X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=merge.tex;h=ba7f0f84962b25b5da791f7508388de2c7e87124;hp=d348670ef83555ea6eef6d96aee48d2e25782d6b;hb=HEAD;hpb=c773a9f7d593c5d6ce9dc772914562797de6024e diff --git a/merge.tex b/merge.tex index d348670..ba7f0f8 100644 --- a/merge.tex +++ b/merge.tex @@ -1,4 +1,5 @@ \section{Merge} +\label{commit-merge} Merge commits $L$ and $R$ using merge base $M$: \gathbegin @@ -6,12 +7,13 @@ 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} \[ \eqn{ Ingredients }{ @@ -26,6 +28,16 @@ $L \in \pn$, $R \in \pry$, $M = \baseof{R}$. \text{otherwise} : & \false \end{cases} }\] +\[ \eqn{ Base Merge }{ + L \in \pn \implies + \big[ + R \in \pn + \lor + R \in \foreign + \lor + ( R \in \pqy \land \pq \neq \p ) + \big] +}\] \[ \eqn{ Merge Acyclic }{ L \in \pn \implies @@ -46,24 +58,31 @@ $L \in \pn$, $R \in \pry$, $M = \baseof{R}$. \bigforall_{E \in \pendsof{X}{\py}} E \le Y \right] }\] -\[ \eqn{ Foreign Merges }{ - \patchof{L} = \bot \implies \patchof{R} = \bot +\[ \eqn{ Suitable Tips }{ + \bigforall_{\p \patchisin C, \; \py \neq \patchof{L}} + \bigexists_T + \pendsof{J}{\py} = \{ T \} + \land + \forall_{E \in \pendsof{K}{\py}} T \ge E + , \text{where} \{J,K\} = \{L,R\} +}\] +\[ \eqn{ Foreign Merge }{ + \isforeign{L} \implies \isforeign{R} }\] \subsection{Non-Topbloke merges} -We require both $\patchof{L} = \bot$ and $\patchof{R} = \bot$ -(Foreign Merges, above). +We require both $\isforeign{L}$ and $\isforeign{R}$ +(Foreign Merge, 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. -So by Foreign Contents for any $A \in \{L,M,R\}$, +By Foreign Ancestry of $L$, $\isforeign{M}$ as well. +So by Foreign Ancestry for any $A \in \{L,M,R\}$, $\forall_{\p, D \in \py} D \not\le A$ -so by No Replay for $A$, $D \not\isin A$. -Thus $\pendsof{A}{\py} = \{ \}$ and the RHS of both Merge Ends +so $\pendsof{A}{\py} = \{ \}$ and the RHS of both Merge Ends conditions are satisifed. So a plain git merge of non-Topbloke branches meets the conditions and @@ -71,7 +90,7 @@ 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. $\qed$ @@ -112,79 +131,97 @@ $\qed$ \subsection{Coherence and Patch Inclusion} -Need to determine $C \haspatch \p$ based on $L,M,R \haspatch \p$. -This involves considering $D \in \py$. +$C$ satisfies +\gathbegin + C \haspatch \p \lor C \nothaspatch \p +\gathnext +C \haspatch \p \equiv + \stmtmergeof{L \haspatch \p}{M \haspatch \p}{R \haspatch \p} +\end{gather} +which (given Coherence of $L$,$M$,$R$) is equivalent to +$$ +\begin{cases} + L \nothaspatch \p \land R \nothaspatch \p : & C \nothaspatch \p \\ + L \haspatch \p \land R \haspatch \p : & C \haspatch \p \\ + \text{otherwise} \land M \haspatch \p : & C \nothaspatch \p \\ + \text{otherwise} \land M \nothaspatch \p : & C \haspatch \p +\end{cases} +$$ +\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 $\neg[ L \nothaspatch \p ]$ by Tip Self Inpatch for $L$). +\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 $D \isin R \equiv D \le R$. (Likewise $D \isin X \equiv D \le X$ and $D \isin Y \equiv D \le Y$.) -Consider $D = C$: $D \isin C$, $D \le C$, OK for $C \haspatch \p$. +Consider $D = C$: $D \isin C$, $D \le C$, OK for $C \zhaspatch \p$. For $D \neq C$: $D \le C \equiv D \le L \lor D \le R \equiv D \isin L \lor D \isin R$. (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 $D \le X$ -so $D \le C$. OK for $C \haspatch \p$. +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 $C \haspatch \p$. +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 $D \le C$. -OK for $C \haspatch \p$. +Thus by \commitmergename, $D \isin C$. And $D \le Y$ so $D \le C$. +OK for $C \zhaspatch \p$. -So indeed $L \haspatch \p \land R \haspatch \p \implies C \haspatch \p$. +So, in all cases, $C \zhaspatch \p$. +And by $L \haspatch \p$, $\exists_{F \in \py} F \le L$ +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 $D \isin C \equiv M \nothaspatch \p \land D \le C$ -(which suffices by definition of $\haspatch$ and $\nothaspatch$). +various cases that +if $M \haspatch \p$, $D \not\isin C$, +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 Self Inpatch, $\neg[ L \nothaspatch \p ]$ 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 $\merge$, $D \isin C$, -and $D \le C$, consistent with $C \haspatch \p$. OK. +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. $\qed$ @@ -224,7 +261,7 @@ $C \haspatch \p$ 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. @@ -242,16 +279,27 @@ 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 $L, M, R$: $D \isin L \equiv D \le L$; $D \isin M \equiv D \le M$; @@ -264,24 +312,46 @@ $D \isin C$ 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 $\qed$ -\subsection{Foreign Contents} +\subsection{Foreign Ancestry} + +Only relevant if $\isforeign{L}$, in which case +$\isforeign{C}$ and by Foreign Merge $\isforeign{R}$, +so Totally Foreign Ancestry applies. $\qed$ + +\subsection{Bases' Children} + +If $L \in \py, R \in \py$: not applicable for either $D=L$ or $D=R$. + +If $L \in \py, R \in \pn$: not applicable for $L$, OK for $R$. + +Other possibilities for $L \in \py$ are excluded by Tip Merge. -Only relevant if $\patchof{L} = \bot$, in which case -$\patchof{C} = \bot$ and by Foreign Merges $\patchof{R} = \bot$, -so Totally Foreign Contents applies. $\qed$ +If $L \in \pn, R \in \pn$: satisfied for both $L$ and $R$. + +If $L \in \pn, R \in \foreign$: satisfied for $L$, not applicable for +$R$. + +If $L \in \pn, R \in \pqy$: satisfied for $L$, not applicable for +$R$. + +Other possibilities for $L \in \pn$ are excluded by Base Merge. + +If $L \in \foreign$: not applicable for $L$; nor for $R$, by Foreign Merge. + +$\qed$