X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=strategy.tex;h=35049b56424cca0746781e9743eda0909a921005;hp=7b977e5870ea2a34256850fee8ab34eee2c2f54e;hb=63cc1534200cc7fcafa007f8c6704fc8ac9c9fec;hpb=cc6f8a852918817eecd961f9d2ce85b7ba13eb6f

diff --git a/strategy.tex b/strategy.tex
index 7b977e5..35049b5 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[ $g : \pc, \Gamma \mapsto \Gamma'$ ]
@@ -80,33 +81,196 @@ 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).
 
 \end{basedescript}
 
 \section{Ranking phase}
 
-{\bf Ranking} is:
+We run the following algorithm:
 \begin{enumerate}
 \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)
-     \cup \{ \baseof{E} \; | \; \pendsof{ \left[
-         \bigcup_{\p \in \allpatches} h(\pn) \cup h(\py)
-         \right]
-       }{ \pcy } \} $
+
+\item Set
+$$
+  \set S \iassign h(\pcn)
+     \cup 
+        \bigcup_{\p \in \allpatches}
+        \bigcup_{H \in h(\pn) \lor H \in h(\py)}
+         \{ \baseof{E} \; | \; E \in \pendsof{H}{\pcy} \}
+$$
+
+and $W \iassign w(h(\pcn))$
+
+\item While $\exists_{S \in \set S} S \ge W$,
+update $W \assign S$ and $\set S \assign \set S \, \backslash \{ S \}$
+
+(This will often remove $W$ from $\set S$.  Afterwards, $\set S$
+is a collection of heads to be merged into $W$.)
+
+\item Choose an ordering of $\set S$, $S_i$ for $i=1 \ldots n$.
+
+\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}
 
+\end{enumerate}
+
+\subsection{Results of the ranking phase}
+
+By the end of the ranking phase, we have recorded the following
+information:
+
+\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 $W^{\pcn} = W$.
+
+\item
+For each $\pc$,
+the direct dependencies $\Gamma^{\pc} = \Gamma$.
+
+\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 $M^{\pcn}_i = M_i$.
+
+\end{itemize}
+
+\subsection{Proof of termination}
+
+$\alg{Rank-Recurse}(\pc)$ recurses but only downwards through the
+finite graph $\hasdirdep$, so it must terminate.  
+
+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.
+
+$\qed$
+
+\section{Traversal phase}
+
+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.
+
+\item If this didn't succeed, or was not attempted, execute
+ $\alg{Recreate-Base}(\pc)$.
+
+\item Then in any case, execute
+ $\alg{Merge-Tip}(\pc)$.
+
+\end{enumerate}
+
+After processing each $\pc$
+
+\subsection{$\alg{Merge-Base}(\pc)$}
+
+This algorithm attempts to construct a suitably updated version of the
+base branch $\pcn$.
+
+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.
+
+\subsubsection{Bases and sources}
+
+In some order, perhaps interleaving the two kinds of merge:
+
+\begin{enumerate}
+
+\item For each $\pd \isdirdep$
+
+\item
+
+\end{enumerate}
+
+
+
+
 \section{Planning phase}
 
 The results of the planning phase consist of: