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Table 6 Axioms for abstraction operator

From: RETRACTED ARTICLE: An algebra of reversible computation

No.

Axiom

RTI1

\(\upsilon \notin I \quad \tau _I(\upsilon )=\upsilon \)

RTI2

\(\upsilon \in I \quad \tau _I(\upsilon )=\tau \)

RTI3

\(\upsilon [m]\notin I \quad \tau _I(\upsilon [m])=\upsilon [m]\)

RTI4

\(\upsilon [m]\in I \quad \tau _I(\upsilon [m])=\tau \)

RTI5

\(\tau _I(\delta )=\delta \)

RTI6

\(\tau _I(x+y)=\tau _I(x)+\tau _I(y)\)

RTI7

\(\tau _I(x\cdot y)=\tau _I(x)\cdot \tau _I(y)\)