foreign notation: change \bot to \foreign everywhere

diff --git a/anticommit.tex b/anticommit.tex
index 2306a73e151075757b87891b3f9d17a447b9d88d..72469b80d69fa67aa410381faf5768262d15964e 100644 (file)
--- a/anticommit.tex
+++ b/anticommit.tex
@@ -131,7 +131,7 @@ Single Parent Unique Tips applies.  $\qed$
 
 \subsection{Foreign Inclusion}
 
-Consider some $D$ s.t. $\patchof{D} = \bot$.  $D \neq C$.
+Consider some $D$ s.t. $\patchof{D} = \foreign$.  $D \neq C$.
 So by Desired Contents $D \isin C \equiv D \isin L$.
 By Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.
 

diff --git a/article.tex b/article.tex
index fb7eab4b2619f8e2d5e7bbdac43d636ed2253fef..ffd940fbb32410e9fbf755a4c0615ed31b170f08 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -96,6 +96,8 @@
 \newcommand{\baseof}[1]{\base ( #1 ) }
 \newcommand{\depsreqof}[1]{\depsreq ( #1 ) }
 
+\newcommand{\foreign}{\bot}
+
 \newcommand{\allpatches}{\Upsilon}
 \newcommand{\assign}{\leftarrow}
 \newcommand{\iassign}{\leftarrow}

diff --git a/invariants.tex b/invariants.tex
index 0cac868d3e6b8aaf7de01d375a4a28c8b229d77c..736fb8ee569ed5a2791bfae5b1c817cd95cfaa23 100644 (file)
--- a/invariants.tex
+++ b/invariants.tex
@@ -22,11 +22,11 @@ We maintain these each time we construct a new commit. \\
   \bigforall_{C,\p} C \haspatch \p \implies \pendsof{C}{\py} = \{ T \}
 }\]
 \[\eqn{Foreign Inclusion}{
-  \bigforall_{D \text{ s.t. } \patchof{D} = \bot} D \isin C \equiv D \leq C
+  \bigforall_{D \text{ s.t. } \patchof{D} = \foreign} D \isin C \equiv D \leq C
 }\]
 \[\eqn{Foreign Contents}{
-  \bigforall_{C \text{ s.t. } \patchof{C} = \bot}
-    D \le C \implies \patchof{D} = \bot
+  \bigforall_{C \text{ s.t. } \patchof{C} = \foreign}
+    D \le C \implies \patchof{D} = \foreign
 }\]
 
 We also assign each new commit $C$ to zero or one of the sets $\p$, as

diff --git a/lemmas.tex b/lemmas.tex
index 937398207615e337585cdf7773d0c33f66f6a9f6..72e00d61fc5b23d82252989bc578c8f18596a289 100644 (file)
--- a/lemmas.tex
+++ b/lemmas.tex
@@ -175,12 +175,12 @@ $$
   \right]
  \implies
   \left[
-   \bigforall_{D \text{ s.t. } \patchof{D} = \bot}
+   \bigforall_{D \text{ s.t. } \patchof{D} = \foreign}
      D \isin C \equiv D \le C
   \right]
 $$
 \proof{
-Consider some $D$ s.t. $\patchof{D} = \bot$.
+Consider some $D$ s.t. $\patchof{D} = \foreign$.
 If $D = C$, trivially true.  For $D \neq C$,
 by Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.
 And by Exact Ancestors $D \le L \equiv D \le C$.
@@ -192,20 +192,20 @@ Given conformant commits $A \in \set A$,
 $$
    \left[
     C \hasparents \set A \land
-    \patchof{C} = \bot \land
-      \bigforall_{A \in \set A} \patchof{A} = \bot
+    \patchof{C} = \foreign \land
+      \bigforall_{A \in \set A} \patchof{A} = \foreign
    \right]
   \implies
    \left[
   \bigforall_{D}
     D \le C
    \implies
-    \patchof{D} = \bot
+    \patchof{D} = \foreign
    \right]
 $$
 \proof{
-Consider some $D \le C$.  If $D = C$, $\patchof{D} = \bot$ trivially.
+Consider some $D \le C$.  If $D = C$, $\patchof{D} = \foreign$ trivially.
 If $D \neq C$ then $D \le A$ where $A \in \set A$.  By Foreign
-Contents of $A$, $\patchof{D} = \bot$.
+Contents of $A$, $\patchof{D} = \foreign$.
 }
 

diff --git a/merge.tex b/merge.tex
index 6ff5d81e51d67193858caf678fa0a1185a60c7fd..6ba1387886a8bc6f90fb4cd5254ce544f962e4e7 100644 (file)
--- a/merge.tex
+++ b/merge.tex
@@ -56,19 +56,19 @@ satisfied; in particular, provided that $L \ge \baseof{R}$.
     , \text{where} \{J,K\} = \{L,R\}
 }\]
 \[ \eqn{ Foreign Merges }{
-    \patchof{L} = \bot \implies \patchof{R} = \bot
+    \patchof{L} = \foreign \implies \patchof{R} = \foreign
 }\]
 
 \subsection{Non-Topbloke merges}
 
-We require both $\patchof{L} = \bot$ and $\patchof{R} = \bot$
+We require both $\patchof{L} = \foreign$ and $\patchof{R} = \foreign$
 (Foreign Merges, above).
 I.e. not only is it forbidden to merge into a Topbloke-controlled
 branch without Topbloke's assistance, it is also forbidden to
 merge any Topbloke-controlled branch into any plain git branch.
 
 Given those conditions, Tip Merge and Merge Acyclic do not apply.
-By Foreign Contents of $L$, $\patchof{M} = \bot$ as well.
+By Foreign Contents of $L$, $\patchof{M} = \foreign$ as well.
 So by Foreign Contents for any $A \in \{L,M,R\}$,
 $\forall_{\p, D \in \py} D \not\le A$
 so $\pendsof{A}{\py} = \{ \}$ and the RHS of both Merge Ends
@@ -280,7 +280,7 @@ $\qed$
 
 \subsection{Foreign Inclusion}
 
-Consider some $D$ s.t. $\patchof{D} = \bot$.
+Consider some $D$ s.t. $\patchof{D} = \foreign$.
 By Foreign Inclusion of $L, M, R$:
 $D \isin L \equiv D \le L$;
 $D \isin M \equiv D \le M$;
@@ -311,6 +311,6 @@ $\qed$
 
 \subsection{Foreign Contents}
 
-Only relevant if $\patchof{L} = \bot$, in which case
-$\patchof{C} = \bot$ and by Foreign Merges $\patchof{R} = \bot$,
+Only relevant if $\patchof{L} = \foreign$, in which case
+$\patchof{C} = \foreign$ and by Foreign Merges $\patchof{R} = \foreign$,
 so Totally Foreign Contents applies.  $\qed$

diff --git a/notation.tex b/notation.tex
index bee8eff2615d1937d73e44f305921410f392306b..bae94bbafa3534d093f2846ddcb005855340b893 100644 (file)
--- a/notation.tex
+++ b/notation.tex
@@ -38,7 +38,7 @@ 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} $ ]

diff --git a/pseudomerge.tex b/pseudomerge.tex
index 1e9422c447b6f143837553c40a9afefe2cfeeed4..d884be84896b2ded5681bf2026f093c8f45db009 100644 (file)
--- a/pseudomerge.tex
+++ b/pseudomerge.tex
@@ -25,7 +25,7 @@ but whose contents are exactly those of $L$.
 }\]
 
 \[ \eqn{ Foreign Unaffected }{
- \bigforall_{ D \text{ s.t. } \patchof{D} = \bot }
+ \bigforall_{ D \text{ s.t. } \patchof{D} = \foreign }
   \left[ \bigexists_{A \in \set A} D \le A \right]
    \implies
   D \le L
@@ -34,7 +34,7 @@ but whose contents are exactly those of $L$.
 
 \subsection{Lemma: Foreign Identical}
 
-$\patchof{D} = \bot \implies \big[ D \le C \equiv D \le L \big]$.
+$\patchof{D} = \foreign \implies \big[ D \le C \equiv D \le L \big]$.
 
 \proof{
 If $D \le L$, trivially $D \le C$; so conversely

diff --git a/simple.tex b/simple.tex
index b22fdbe9d15bc65321f58b6cd85ae65fb3ba250f..f714edbc54562e454fe3cb912ac9b073546e4ec1 100644 (file)
--- a/simple.tex
+++ b/simple.tex
@@ -100,6 +100,6 @@ Simple Foreign Inclusion applies.  $\qed$
 
 \subsection{Foreign Contents:}
 
-Only relevant if $\patchof{C} = \bot$, and in that case Totally
+Only relevant if $\patchof{C} = \foreign$, and in that case Totally
 Foreign Contents applies. $\qed$