GENERAL

 C >= D			C is descendant of D, partial order
 C \haspatch D		C contains changes from D, partial order
 Patch P has two sets P+, P-
 Ancestors A(C,P) = { Ca \elem C | Ca \elem P }
 Ends E(C,P) = maximal elements of A(C,P)
 Patch inclusion
   C \haspatch P    <=> [ \forall D \elem P+: D \isin C <=> D <= C ]
   C \nothaspatch P <=> [ \forall D \elem P+: D \notisin C ]

COMMIT ANNOTATIONS

 Commit C is annotated with:

 P(C)
   Either P s.t. C \elem P
   or \bottom meaning \notexists_{P} C \elem P.

 For every Px, E(C,Px+)
   Implicitly for C \elem Pc+, E(C,Pc+) = { C } 
   and this is not annotated explicitly.
   Also implicitly for P(C) = \bottom, \forall_{Px} E(C,Px+) = { }
   and this is also not annotated explicitly.

SIMPLE COMMIT

 make C >1 { A } 
 from A

 with contents
  D \isin C <=> D \isin A v D = C

 results
  P(C) = P(A)
  A \haspatch P <=> C \haspatch P
  For A \notelem Px+: E(C,Px+) = E(A,Px+)
      A \elem Px+: E(C,Px+) = { C } -- not annotated

ANTICOMMIT

 make C >1 { L }
 from L, R+, R- 

 with contents
  D \isin C <=> D \notelement Pr+ ^ D \isin L

 where
  P(R+) = Pr+, P(R-) = Pr-
  E(L,Pr+) = { R+ }    -- nontrivial, may need R+' = merge of E(L,Pr+)
  B(R+) = R-
  L \haspatch Pr

 results
  P(C) = P(L) = Pl-
  If C \elem P+, B(C) = B(L); otherwise B(C) n/a
  For P = Pr:  C \nothaspatch Pr
               E(C,Pr+) = E(L,Pr+) = { R+ }
      P != Pr: C \haspatch P <=> L \haspatch P
               E(C,P+) = E(L,P+)

MERGE

 make C >1 { L, R }
 from L, R, M

 with contents
  D \isin C <=> [ (D \isin    L ^ D \isin    R) v D =  C : T            ]
                [  D \notisin L ^ D \notisin R  ^ D != C : F            ]
                [  otherwise                             : D \notisin M ]

 where
  M < L, M < R
  If L \elem P+:
      R \elem P+ ^ B(R) = B(L)            -- only merge tips with same base
    v R \elem P- ^ R >= B(L) ^ M = B(L)   -- base when merging into tip
  If L \elem P-:
      R \nothaspatch P
  If L \haspatch P <=/=> R \haspatch P:
      \forall Ce \elem E(R,P+): Ce <= L   -- may need to merge E(R,P+) into L

 results
  P(C) = P(L)
  B(C) = 
    For C \notelem P+:             n/a
        C \elem P+, R \elem P+:    B(L) = B(R)
        C \elem P+, R \notelem P+: R >= B(L)

  C \haspatch P =
    For L \nothaspatch P, R \nothaspatch P: F
        L \haspatch P,    R \haspatch P:    T
        otherwise:                          M \nothaspatch P
  E(C,P+) = maximal elements of E(L,P+) \union E(R,P+)
          = { Cl | \notexist Cr \elem E(R,P+): Cr >= Cl } \union
            { Cr | \notexist Cl \elem E(L,P+): Cl >= Cr }

 -- to reintroduce a dep, set P(C)=P(L)=Pl-, P(R)=Pr+, M=B(R)
    where L \notelem Pr obv.


CREATE BASE

 make B >1 { L }
 from L, P

 where
  P(L) = Pl+ v P(L) = \bottom
  P(L) != P(B)
  E(B,P+) = { }

 with contents
  D \isin B <=> D \isin L v D = B

 results
  P(B) = Pb-
  B(C) n/a
  E(B,Px+) = E(L,Px+)
  B \haspatch P <=> L \haspatch P


CREATE TIP

 make C >1 { B}
 from B

 where
  B \elem Pb-
  E(B,P+) = { }

 with contents
  D \isin C <=> D \isin B v D = C

 results
  P(C) = Pb+
  B(C) = B
  C \haspatch P =
    For P != Pb: B \haspatch P
        P = Pb:  T