### [wp/doc] Document Sequence tactic

parent 1e2952f1
 ... ... @@ -532,6 +532,54 @@ This is a variant of the \texttt{Lemma} tactic dedicated to \texttt{Havoc} predi \paragraph{Separated} Expand Separation Cases\\ This tactic decompose a \texttt{separated}$(a,n,b,m)$ predicate into its four base cases: $a$ and $b$ have different bases, $a+n \leq b$, $b+m \leq a$, and $a[0..n-1]$ and $b[0..m-1]$ overlaps. The regions are separated in the first three cases, and not separated in the overlapping case. This is kind of normal disjunctive form of the separation clause. \subsection{Lists Tactics} \paragraph{Sequence} Unroll repeat-sequence operator\\ In this section, let us use $A^n$ for the ACSL notation \lstinline{A *^ n}, the repeat list operation, and $A \oplus l$ for the list concatenation. This tactics is used to transform $A^n$ sequences. Threes behaviors can be selected: unroll left that rewrites the list $A^n$ into $A \oplus A^{n-1}$, unroll right that rewrites the list $A^n$ into $A^{n-1} \oplus A$ and unroll sum that rewrites the list $A ^{n_1 + ... + n_k}$ into $A^{n_1} \oplus ... \oplus A^{n_k}$. For unroll left and right, a negative value leads to an empty list. For unroll sum, one must prove that all $nI$ are positive. Rule for unroll left: $\TACTIC{\Delta\models\,G}{% \begin{array}[t]{lll} \Delta[A^n\leftarrow A \oplus A^{n-1}],& n > 0 & \models G[A^n\leftarrow A \oplus A^{n-1}]\\ \Delta[A^n\leftarrow []],& n \leq 0 & \models G[A^n\leftarrow []] \end{array} }$ Rule for unroll right: $\TACTIC{\Delta\models\,G}{% \begin{array}[t]{lll} \Delta[A^n\leftarrow A^{n-1} \oplus A],& n > 0 & \models G[A^n\leftarrow A^{n-1} \oplus A]\\ \Delta[A^n\leftarrow []],& n \leq 0 & \models G[A^n\leftarrow []] \end{array} }$ Rule for unroll sum: $\TACTIC{\Delta\models\,G}{% \begin{array}[t]{ll} \Delta & \models\bigwedge_{i=1}^{k} 0 \leq n_i\\ &\\ \Delta[A^{\sum_{i=1}^{k}n_i}\leftarrow \bigoplus_{i=1}^{k} A^{n_i}] & \models G[A^{\sum_{i=1}^{k}n_i}\leftarrow \bigoplus_{i=1}^{k} A^{n_i}] \end{array} }$ \subsection{Custom Tactics and Strategies} \label{wp-custom-tactics} ... ...
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