strategy: wip

[topbloke-formulae.git] / invariants.tex

diff --git a/invariants.tex b/invariants.tex
index 25d51c508c167005c48d7642108e961785aa1258..0cac868d3e6b8aaf7de01d375a4a28c8b229d77c 100644 (file)
--- a/invariants.tex
+++ b/invariants.tex
@@ -1,27 +1,41 @@
 \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:}{
-  \bigforall_{B \in \pn} D \isin B \implies D \notin \py
+\[\eqn{Base Acyclic}{
+  \bigforall_{C \in \pn} D \isin C \implies D \notin \py
 }\]
-\[\eqn{Coherence:}{
+\[\eqn{Coherence}{
   \bigforall_{C,\p} C \haspatch \p \lor C \nothaspatch \p
 }\]
-\[\eqn{Foreign Inclusion:}{
+\[\eqn{Unique Tips}{
+  \bigforall_{C,\p} C \haspatch \p \implies \pendsof{C}{\py} = \{ T \}
+}\]
+\[\eqn{Foreign Inclusion}{
   \bigforall_{D \text{ s.t. } \patchof{D} = \bot} D \isin C \equiv D \leq C
 }\]
-\[\eqn{Foreign Contents:}{
+\[\eqn{Foreign Contents}{
   \bigforall_{C \text{ s.t. } \patchof{C} = \bot}
     D \le C \implies \patchof{D} = \bot
 }\]
+
+We also assign each new commit $C$ to zero or one of the sets $\p$, as
+stated in the definition of $\patchof{C}$ in the summary for each kind
+of commit.
+
+A commit $C$ which satisfies all of the above is said to be
+``conformant''.
+
+For each operation we will perform which generates a new commit, we
+will assume the conformance of the existing history and prove the
+conformance of the new commit.