-When we are trying to do a merge of some kind, in general,
-we want to merge some source commits $S_0 \ldots S_n$.
-We'll write $S_0 = L$. We require that $L$ is the current git ref
-for $\patchof{L}$.
-
-\stdsection{Notation}
+Here we describe the update algorithm. This is responsible for
+refreshing patches against updated versions of their dependencies,
+for merging different versions of the various braches created by
+distributed development, and for implementing decisions to add and
+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
+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
+branch head commit. These new head commits are maximums - that is,
+each has as ancestors all of its branches' sources and indeed all
+relevant commits in that branch.
+
+We have two possible strategies for constructing new base branch
+heads: we can either Merge (works incrementally even if there the
+patch has multiple dependencies, but may sometimes not be possible) or
+we can Regenerate (trivial if there is a single dependency, and is
+always possible, but may involve the user re-resolving conflicts if
+there are multiple dependencies).
+
+\section{Notation}
\begin{basedescript}{
\desclabelwidth{5em}
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 contributors the
+The Topbloke commit set $\pc$ has as a direct contributor the
commit set $\p$. This is an acyclic relation.
\item[ $\p \hasdep \pq$ ]
Acyclic; the completion of $\hasdirdep$ into a
partial order.
-\item[ $\set E_{\pc}$ ]
-$ \bigcup_i \pendsof{S_i}{\pc} $.
-All the ends of $\pc$ in the sources.
+\item[ $\pendsof{\set J}{\p}$ ]
+Convenience notation for
+the maximal elements of $\bigcup_{J \in \set J} \pendsof{J}{\p}$
+(where $\set J$ is some set of commits).
+
+\item[ $\pendsof{\set X}{\p} \le T$ ]
+Convenience notation for
+$\bigforall_{E \in \pendsof{\set X}{\p}} E \le T$
+
+%\item[ $\set E_{\pc}$ ]
+%$ \bigcup_i \pendsof{S_{\pc,i}}{\pc} $.
+%All the ends of $\pc$ in the sources.
+
+%\item[ $ \tipzc, \tipcc, \tipuc, \tipfc $ ]
+%The git ref for the Topbloke commit set $\pc$: respectively,
+%the original, current, updated, and final values.
+
+\end{basedescript}
+
+\stdsection{Inputs to the update algorithm}
-\item[ $ \tipzc, \tipcc, \tipuc, \tipfc $ ]
-The git ref for the Topbloke commit set $\pc$: respectively,
-the original, current, updated, and final values.
+\begin{basedescript}{
+\desclabelwidth{5em}
+\desclabelstyle{\nextlinelabel}
+}
+\item[ $\pc_0$ ]
+The topmost patch which we are trying to update. This and
+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 $\pc^{+/-}$.
+This will include the current local and remote git refs, as desired.
+
+\item[ $g : \pc, \Gamma \mapsto \Gamma'$ ]
+Function to allow explicit adjustment of the direct dependencies
+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 $\hasdirdep$.
\end{basedescript}
+\section{Ranking phase}
+
+{\bf Ranking} is:
+\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 Until $\allpatches$ remains unchanged.
+\end{enumerate}
+\end{enumerate}
+
+{\bf Rank-Recurse}($\pc$) is:
+\begin{enumerate}
+\item Add $\pc$ to $\allpatches$ if it is not there already.
+\item Let $\set S_{\pcn} = h(\pcn)
+ \cup
+ \bigcup_{\p \in \allpatches}
+ \bigcup_{H \in h(\pn) \lor H \in h(\py)}
+ \{ \baseof{E} \; | \; E \in \pendsof{H}{\pcy} \} $.
+
+(We write $\set S = \set S_{\pcn}$ when it's not ambiguous.)
+\end{enumerate}
+
\section{Planning phase}
-The planning phase computes:
+The results of the planning phase consist of:
\begin{itemize*}
-\item{ The relation $\hasdirdep$ and hence the ordering $\hasdep$. }
-\item{ For each commit set $\pc$, the order in which to merge
+\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*}