X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=notation.tex;h=48ea1b7e2ceec9002f67b2d41335e5c227b69f25;hp=04f8c2e7494017f901803559e2340260b5e00625;hb=c497f56e8a7f09c4c328bd7560631d8773b7e676;hpb=d00298b5b6d70bd919824ab8b79d71663f3cdfa6

diff --git a/notation.tex b/notation.tex
index 04f8c2e..48ea1b7 100644
--- a/notation.tex
+++ b/notation.tex
@@ -1,4 +1,7 @@
-\section{Notation}
+\stdsection{Notation}
+
+Throughout, any free variables are implicitly universally quantified
+at the outermost level.
 
 \begin{basedescript}{
 \desclabelwidth{5em}
@@ -27,10 +30,19 @@ A patch $\p$ consists of two sets of commits $\pn$ and $\py$, which
 are respectively the base and tip git branches.  $\p$ may be used
 where the context requires a set, in which case the statement
 is to be taken as applying to both $\py$ and $\pn$.
-All of these sets are disjoint.  Hence:
+All of these sets will be disjoint by construction
+(see Invariants, below).  Hence:
+
+\item[ $\foreign$ ]
+The set of all commits which are not part of a Topbloke branch.  We
+call these foreign commits.
+
+\item[ $\set A$, $\set P$, $\ldots$ ]
+Arbitrary sets of commits.  Maybe $\set P = \p$ i.e.\ some $\py$ or $\pn$, but
+maybe not.
 
 \item[ $ \patchof{ C } $ ]
-Either $\p$ s.t. $ C \in \p $, or $\bot$.
+Either $\p$ s.t. $ C \in \p $, or $\foreign$.
 A function from commits to patches' sets $\p$.
 
 \item[ $ \pancsof{C}{\set P} $ ]
@@ -49,20 +61,22 @@ $ \pendsof{C}{\pn} = \{ \baseof{C} \} $ where $ C \in \py $.
 A partial function from commits to commits.
 See Unique Base, below.
 
+\item[ $ C \nothaspatch \p $ ]
+$\displaystyle \bigforall_{D \in \py} D \not\isin C $.
+~ Informally, $C$ has none of the contents of $\p$.
+
 \item[ $ C \zhaspatch \p $ ]
 $\displaystyle \bigforall_{D \in \py} D \isin C \equiv D \le C $.
 ~ Informally, $C$ has all the reachable contents of $\p$.
 
 \item[ $ C \haspatch \p $ ]
-$\displaystyle C \zhaspatch \p \land \exists_{D \in \py} D \le C $.
+$\displaystyle C \zhaspatch \p \land \exists_{F \in \py} F \le C $.
 ~ Informally, $C$ nontrivially has all the reachable contents of $\p$.
 
-\item[ $ C \nothaspatch \p $ ]
-$\displaystyle \bigforall_{D \in \py} D \not\isin C $.
-~ Informally, $C$ has none of the contents of $\p$.
-
-Note that $\zhaspatch$ and $\nothaspatch$ are not mutually exclusive.
-$\haspatch$ and $\nothaspatch$ are.
+Note that $\zhaspatch$ and $\nothaspatch$ are neither
+mutually exclusive nor exhaustive.
+$\haspatch$ and $\nothaspatch$ are mutually exclusive but not
+necessarily exhaustive.
 
 Commits on Non-Topbloke branches are $\nothaspatch \p$ for all $\p$.  This
 includes commits on plain git branches made by applying a Topbloke