FRET-FreeRTOS/FreeRTOS/Test/VeriFast/queue/README.md

FreeRTOS queue proofs

In the queue predicates and proofs we use the following variable names.

• Storage : The concrete queue storage of N*M bytes. The buffer predicate, defined in include/proof/queue.h allows us to treat the storage as a list contents of N items, each of which is M bytes.
• N : queue length (i.e., the maximum number of items the queue can store)
• M : size in bytes of each element
• W : logical index of the write pointer, necessarily between 0..(N-1) such that the write pointer pcWriteTo == Storage + W * M.
• R : logical index of the read pointer, necessarily between 0..(N-1) such that the read pointer pcReadFrom == Storage + R * M.
• K : number of items currently in the queue corresponding to uxMessagesWaiting

The queue predicate, defined in include/proof/queue.h, relates the concrete queue storage to an abstract list abs of K items. More precisely, the key queue invariant is:

abs == take(K, rotate_left((R+1)%N, contents)) &*&
W == (R + 1 + K) % N

where (R+1)%N is the front of the queue, W is the back of the queue, rotate_left allows for the wraparound of queue storage, and take gives the first K elements.