb] $$ @@ -1059,191 +1045,230 @@ $$ \caption{Semantic objects in GHC} \label{fig:typecheck-more} \end{figure} -Type checking, thus, is a delicate balancing act between module -interfaces and our semantic objects. Given a shaping, here -are some important operations we have to do in type checking: - -\paragraph{Imports} When a module/signature imports a module name, -we must consult the exports of \I{ModIface}s associated with this -module name, modulo what we calculated into the shaping pass. -(In fact, we can get all of this information directly from the -shaping pass.) +Thus, a \I{ModIface} can be type-checked into a \I{ModDetails}, described in +Figure~\ref{fig:typecheck-more}. Notice that a \I{ModDetails} is just +a bag of type-checkable entities which GHC knows about. We +define the \emph{external package state (EPT)} to +simply be the union of the \I{ModDetails} +of all external modules. + +Type checking is a delicate balancing act between module +interfaces and our semantic objects. A \I{ModIface} may get +type-checked multiple times with different hole instantiations +to provide multiple \I{ModDetails}. +Furthermore complicating matters +is that GHC does this resolution \emph{lazily}: a \I{ModIface} +is only converted to a \I{ModDetails} when we are looking up +the type of a \I{Name} that is described by the interface; +thus, unlike usual theoretical treatments of type checking, we can't +eagerly go ahead and perform substitutions on \I{ModIface}s when +they get included. + +In a separate compiler like GHC, there are two primary functions we must provide: + +\paragraph{\textit{ModuleName} to \textit{ModIface}} Given a \I{ModuleName} which +was explicitly imported by a user, we must produce a \I{ModIface} +that, among other things, specifies what \I{Name}s are brought +into scope. This is used by the renamer to resolve plain references +to identifiers to real \I{Name}s. (By the way, if shaping produced +renamed trees, it would not be necessary to do this step!) + +\paragraph{\textit{Module} to \textit{ModDetails}/EPT} Given a \I{Module} which may be +a part of a \I{Name}, we must be able to type check it into +a \I{ModDetails} (usually by reading and typechecking the \I{ModIface} +associated with the \I{Module}, but this process is involved). This +is used by the type checker to find out type information on things. \\ + +There are two points in the type checker where these capabilities are exercised: + +\paragraph{Source-level imports} When a user explicitly imports a +module, the \textit{ModuleName} is mapped to a \textit{ModIface} +to find out what exports are brought into scope (\I{mi\_exports}) +and what orphan instances must be loaded (\I{dep\_orphs}). Additionally, +the \textit{Module} is loaded to the EPT to bring instances from +the module into scope. + +\paragraph{Internal name lookup} During type checking, we may have +a \I{Name} for which we need type information (\I{TyThing}). If it's not already in the +EPT, we type check and load +into the EPT the \I{ModDetails} of the \I{Module} in the \I{Name}, +and then check the EPT again. (\verb|importDecl|) + +\subsection{\textit{ModName} to \textit{ModIface}} + +In all cases, the \I{mi\_exports} can be calculated directly from the +shaping process, which specifies exactly for each \I{ModName} in scope +what will be brought into scope. + +\paragraph{Modules} Modules are straightforward, as for any +\I{Module} there is only one possibly \I{ModIface} associated +with it (the \I{ModIface} for when we type-checked the (unique) \verb|module| +declaration.) + +\paragraph{Signatures} For signatures, there may be multiple \I{ModIface}s +associated with a \I{ModName} in scope, e.g. in this situation: -\paragraph{Includes and name lookups} When we include a package, -take all of the \I{ModIface}s it brings into scope, type-check -them with respect to the instantiation of holes and shaping, and add -them to the EPT. - -Even better, this process should be done lazily on name lookup. -When we have a renamed identifier, e.g. a \I{Name}, -we first check if we know about this object in EPT, and if not, -we must find the \I{ModIface}(s) (plural!) that would have brought the object into -scope, add them to EPT and try again. The process of adding semantic -objects to the EPT may cause us to learn \emph{more} information -about an object than we knew previously. - -\paragraph{Cross-package compilation} When we begin type-checking a new -indefinite package, we must \emph{clear} all \I{ModDetails} which depend on -holes. This is because shaping may cause the type-checked entities to refer -to different semantic objects. - -\subsection{The basic plan} +\begin{verbatim} + package p where + signature S where + data A + package q where + include p + signature S where + data B + module M where + import S +\end{verbatim} +% +Each literal \verb|signature| has a \I{ModIface} associated with it; and +the import of \verb|S| in \verb|M|, we want to see the \emph{merged} +\I{ModIface}s. We can determine the \I{mi\_exports} from the shape, +but we also need to pull in orphan instances for each signature, and +produce a warning for each deprecated signature. -Given a module or signature of a package, we can type check given these two assumptions: +\begin{aside} +\textbf{Does hiding a signature hide its orphans.} Suppose that we have +extended Backpack to allow hiding signatures from import. -\begin{itemize} - \item We have a renamed syntax tree, whose identifiers have been - resolved as according to the result of the shaping pass. - \item For any \I{Name} in the renamed tree, the corresponding - \I{ModDetails} for the \I{Module} has been loaded - (or can be lazily loaded). -\end{itemize} +\begin{verbatim} + package p requires (H) where -- H is hidden from import + module A where + instance Eq (a -> b) where -- orphan + signature H {-# DEPRECATED "Don't use me" #-} where + import A -The result of type checking is a \I{ModDetails} which can then be -converted into a \I{ModIface}, because we assumed each signature -to serve as an uninstantiated hole (thus, the computed \I{ModDetails} is -in its most general form). -Arranging for these two assumptions to be true is the bulk of the -complexity of type checking. + package q where + include p + signature H where + data T + module M where + import H -- warn deprecated? + instance Eq (a -> b) -- overlap? +\end{verbatim} -\subsection{Loading modules from indefinite packages} +It is probably the most consistent to not pull in orphan instances +and not give the deprecated warning: this corresponds to merging +visible \I{ModIface}s, and ignoring invisible ones. +\end{aside} -\paragraph{Everything is done modulo a shape} Consider -this package: +\subsection{\textit{Module} to \textit{ModDetails}} -\begin{verbatim} -package p where - signature H(T) where - data T = T - module A(T) where - data T = T - signature H(T) where - import A(T) +\paragraph{Modules} For modules, we have a \I{Module} of +the form $\I{p}\verb|(|m\; \verb|->|\; \I{Module}\verb|,|\, \ldots\verb|)|$, +and we also have a unique \I{ModIface}, where each hole instantiation +is $\verb|HOLE:|m$. --- provides: A -> THIS:A { THIS:A.T } --- H -> HOLE:H { THIS:A.T } --- requires: H -> { THIS:A.T } -\end{verbatim} +To generate the \I{ModDetails} associated with the specific instantiation, +we have to type-check the \I{ModIface} with the following adjustments: -With this shaping information, when we are type-checking the first -signature for \verb|H|, it is completely wrong to try to create -a definition for \verb|HOLE:H.T|, since we know that it refers -to \verb|THIS:A.T| via the requirements of the shape. This applies -even if \verb|H| is included from another package. Thus, when -we are loading \I{ModDetails} into memory, it is always done -\emph{with respect to some shaping}. Whenever you reshape, -you must clear the module environment. +\begin{enumerate} + \item Perform a \I{Module} substitution according to the instantiation + of the \I{ModIface}'s \I{Module}. (NB: we \emph{do} + substitute \verb|HOLE:A.x| to \verb|HOLE:B.x| if we instantiated + \verb|A -> HOLE:B|, \emph{unlike} the disjoint + substitutions applied by shaping.) + \item Perform a \I{Name} substitution as follows: for any name + with a package key that is a $\verb|HOLE|$, + substitute with the recorded \I{Name} in the requirements of the shape. + Otherwise, look up the (unique) \I{ModIface} for the \I{Module}, + and subsitute with the corresponding \I{Name} in the \I{mi\_exports}. +\end{enumerate} -\paragraph{Figuring out where to consult for shape information} +\paragraph{Signatures} For signatures, we have a \I{Module} of the form +$\verb|HOLE:|m$. Unlike modules, there are multiple \I{ModIface}s associated with a hole. +We distinguish each separate \I{ModIface} by considering the full \I{PkgKey} +it was defined in, e.g. \verb|p(A -> HOLE:C, B -> q():B)|; call this +the hole's \emph{defining package key}; the set of \I{ModIface}s for a hole +and their defining package keys can easily be calculated during shaping. -For this example, let's suppose we have already type-checked -this package \verb|p|: +To generate the \I{ModDetails} associated with a hole, we type-check each +\I{ModIface}, with the following adjustments: -\begin{verbatim} -package p (A) requires (S) where - signature S where - data S - data T - module A(A) where - import S - data A = A S T -\end{verbatim} +\begin{enumerate} + \item Perform a \I{Module} substitution according to the instantiation + of the defining package key. (NB: This may rename the hole itself!) + \item Perform a \I{Name} substitution as follows, in the same manner + as would be done in the case of modules. + \item When these \I{ModDetails} are merged into the EPT, some merging + of duplicate types may occur; a type + may be defined multiple times, in which case we check that each + definition is compatible with the previous ones. A concrete + type is always compatible with an abstract type. +\end{enumerate} -giving us the following \I{ModIface}s: +\paragraph{Invariants} When we perform \I{Name} substitutions, we must be +sure that we can always find out the correct \I{Name} to substitute to. +This isn't obviously true, consider: \begin{verbatim} -module HOLE:S.S where - data S - data T -module THIS:A where - data A = A HOLE:S.S HOLE:S.T --- where THIS = p(S -> HOLE:S) + package p where + signature S(foo) where + data T + foo :: T + module M(bar) where + import S + bar = foo + package q where + module A(T(..)) where + data T = T + foo = T + module S(foo) where + import A + include p + module A where + import M + ... bar ... \end{verbatim} - -Next, we'd like to type check a package which includes \verb|p|: +% +When we type check \verb|p|, we get the \I{ModIface}s: \begin{verbatim} -package q (T, A, B) requires (H) where - include p (A) requires (S as H) - module T(T) where - data T = T - signature H(T) where - import T(T) - module B(B) where - import A - data B = B A + module HOLE:S(HOLE:S.foo) where + data T + foo :: HOLE:S.T + module THIS:M(THIS:M.bar) where + bar :: HOLE:S.T \end{verbatim} +% +Now, when we type check \verb|A|, we pull on the \I{Name} \verb|p(S -> q():S):M.bar|, +which means we have to type check the \I{ModIface} for \verb|p(S -> q():S):M|. +The un-substituted type of \verb|bar| has a reference to \verb|HOLE:S.T|; +this should be substituted to \verb|q():S.T|. But how do we discover this? +We know that \verb|HOLE:S| was instantiated to \verb|q():S|, so we might try +and look for \verb|q():S.T|. However, this \I{Name} does not exist because +the \verb|module S| reexports the selector from \verb|A|! Nor can we consult +the (unique) \I{ModIface} for the module, as it doesn't reexport the relevant +type. + +The conclusion, then, is that a module written this way should be disallowed. +Specifically, the correctness condition for a signature is this: \emph{Any \I{Name} +mentioned in the \I{ModIface} of a signature must either be from an external module, or be +exported by the signature}. -% package r where -% include q -% module H(S,T) where -% import T(T) -% data S = S -% module C where -% import A -% import B -% ... - -Prior to typechecking, we compute its shape: - +\begin{aside} +\textbf{Special case export rule for record selectors.} Here is the analogous case for +record selectors: \begin{verbatim} -provides: (elided) -requires: H -> { HOLE:H.S, THIS:T.T } --- where THIS = q(H -> HOLE:H) + package p where + signature S(foo) where + data T = T { foo :: Int } + module M(bar) where + import S + bar = foo + package q where + module A(T(..)) where + data T = T { foo :: Int } + module S(foo) where + import A + include p + module A where + import M + ... bar ... \end{verbatim} -Our goal is to get the following type: - -\begin{verbatim} -module THIS:T where - data T = T -module THIS:B where - data B = B p(S -> HOLE:H):A.A - -- where data A = A HOLE:H.S THIS:T.T --- where THIS = q(H -> HOLE:H) -\end{verbatim} +We could reject this, but technically we can find the right substitution +for \verb|T|, because the export of \verb|foo| is an \I{AvailTC} which +does mention \verb|T|. +\end{aside} -This type information does \emph{not} match the pre-existing -type information from \verb|p|: when we translate the \I{ModIface} for -\verb|A| in the context into a \I{ModDetails} from this typechecking, -we need to substitute \I{Name}s and \I{Module}s -as specified by shaping. Specifically, when we load \verb|p(S -> HOLE:H):A| -to find out the type of \verb|p(S -> HOLE:H):A.A|, -we need to take \verb|HOLE:S.S| to \verb|HOLE:H.S| and \verb|HOLE:S.T| to \verb|THIS:T.T|. -In both cases, we can determine the right translation by looking at how \verb|S| is -instantiated in the package key for \verb|p| (it is instantiated with \verb|HOLE:H|), -and then consulting the shape in the requirements. - -This process is done lazily, as we may not have typechecked the original -\I{Name} in question when doing this. \verb|hs-boot| considerations apply -if things are loopy: we have to treat the type abstractly and re-typecheck it -to the right type later. - - -\subsection{Re-renaming} - -Theoretically, the cleanest way to do shaping and typechecking is to have shaping -result in a fully renamed syntax tree, which we then typecheck: when done this way, -we don't have to worry about logical contexts (i.e., what is in scope) because -shaping will already have complained if things were not in scope. - -However, for practical purposes, it's better if we don't try to keep -around renamed syntax trees, because this could result in very large -memory use; additionally, whenever a substitution occurs, we would have -to substitute over all of the renamed syntax trees. Thus, while -type-checking, we'll also re-compute what is in scope (i.e., just the -\I{OccName} bits of \verb|provided|). Nota bene: we still use the -\I{Name}s from the shape as the destinations of these -\I{OccName}s! Note that we can't just use the final shape, because -this may report more things in scope than we actually want. (It's also -worth noting that if we could reduce the set of provided things in -scope in a single package, just the \I{Shape} would not be enough.) - -\subsection{Merging \texttt{ModDetails}} - -After type-checking a signature, we may turn to add it to our module -environment and discover there is already an entry for it! In that case, -we simply merge it with the existing entry, erroring if there are incompatible -entries. - -\end{document} +\end{document} % chktex 16 -- GitLab