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foreign notation: introduce \isforeign
[topbloke-formulae.git]
/
invariants.tex
diff --git
a/invariants.tex
b/invariants.tex
index bc3813e6b83593e5d5ad0ad9c2b59c9a0f53d000..6cebb053d65db879fe6ad327ab58f434bef93d74 100644
(file)
--- a/
invariants.tex
+++ b/
invariants.tex
@@
-1,32
+1,32
@@
\section{Invariants}
We maintain these each time we construct a new commit. \\
\section{Invariants}
We maintain these each time we construct a new commit. \\
-\[ \eqn{No Replay
:
}{
+\[ \eqn{No Replay}{
C \has D \implies C \ge D
}\]
C \has D \implies C \ge D
}\]
-\[\eqn{Unique Base
:
}{
+\[\eqn{Unique Base}{
\bigforall_{C \in \py} \pendsof{C}{\pn} = \{ B \}
}\]
\bigforall_{C \in \py} \pendsof{C}{\pn} = \{ B \}
}\]
-\[\eqn{Tip Contents
:
}{
+\[\eqn{Tip Contents}{
\bigforall_{C \in \py} D \isin C \equiv
{ D \isin \baseof{C} \lor \atop
(D \in \py \land D \le C) }
}\]
\bigforall_{C \in \py} D \isin C \equiv
{ D \isin \baseof{C} \lor \atop
(D \in \py \land D \le C) }
}\]
-\[\eqn{Base Acyclic
:
}{
+\[\eqn{Base Acyclic}{
\bigforall_{C \in \pn} D \isin C \implies D \notin \py
}\]
\bigforall_{C \in \pn} D \isin C \implies D \notin \py
}\]
-\[\eqn{Coherence
:
}{
+\[\eqn{Coherence}{
\bigforall_{C,\p} C \haspatch \p \lor C \nothaspatch \p
}\]
\bigforall_{C,\p} C \haspatch \p \lor C \nothaspatch \p
}\]
-\[\eqn{Unique Tips
:
}{
- \bigforall_{C,\p} C \haspatch \p \implies \pendsof{C}{\p} = \{ T \}
+\[\eqn{Unique Tips}{
+ \bigforall_{C,\p} C \haspatch \p \implies \pendsof{C}{\p
y
} = \{ T \}
}\]
}\]
-\[\eqn{Foreign Inclusion
:
}{
- \bigforall_{D \text{ s.t. } \
patchof{D} = \bot
} D \isin C \equiv D \leq C
+\[\eqn{Foreign Inclusion}{
+ \bigforall_{D \text{ s.t. } \
isforeign{D}
} D \isin C \equiv D \leq C
}\]
}\]
-\[\eqn{Foreign Contents
:
}{
- \bigforall_{C \text{ s.t. } \
patchof{C} = \bot
}
- D \le C \implies \
patchof{D} = \bot
+\[\eqn{Foreign Contents}{
+ \bigforall_{C \text{ s.t. } \
isforeign{C}
}
+ D \le C \implies \
isforeign{D}
}\]
We also assign each new commit $C$ to zero or one of the sets $\p$, as
}\]
We also assign each new commit $C$ to zero or one of the sets $\p$, as