X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=strategy.tex;h=0f03ddb9883200fed514b821df14948994e78aca;hp=6fb4b4f9d2b72837ccfc8b602c7696cb93c74fd6;hb=d1a680abdf1985a08c1a88157588ef881df7fb29;hpb=bb9635f169e0014d28a8ba992e5ab285b1ff16ea

diff --git a/strategy.tex b/strategy.tex
index 6fb4b4f..0f03ddb 100644
--- a/strategy.tex
+++ b/strategy.tex
@@ -6,7 +6,7 @@ remove dependencies from patches.
 
 Broadly speaking the update proceeds as follows: during the Ranking
 phase we construct the intended graph of dependencies between patches
-(which involves select a merge order for the base branch of each
+(and incidentally select a merge order for the base branch of each
 patch).  Then during the Traversal phase we walk that graph from the
 bottom up, constructing for each patch by a series of merges and other
 operations first a new base branch head commit and then a new tip
@@ -32,18 +32,18 @@ The set of direct dependencies (in the form $\py$)
 requested in the commit $K$ ($K \in \pn$) for the patch $\p$.
 
 \item[ $\pc \hasdirdep \p$ ]
-The Topbloke commit set $\pc$ has as a direct contributor the
-commit set $\p$.  This is an acyclic relation.
+The patch $\pc$ has as a direct dependency the
+patch $\p$.  This is an acyclic relation.
 
 \item[ $\p \hasdep \pq$ ]
-The commit set $\p$ has as direct or indirect contributor the commit
-set $\pq$.
+The patch $\p$ has as direct or indirect dependency the
+patch $\pq$.
 Acyclic; the completion of $\hasdirdep$ into a
 partial order.
 
 \item[ $\pendsof{\set J}{\p}$ ]
 Convenience notation for
-the maximal elements of $\bigcup_{J \in \set J} \pendsof{J}{\p}$
+the $\le$-maximal elements of $\bigcup_{J \in \set J} \pendsof{J}{\p}$
 (where $\set J$ is some set of commits).
 
 \item[ $\pendsof{\set X}{\p} \le T$ ]
@@ -72,6 +72,7 @@ all of its dependencies will be updated.
 
 \item[ $h : \pc^{+/-} \mapsto \set H_{\pc^{+/-}}$ ]
 Function for getting the existing heads $\set H$ of the branch $\pc^{+/-}$.
+These are the heads which will be merged and used in this update.
 This will include the current local and remote git refs, as desired.
 
 \item[ $g : \pc, \Gamma \mapsto \Gamma'$ ]
@@ -80,7 +81,27 @@ of $\pc$.  It is provided with a putative set of direct dependencies
 $\Gamma$ computed as an appropriate merge of the dependencies requested by the
 sources and should return the complete actual set $\Gamma'$ of direct
 dependencies to use.  This allows the specification of any desired
-(acyclic) relation $\hasdirdep$.
+(acyclic) relations $\hasdirdep$ and $\hasdep$.
+
+\end{basedescript}
+
+\stdsection{Important variables and values in the update algorithm}
+
+\begin{basedescript}{
+\desclabelwidth{5em}
+\desclabelstyle{\nextlinelabel}
+}
+\item[ $\Gamma_{\pc}$ ]
+The desired direct dependencies of $\pc$, a set of patches.
+
+\item[ $\allpatches$ ]
+The set of all the patches we are dealing with (constructed
+during the update algorithm).
+
+\item[ $\tipcn, \tipcy$ ]
+The new tips of the git branches $\pcn$ and $\pcy$, containing
+all the correct commits (and the correct other patches), as
+generated by the Traversal phase of the update algorithm.
 
 \end{basedescript}
 
@@ -91,187 +112,266 @@ We run the following algorithm:
 \item Set $\allpatches = \{ \}$.
 \item Repeatedly:
 \begin{enumerate}
-\item Clear out the graph $\hasdirdep$ so it has neither nodes nor edges.
-\item Execute {\bf Rank-Recurse}($\pc_0$)
+\item Clear out the graph $\hasdirdep$ so it has no edges.
+\item Execute $\alg{Rank-Recurse}(\pc_0)$
 \item Until $\allpatches$ remains unchanged.
 \end{enumerate}
 \end{enumerate}
 
-{\bf Rank-Recurse}($\pc$) is:
+$\alg{Rank-Recurse}(\pc)$ is:
 \begin{enumerate}
+
+\item If we have already done $\alg{Rank-Recurse}(\pc)$ in this
+ranking iteration, do nothing.  Otherwise:
+
 \item Add $\pc$ to $\allpatches$ if it is not there already.
-\item Let $\set S_{\pcn} = h(\pcn)
+
+\item Set
+$$
+  \set S \iassign h(\pcn)
      \cup 
         \bigcup_{\p \in \allpatches}
         \bigcup_{H \in h(\pn) \lor H \in h(\py)}
-         \{ \baseof{E} \; | \; E \in \pendsof{H}{\pcy} \} $
+         \{ \baseof{E} \; | \; E \in \pendsof{H}{\pcy} \}
+$$
+
+and $W \iassign w(h(\pcn))$
+
+\item While $\exists_{S \in \set S} S \ge W$,
+update $W \assign S$ and $\set S \assign \set S \, \backslash \{ S \}$
 
-and $W = w(h(\pcn))$
+(This will often remove $W$ from $\set S$.  Afterwards, $\set S$
+is a collection of heads to be merged into $W$.)
 
-We write $\set S = \set S_{\pcn}$ where unambiguous.
-\item While $\exists_{S \in \set S} S \ge W$:
+\item Choose an ordering of $\set S$, $S_i$ for $i=1 \ldots n$.
 
-Update $W \assign S$ and $\set S \assign \set S \, \backslash \{ S \}$
+\item For each $S_i$ in turn, choose a corresponding $M_i$
+such that $$
+   M_i \le S_i \land \left[
+   M_i \le W \lor \bigexists_{j<i} M_i \le S_j
+   \right]
+$$
+
+\item Set $\Gamma \iassign \depsreqof{W}$.
+
+If there are multiple candidates we prefer $M_i \in \pcn$
+if available.
+
+\item For each $i \ldots 1..n$, update our putative direct
+dependencies:
+$$
+\Gamma \assign \setmergeof{
+    \Gamma
+  }{
+    \begin{cases}
+     M_i \in \pcn :     & \depsreqof{M_i} \\
+     M_i \not\in \pcn : & \{ \}
+    \end{cases}
+  }{
+    \depsreqof{S_i}
+  }
+$$
+
+TODO define $\setmerge$
+
+\item Finalise our putative direct dependencies
+$
+\Gamma \assign g(\pc, \Gamma)
+$
+
+\item For each direct dependency $\pd \in \Gamma$,
+
+\begin{enumerate}
+\item Add an edge $\pc \hasdirdep \pd$ to the digraph (adding nodes
+as necessary).
+If this results in a cycle, abort entirely (as the function $g$ is
+inappropriate; a different $g$ could work).
+\item Run $\alg{Rank-Recurse}(\pd)$.
 \end{enumerate}
 
-\section{Planning phase}
+\end{enumerate}
 
-The results of the planning phase consist of: 
-\begin{itemize*}
-\item{ The relation $\hasdirdep$ and hence the partial order $\hasdep$. }
-\item{ For each commit set $\pc$, a confirmed set of sources $\set S_{\pc}$. }
-\item{ For each commit set $\pc$, the order in which to merge the sources
-        $E_{\pc,j} \in \set E_{\pc}$. }
-\item{ For each $E_{\pc,j}$ an intended merge base $M_{\pc,j}$. }
-\end{itemize*}
+\subsection{Results of the ranking phase}
 
-We use a recursive planning algorith, recursing over Topbloke commit
-sets (ie, sets $\py$ or $\pn$).  We'll call the commit set we're
-processing at each step $\pc$.
-At each recursive step 
-we make a plan to merge all $\set E_{\pc} = \{ E_{\pc,j \ldots} \}$
-and all the direct contributors of $\pc$ (as determined below)
-into $\tipzc$, to make $\tipfc$.
+By the end of the ranking phase, we have recorded the following
+information:
 
-We start with $\pc = \pl$ where $\pl = \patchof{L}$.
+\begin{itemize}
+\item
+$ \allpatches, \hasdirdep $ and hence the completion of $\hasdirdep$
+into the partial order $\hasdep$.
 
+\item
+For each $\pc \in \allpatches$,
+the base branch starting point commit $W^{\pcn} = W$.
 
-\subsection{Direct contributors for $\pc = \pcn$}
+\item
+For each $\pc$,
+the direct dependencies $\Gamma^{\pc} = \Gamma$.
 
-The direct contributors of $\pcn$ are the commit sets corresponding to
-the tip branches for the direct dependencies of the patch $\pc$.  We
-need to calculate what the direct dependencies are going to be.
+\item
+For each $\pc$,
+the ordered set of base branch sources $\set S^{\pcn} = \set S,
+S^{\pcn}_i = S_i$
+and corresponding merge bases $M^{\pcn}_i = M_i$.
 
-Choose an (arbitrary, but ideally somehow optimal in
-a way not discussed here) ordering of $\set E_{\pc}$, $E_{\pc,j}$
-($j = 1 \ldots m$).
-For brevity we will write $E_j$ for $E_{\pc,j}$.
-Remove from that set (and ordering) any $E_j$ which
-are $\le$ and $\neq$ some other $E_k$.
+\end{itemize}
 
-Initially let $\set D_0 = \depsreqof{\tipzc}$.
-For each $E_j$ starting with $j=1$ choose a corresponding intended
-merge base $M_j$ such that $M_j \le E_j \land M_j \le T_{\pc,j-1}$.
-Calculate $\set D_j$ as the 3-way merge of the sets $\set D_{j-1}$ and
-$\depsreqof{E_j}$ using as a base $\depsreqof{M_j}$.  This will
-generate $D_m$ as the putative direct contributors of $\pcn$.
+\subsection{Proof of termination}
 
-However, the invocation may give instructions that certain direct
-dependencies are definitely to be included, or excluded.  As a result
-the set of actual direct contributors is some arbitrary set of patches
-(strictly, some arbitrary set of Topbloke tip commit sets).
+$\alg{Rank-Recurse}(\pc)$ recurses but only downwards through the
+finite graph $\hasdirdep$, so it must terminate.  
 
-\subsection{Direct contributors for $\pc = \pcy$}
+The whole ranking algorithm iterates but each iteration involves
+adding one or more patches to $\allpatches$.  Since there are
+finitely many patches and we never remove anything from $\allpatches$
+this must complete eventually.
 
-The sole direct contributor of $\pcy$ is $\pcn$.
+$\qed$
 
-\subsection{Recursive step}
+\section{Traversal phase --- algorithm}
 
-For each direct contributor $\p$, we add the edge $\pc \hasdirdep \p$
-and augment the ordering $\hasdep$ accordingly.
+(In general, unless stated otherwise below, when we generate a new
+commit $C$ using one of the commit kind algorith, we update
+$W \assign C$.  In any such case where we say we're going to Merge
+with $L = W$, if $R \ge W$ we do not Merge but instead simply set
+$W \assign R$.)
 
-If this would make a cycle in $\hasdep$, we abort . The operation must
-then be retried by the user, if desired, but with different or
-additional instructions for modifying the direct contributors of some
-$\pqn$ involved in the cycle.
 
-For each such $\p$, after updating $\hasdep$, we recursively make a plan
-for $\pc' = \p$.
+For each patch $\pc \in \allpatches$ in topological order by $\hasdep$,
+lowest first:
 
+\begin{enumerate}
 
+\item Optionally, attempt
+ $\alg{Merge-Base}(\pc)$.  This may or may not succeed.
 
-\section{Execution phase}
+\item If this didn't succeed, or was not attempted, execute
+ $\alg{Recreate-Base}(\pc)$.
 
-We process commit sets from the bottom up according to the relation
-$\hasdep$.  For each commit set $\pc$ we construct $\tipfc$ from
-$\tipzc$, as planned.  By construction, $\hasdep$ has $\patchof{L}$
-as its maximum, so this operation will finish by updating
-$\tipca{\patchof{L}}$ with $\tipfa{\patchof{L}}$.
+\item Then in any case, execute
+ $\alg{Merge-Tip}(\pc)$.
 
-After we are done with each commit set $\pc$, the
-new tip $\tipfc$ has the following properties:
-\[ \eqn{Tip Sources}{
-  \bigforall_{E_i \in \set E_{\pc}} \tipfc \ge E_i
-}\]
-\[ \eqn{Tip Dependencies}{
-  \bigforall_{\pc \hasdep \p} \tipfc \ge \tipfa \p
-}\]
-\[ \eqn{Perfect Contents}{
-  \tipfc \haspatch \p \equiv \pc \hasdep \py
-}\]
+\end{enumerate}
 
-For brevity we will sometimes write $\tipu$ for $\tipuc$, etc.  We will start
-out with $\tipc = \tipz$, and at each step of the way construct some
-$\tipu$ from $\tipc$.  The final $\tipu$ becomes $\tipf$.
+After processing each $\pc$ we will have created:
 
-\subsection{Preparation}
+\begin{itemize}
 
-Firstly, we will check each $E_i$ for being $\ge \tipc$.  If
-it is, are we fast forward to $E_i$
---- formally, $\tipu = \text{max}(\tipc, E_i)$ ---
-and drop $E_i$ from the planned ordering.
+\item $\tipcn$ and $\tipcy$ such that $\baseof{\tipcy} = \tipcn$.
 
-Then we will merge the direct contributors and the sources' ends.
-This generates more commits $\tipuc \in \pc$, but none in any other
-commit set.  We maintain
-$$
- \bigforall_{\p \isdep \pc}
- \pancsof{\tipcc}{\p} \subset
-   \pancsof{\tipfa \p}{\p}
-$$
-\proof{
- For $\tipcc = \tipzc$, $T$ ...WRONG WE NEED $\tipfa \p$ TO BE IN $\set E$ SOMEHOW
-}
+\end{itemize}
+
+\subsection{$\alg{Merge-Base}(\pc)$}
 
-\subsection{Merge Contributors for $\pcy$}
+This algorithm attempts to construct a suitably updated version of the
+base branch $\pcn$ using some existing version of $\pcn$ as a starting
+point.
 
-Merge $\pcn$ into $\tipc$.  That is, merge with
-$L = \tipc, R = \tipfa{\pcn}, M = \baseof{\tipc}$.
-to construct $\tipu$.
+It should be executed noninteractively.  Specifically, if any step
+fails with a merge conflict, the whole thing should be abandoned.
+This avoids asking the user to resolve confusing conflicts.  It also
+avoids asking the user to pointlessly resolve conflicts in situations
+where we will later discover that $\alg{Merge-Base}$ wasn't feasible
+after all.
 
-Merge conditions:
+If $\pc$ has only one direct dependency, this algorithm should not be
+used as in that case $\alg{Recreate-Base}$ is trivial and guaranteed
+to generate a perfect answer, whereas this algorithm might involve
+merges and therefore might not produce a perfect answer if the
+situation is complicated.
 
-Ingredients satisfied by construction.
-Tip Merge satisfied by construction.  Merge Acyclic follows
-from Perfect Contents and $\hasdep$ being acyclic.
+Initially, set $W \iassign W^{\pcn}$.
 
-Removal Merge Ends: For $\p = \pc$, $M \nothaspatch \p$; OK.
-For $\p \neq \pc$, by Tip Contents,
-$M \haspatch \p \equiv L \haspatch \p$, so we need only
-worry about $X = R, Y = L$; ie $L \haspatch \p$,
-$M = \baseof{L} \haspatch \p$.
-By Tip Contents for $L$, $D \le L \equiv D \le M$.  OK.~~$\qed$
+\subsubsection{Bases and sources}
 
-WIP UP TO HERE
+In some order, perhaps interleaving the two kinds of merge:
 
-Addition Merge Ends: If $\py \isdep \pcn$, we have already
-done the execution phase for $\pcn$ and $\py$.  By
-Perfect Contents for $\pcn$, $\tipfa \pcn \haspatch \p$ i.e.
-$R \haspatch \p$.  So we only need to worry about $Y = R = \tipfa \pcn$.
-By Tip Dependencies $\tipfa \pcn \ge \tipfa \py$.
-And by Tip Sources $\tipfa \py \ge $
+\begin{enumerate}
 
-want to prove $E \le \tipfc$ where $E \in \pendsof{\tipcc}{\py}$
+\item For each $\pd \isdirdep \pc$, find a merge base
+$M \le W,\; \le \tipdy$ and merge $\tipdy$ into $W$.
+That is, use $\alg{Merge}$ with $L = W,\; R = \tipdy$.
+(Dependency Merge.)
 
-$\pancsof{\tipcc}{\py} = $
+\item For each $S \in S^{\pcn}_i$, merge it into $W$.
+That is, use $\alg{Merge}$ with $L = W,\; R = S,\; M = M^{\pcn}_i$.
+(Base Sibling Merge.)
+
+\end{enumerate}
 
+\subsubsection{Fixup}
 
-computed $\tipfa \py$, and by Perfect Contents for $\py$
+Execute $\alg{Fixup-Base}(W,\pc)$.
+
+
+\subsection{$\alg{Recreate-Base}(\pc)$}
+
+\begin{enumerate}
 
+\item
 
-with $M=M_j, L=T_{\pc,j-1}, R=E_j$,
-and calculate what the resulting desired direct dependencies file
-(ie, the set of patches $\set D_j$)
-would be.  Eventually we 
+Choose a $\hasdep$-maximal direct dependency $\pd$ of $\pc$.
 
-So, formally, we select somehow an order of sources $S_i$.  For each 
+\item
 
+Use $\alg{Create Base}$ with $L$ = $\pdy,\; \pq = \pc$ to generate $C$
+and set $W \iassign C$.  (Recreate Base Beginning.)
 
-Make use of the following recursive algorithm, Plan 
+\item
+
+Execute the subalgorithm $\alg{Recreate-Recurse}(\pc)$.
+
+\item
+
+Declare that we contain all of the relevant information from the
+sources.  That is, use $\alg{Pseudo-merge}$ with $L = W, \;
+\set R = \{ W \} \cup \set S^{\pcn}$.
+(Recreate Base Final Declaration.)
+
+\end{enumerate}
+
+\subsubsection{$\alg{Recreate-Recurse}(\pd)$}
+
+\begin{enumerate}
+
+\item Is $W \haspatch \pd$ ?  If so, there is nothing to do: return.
+
+\item TODO what about non-Topbloke base branches
+
+\item Use $\alg{Pseudo-Merge}$ with $L = W,\; \set R = \{ \tipdn \}$.
+(Recreate Base Dependency Base Declaration.)
+
+\item For all $\hasdep$-maximal $\pd' \isdirdep \pd$,
+execute $\alg{Recreate-Recurse}(\pd')$.
+
+\item Use $\alg{Merge}$ to apply $\pd$ to $W$.  That is,
+$L = W, \; R = \tipdy, \; M = \baseof{R} = \tipdn$.
+(Recreate Reapply.)
+
+\end{enumerate}
+
+
+\subsection{$\alg{Merge-Tip}(\pc)$}
+
+\begin{enumerate}
+
+\item TODO CHOOSE/REFINE W AND S as was done during Ranking for bases
+
+\item $\alg{Merge}$ from $\tipcn$.  That is, $L = W, \;
+R = \tipcn$ and choose any suitable $M$.  (Tip Base Merge.)
+
+\item For each source $S \in \set S^{\pcy}$,
+$\alg{Merge}$ with $L = W, \; R = S$ and any suitable $M$.
+(Tip Source Merge.)
+
+\end{enumerate}
 
 
+\section{Traversal phase --- proofs}
 
+For each operation called for by the traversal algorithms, we prove
+that the commit generation preconditions are met.
 
- recursively make a plan to merge all $E = \pends$
+\subsection{Tip Base Merge}
 
-Specifically, in