Abstraction function ($\alpha :R_{\mathrm{valid}}\to Q$)

An abstraction function maps a valid concrete representation to its abstract value. Write $R_{\mathrm{valid}}=\{r:I(r)\}$ and $\alpha :R_{\mathrm{valid}}\to Q$. Different storage states can denote the same abstract value. Correct implementation requires both preservation of the representation invariant and agreement with the specified operation after applying the abstraction function; preserving a length bound alone would not prove first-in, first-out behavior.