From: Ian Jackson <ijackson@chiark.greenend.org.uk>
Date: Sat, 7 Jul 2012 22:26:16 +0000 (+0100)
Subject: traversal: wip prove Recreate Base Beginning OK, currently need to prove Tip Correct... 
X-Git-Url: https://www.chiark.greenend.org.uk/ucgi/~ian/git?a=commitdiff_plain;h=d29c556b0ebedf4081684216f426b83ee9f04573;p=topbloke-formulae.git

traversal: wip prove Recreate Base Beginning OK, currently need to prove Tip Correct Contents
---

diff --git a/trav-alg.tex b/trav-alg.tex
index abe2441..8a9a68a 100644
--- a/trav-alg.tex
+++ b/trav-alg.tex
@@ -29,6 +29,11 @@ such that:
 \statement{Correct Base}{
   \baseof{\tipcy} = \tipcn
 }
+\statement{Base Correct Contents}{
+  \tipcn \haspatch \pd
+   \equiv
+  \pc \hasdep \pd
+}
 \statement{Tip Exceeds Inputs}{
   \tipcy \ge \pendsof{\allsrcs}{\pcy}
 }
@@ -97,7 +102,7 @@ Choose a $\hasdep$-maximal direct dependency $\pd$ of $\pc$.
 
 \item
 
-Use $\alg{Create Base}$ with $L$ = $\pdy,\; \pq = \pc$ to generate $C$
+Use $\alg{Create Base}$ with $L$ = $\tipdy,\; \pq = \pc$ to generate $C$
 and set $W \iassign C$.  (Recreate Base Beginning.)
 
 \item
diff --git a/trav-proofs.tex b/trav-proofs.tex
index 981483e..3c2a175 100644
--- a/trav-proofs.tex
+++ b/trav-proofs.tex
@@ -5,6 +5,19 @@ that the commit generation preconditions are met.
 
 WIP WHAT ABOUT PROVING ALL THE TRAVERSAL RESULTS
 
+\subsection{Traversal Lemmas}
+
+Firstly, some lemmas.
+
+\statement{Tip Correct Contents}{
+  \tipcy \haspatch \pd
+    \equiv
+  \pc = \pd \lor \pc \hasdep \pd
+}
+\proof{
+   WIP
+}
+
 \subsection{Base Dependency Merge, Base Sibling Merge}
 
 We do not prove that the preconditions are met.  Instead, we check
@@ -17,8 +30,9 @@ WIP WHAT ABOUT PROVING ALL THE TRAVERSAL RESULTS
 
 \subsection{Recreate Base Beginning}
 
-WHAT IF $\pendsof{L}{\pqy} \neq \{\}$ ?
-FIX BY CHANGE PRECOND OF CREATE BASE
+\subsubsection{Create Acyclic}
+
+$L = \tipdy$ so
 
 \subsection{Tip Base Merge}