X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=merge.tex;h=9daaa00450ae562db1d3af581b856e08de0e4af0;hp=1ca4af73574a7343d367fed94ebc945d105dc7a3;hb=f5f93d74c204fcd773074e61aa4fac1a3e48aa3c;hpb=410132e37a1f6e95cbfa9792d63b50b9390e59e4 diff --git a/merge.tex b/merge.tex index 1ca4af7..9daaa00 100644 --- a/merge.tex +++ b/merge.tex @@ -6,12 +6,13 @@ Merge commits $L$ and $R$ using merge base $M$: \gathnext \patchof{C} = \patchof{L} \gathnext - \mergeof{C}{L}{M}{R} + \commitmergeof{C}{L}{M}{R} \end{gather} We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$. -This can also be used for dependency re-insertion, by setting -$L \in \pn$, $R \in \pry$, $M = \baseof{R}$. +This can also be used for dependency re-insertion, by setting $L \in +\pn$, $R \in \pry$, $M = \baseof{R}$, provided that the Conditions are +satisfied; in particular, provided that $L \ge \baseof{R}$. \subsection{Conditions} \[ \eqn{ Ingredients }{ @@ -46,20 +47,28 @@ $L \in \pn$, $R \in \pry$, $M = \baseof{R}$. \bigforall_{E \in \pendsof{X}{\py}} E \le Y \right] }\] +\[ \eqn{ Suitable Tips }{ + \bigforall_{\p \neq \patchof{L}, \; C \haspatch \p} + \bigexists_T + \pendsof{J}{\py} = \{ T \} + \land + \forall_{E \in \pendsof{K}{\py}} T \ge E + , \text{where} \{J,K\} = \{L,R\} +}\] \[ \eqn{ Foreign Merges }{ - \patchof{L} = \bot \implies \patchof{R} = \bot + \isforeign{L} \implies \isforeign{R} }\] \subsection{Non-Topbloke merges} -We require both $\patchof{L} = \bot$ and $\patchof{R} = \bot$ +We require both $\isforeign{L}$ and $\isforeign{R}$ (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 $L$, $\isforeign{M}$ 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 @@ -70,7 +79,7 @@ is therefore consistent with our model. \subsection{No Replay} -By definition of $\merge$, +By definition of \commitmergename, $D \isin C \implies D \isin L \lor D \isin R \lor D = C$. So, by Ingredients, Ingredients Prevent Replay applies. $\qed$ @@ -111,14 +120,23 @@ $\qed$ \subsection{Coherence and Patch Inclusion} -Need to determine $C \haspatch \p$ based on $L,M,R \haspatch \p$. -This involves considering $D \in \py$. +$$ +\begin{cases} + L \nothaspatch \p \land R \nothaspatch \p : & C \nothaspatch \p \\ + L \haspatch \p \land R \haspatch \p : & C \haspatch \p \\ + \text{otherwise} \land M \haspatch \p : & C \nothaspatch \p \\ + \text{otherwise} \land M \nothaspatch \p : & C \haspatch \p +\end{cases} +$$ +\proofstarts +~ Consider $D \in \py$. \subsubsection{For $L \nothaspatch \p, R \nothaspatch \p$:} $D \not\isin L \land D \not\isin R$. $C \not\in \py$ (otherwise $L \in \py$ ie $L \haspatch \p$ by Tip Own Contents for $L$). So $D \neq C$. -Applying $\merge$ gives $D \not\isin C$ i.e. $C \nothaspatch \p$. +Applying \commitmergename gives $D \not\isin C$ i.e. $C \nothaspatch \p$. +OK. \subsubsection{For $L \haspatch \p, R \haspatch \p$:} $D \isin L \equiv D \le L$ and $D \isin R \equiv D \le R$. @@ -131,17 +149,17 @@ For $D \neq C$: $D \le C \equiv D \le L \lor D \le R (Likewise $D \le C \equiv D \le X \lor D \le Y$.) Consider $D \neq C, D \isin X \land D \isin Y$: -By $\merge$, $D \isin C$. Also $D \le X$ +By \commitmergename, $D \isin C$. Also $D \le X$ so $D \le C$. OK for $C \zhaspatch \p$. Consider $D \neq C, D \not\isin X \land D \not\isin Y$: -By $\merge$, $D \not\isin C$. +By \commitmergename, $D \not\isin C$. And $D \not\le X \land D \not\le Y$ so $D \not\le C$. OK for $C \zhaspatch \p$. Remaining case, wlog, is $D \not\isin X \land D \isin Y$. $D \not\le X$ so $D \not\le M$ so $D \not\isin M$. -Thus by $\merge$, $D \isin C$. And $D \le Y$ so $D \le C$. +Thus by \commitmergename, $D \isin C$. And $D \le Y$ so $D \le C$. OK for $C \zhaspatch \p$. So, in all cases, $C \zhaspatch \p$. @@ -150,45 +168,41 @@ and this $F \le C$ so indeed $C \haspatch \p$. \subsubsection{For (wlog) $X \not\haspatch \p, Y \haspatch \p$:} -$M \haspatch \p \implies C \nothaspatch \p$. -$M \nothaspatch \p \implies C \haspatch \p$. - -\proofstarts - One of the Merge Ends conditions applies. Recall that we are considering $D \in \py$. $D \isin Y \equiv D \le Y$. $D \not\isin X$. We will show for each of various cases that if $M \haspatch \p$, $D \not\isin C$, -whereas if $M \nothaspatch \p$, $D \isin C \equiv \land D \le C$. +whereas if $M \nothaspatch \p$, $D \isin C \equiv D \le C$. And by $Y \haspatch \p$, $\exists_{F \in \py} F \le Y$ and this $F \le C$ so this suffices. Consider $D = C$: Thus $C \in \py, L \in \py$. -By Tip Own Contents, $\neg[ L \nothaspatch \p ]$ so $L \neq X$, +By Tip Own Contents, $L \haspatch \p$ so $L \neq X$, therefore we must have $L=Y$, $R=X$. -By Tip Merge $M = \baseof{L}$ so $M \in \pn$ so -by Base Acyclic $M \nothaspatch \p$. By $\merge$, $D \isin C$, +Conversely $R \not\in \py$ +so by Tip Merge $M = \baseof{L}$. Thus $M \in \pn$ so +by Base Acyclic $M \nothaspatch \p$. By \commitmergename, $D \isin C$, and $D \le C$. OK. Consider $D \neq C, M \nothaspatch \p, D \isin Y$: $D \le Y$ so $D \le C$. -$D \not\isin M$ so by $\merge$, $D \isin C$. OK. +$D \not\isin M$ so by \commitmergename, $D \isin C$. OK. Consider $D \neq C, M \nothaspatch \p, D \not\isin Y$: $D \not\le Y$. If $D \le X$ then $D \in \pancsof{X}{\py}$, so by Addition Merge Ends and Transitive Ancestors $D \le Y$ --- a contradiction, so $D \not\le X$. -Thus $D \not\le C$. By $\merge$, $D \not\isin C$. OK. +Thus $D \not\le C$. By \commitmergename, $D \not\isin C$. OK. Consider $D \neq C, M \haspatch \p, D \isin Y$: $D \le Y$ so $D \in \pancsof{Y}{\py}$ so by Removal Merge Ends and Transitive Ancestors $D \in \pancsof{M}{\py}$ so $D \le M$. -Thus $D \isin M$. By $\merge$, $D \not\isin C$. OK. +Thus $D \isin M$. By \commitmergename, $D \not\isin C$. OK. Consider $D \neq C, M \haspatch \p, D \not\isin Y$: -By $\merge$, $D \not\isin C$. OK. +By \commitmergename, $D \not\isin C$. OK. $\qed$ @@ -228,7 +242,7 @@ $C \haspatch \p$ so by definition of $\haspatch$, $D \isin C \equiv D $D \neq C$. By Tip Contents of $L$, $D \isin L \equiv D \isin \baseof{L}$, so by Tip Merge condition, -$D \isin L \equiv D \isin M$. So by $\merge$, $D \isin +$D \isin L \equiv D \isin M$. So by \commitmergename, $D \isin C \equiv D \isin R$. And $R = \baseof{C}$ by Unique Base of $C$. Thus $D \isin C \equiv D \isin \baseof{C}$. OK. @@ -246,16 +260,27 @@ Whereas if $\baseof{L} = \baseof{M}$, by definition of $\base$, $\patchof{M} = \patchof{L} = \py$, so by Tip Contents of $M$, $D \isin M \equiv D \isin \baseof{M} \equiv D \isin \baseof{L}$. -So $D \isin M \equiv D \isin L$ so by $\merge$, +So $D \isin M \equiv D \isin L$ so by \commitmergename, $D \isin C \equiv D \isin R$. But from Unique Base, $\baseof{C} = \baseof{R}$. Therefore $D \isin C \equiv D \isin \baseof{C}$. OK. $\qed$ +\subsection{Unique Tips} + +For $L \in \py$, trivially $\pendsof{C}{\py} = C$ so $T = C$ is +suitable. + +For $L \not\in \py$, $\pancsof{C}{\py} = \pancsof{L}{\py} \cup +\pancsof{R}{\py}$. So $T$ from Suitable Tips is a suitable $T$ for +Unique Tips. + +$\qed$ + \subsection{Foreign Inclusion} -Consider some $D$ s.t. $\patchof{D} = \bot$. +Consider some $D \in \foreign$. By Foreign Inclusion of $L, M, R$: $D \isin L \equiv D \le L$; $D \isin M \equiv D \le M$; @@ -268,17 +293,17 @@ $D \isin C$ and $D \le C$. OK. \subsubsection{For $D \neq C, D \isin M$:} Thus $D \le M$ so $D \le L$ and $D \le R$ so $D \isin L$ and $D \isin -R$. So by $\merge$, $D \isin C$. And $D \le C$. OK. +R$. So by \commitmergename, $D \isin C$. And $D \le C$. OK. \subsubsection{For $D \neq C, D \not\isin M, D \isin X$:} -By $\merge$, $D \isin C$. +By \commitmergename, $D \isin C$. And $D \isin X$ means $D \le X$ so $D \le C$. OK. \subsubsection{For $D \neq C, D \not\isin M, D \not\isin L, D \not\isin R$:} -By $\merge$, $D \not\isin C$. +By \commitmergename, $D \not\isin C$. And $D \not\le L, D \not\le R$ so $D \not\le C$. OK @@ -286,6 +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 $\isforeign{L}$, in which case +$\isforeign{C}$ and by Foreign Merges $\isforeign{R}$, so Totally Foreign Contents applies. $\qed$