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By J. C. Huang

This ebook offers a different technique for decomposing a working laptop or computer application alongside its execution paths, for simplifying the subprograms so produced, and for recomposing a application from its subprograms. this technique allows us to divide and triumph over the complexity fascinated by knowing the computation played by way of a application by means of decomposing it right into a set of subprograms after which simplifying them to the furthest quantity attainable. The ensuing simplified subprograms are as a rule extra comprehensible than the unique application as an entire. the tactic can also be used to simplify a bit of resource code through following the path-oriented approach to decomposition, simplication, and recomposition. The research will be conducted in one of these manner that the derivation of the research outcome constitutes a correctness facts. the tactic might be utilized to any resource code (or component thereof) that prescribes the computation to be played by way of task statements, conditional statements, and loop constructs, whatever the language or paradigm used.

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Many readers, however, may find it difficult to see its correctness because its logical structure is relatively complex. 4 to decompose the program pathwise and simplify every trace subprogram to the extent possible. 6. 4 we see that 1. 2. 3. 4. 5. Cn implies P4 and Sn computes f4 for all n = 1, 2, . . , 7; C8 implies P3 and S8 computes f3 ; Cn implies P2 and Sn computes f2 for all n = 9, 10, and 11; C12 implies P1 and S12 computes f1 ; C1 ∨ C2 ∨ C3 ∨ C4 ∨ C5 ∨ C6 ∨ C7 ∨ C8 ∨ C9 ∨ C10 ∨ C11 ∨ C12 ≡ T.

For any S, wp(S, F) ≡ F, 2. for any programming construct S and any predicates Q and R, if Q ⊃ R then wp(S, Q) ⊃ wp(S, R), 3. for any programming construct S and any predicates Q and R, (wp(S, Q) ∧ wp(S, R)) ≡ wp(S, Q ∧ R), 22 15:46 P1: KDO/KDQ P2: KDO 9780521882866c03 CUFX211/Huang 978 0 521 88286 6 November 4, 2007 Subprogram Simplification 4. for any deterministic programming construct S and any predicates Q and R, (wp(S, Q) ∨ wp(S, R)) ≡ wp(S, Q ∨ R). 2 /\¬B; if B then S1 else S2 ⇔ /\¬B; S2 .

2 in Appendix A, or (2) recomposing the loop constructs in the trace subprogram as described in Chapter 7, and then analyzing the recomposed program as explained later. The second approach is preferred because the loop construct recomposed from the simplified trace subprogram is in general simpler than the original. To see how to construct the trace subprogram associated with an execution path in a program, it is useful to introduce a graphic programrepresentation scheme. First, it is explained how the path structures in a directed graph can be described by use of a regular expression.

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