Notation used

Last modified 12 Mar 2021 10:22 +01:00

If X is an equivalence strategy, a and b are values, and A and B are sets of values, then:

Notation

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 }

Intersection of A and B under X. [1][2]


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).