Notation
Notation used
If X is an equivalence strategy, a and b are values, and A and B are sets of values, then:
Definition |
Description/Note |
|
a ∼X b |
a and b are equivalent under strategy X |
We also call them X-equivalent. |
a ∈X B |
∃b∈B: a∼Xb |
Value a is present in B (under X) |
a ∉X B |
¬(a∈XB) ⇔ ¬∃b∈B: a∼Xb |
Value a is not present in B (under X) |
A ∩X B |
{ a∈A | a ∈X B } |
1. We could try to define A∩XB also as { a | a∈XA ∧ a∈XB } but this is not quite correct. Such definition would result in infinite set of values, because there are many values that are X-equivalent with any given value. So the set of candidate values must be somehow bound.
2. This also means that ∩X operation is not commutative! In general, A ∩X B can be different from B ∩X A.
|
A -X B |
{ a∈A | a ∉X B } |
Set difference under X. |
When applying delete deltas, a special relation and set operation have to be defined:
Notation |
Definition |
Description/Note |
a ∼del/X b |
aid = bid ≠ null ∨ a ∼X b |
Value a matches deletion pattern b (under X). |
A -del/X B |
A - { a∈A | ∃b∈B such that a ∼del b } |
Result of application of deletion patterns in B to set A (under X). |
The aid denotes ID of prism container value a (or null if a is not a prism container value).
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