strategy: wip reachable etc.

[topbloke-formulae.git] / invariants.tex

diff --git a/invariants.tex b/invariants.tex
index bd77d69d3da86844bd1b74b89ccad2ed902c3187..bb926ea1f71460e1db981d110bf06078ab818a78 100644 (file)
--- a/invariants.tex
+++ b/invariants.tex
@@ -1,32 +1,32 @@
 \section{Invariants}
 
 We maintain these each time we construct a new commit. \\
-\[ \eqn{No Replay:}{
+\[ \eqn{No Replay}{
   C \has D \implies C \ge D
 }\]
-\[\eqn{Unique Base:}{
+\[\eqn{Unique Base}{
  \bigforall_{C \in \py} \pendsof{C}{\pn} = \{ B \}
 }\]
-\[\eqn{Tip Contents:}{
+\[\eqn{Tip Contents}{
   \bigforall_{C \in \py} D \isin C \equiv
     { D \isin \baseof{C} \lor \atop
       (D \in \py \land D \le C) }
 }\]
-\[\eqn{Base Acyclic:}{
+\[\eqn{Base Acyclic}{
   \bigforall_{C \in \pn} D \isin C \implies D \notin \py
 }\]
-\[\eqn{Coherence:}{
+\[\eqn{Coherence}{
   \bigforall_{C,\p} C \haspatch \p \lor C \nothaspatch \p
 }\]
-\[\eqn{Unique Tips:}{
+\[\eqn{Unique Tips}{
   \bigforall_{C,\p} C \haspatch \p \implies \pendsof{C}{\py} = \{ T \}
 }\]
-\[\eqn{Foreign Inclusion:}{
-  \bigforall_{D \text{ s.t. } \patchof{D} = \bot} D \isin C \equiv D \leq C
+\[\eqn{Foreign Inclusion}{
+  \bigforall_{D \in \foreign} D \isin C \equiv D \leq C
 }\]
-\[\eqn{Foreign Contents:}{
-  \bigforall_{C \text{ s.t. } \patchof{C} = \bot}
-    D \le C \implies \patchof{D} = \bot
+\[\eqn{Foreign Contents}{
+  \bigforall_{C \in \foreign}
+    D \le C \implies \isforeign{D}
 }\]
 
 We also assign each new commit $C$ to zero or one of the sets $\p$, as