By J. C. Huang

This publication provides a special strategy 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 system allows us to divide and triumph over the complexity interested in realizing the computation played via a software by way of decomposing it right into a set of subprograms after which simplifying them to the furthest volume attainable. The ensuing simplified subprograms are ordinarily extra comprehensible than the unique software as an entire. the strategy can also be used to simplify a bit of resource code through following the path-oriented approach to decomposition, simplication, and recomposition. The research should be conducted in this type of approach that the derivation of the research consequence constitutes a correctness facts. the tactic might be utilized to any resource code (or element 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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Among all the subprograms we can create from a given program, we would be particularly interested in its trace subprograms. , Si contains no branches). 40 22:32 P1: KDO 9780521882866c05 CUFX211/Huang 978 0 521 88286 6 November 3, 2007 Pathwise Decomposition We are interested in trace subprograms because they can be readily obtained. As mentioned previously, the symbolic trace of an execution path is the trace subprogram associated with that path if we treat each true branch predicate on the path as a constraint.

11, wp({/ \x > 2; y := 1, / \x > 2; y := 2}, y = 1) ≡ x > 2 ∨ F ≡ x > 2. That is, the expanded set of programs still has the old capability to set y to 1 if x > 2. What will happen if we adopt Dijkstra’s definition and let the semantics of {/ \C1 ;P1 , / \C2 ;P2 , . . , / \Cn ;Pn } be identical to that of if C1 → P1 C2 → P2 . . Cn → Pn fi? One immediate consequence is that wp({/ \C1 ; P1 , / \C2 ; P2 }, R) ≡ wp(if C1 → P1 C2 → P2 fi, R) ≡ (C1 ∨ C2 ) ∧ (C1 ⊃ wp(P1 , R)) ∧ (C2 ⊃ wp(P2 , R)) 37 15:28 P1: KDO/KDQ P2: KDO 9780521882866c04 CUFX211/Huang 978 0 521 88286 6 November 4, 2007 Path-Oriented Program Analysis ≡ C1 ∧ ¬C2 ∧ wp(P1 , R) ∨ C2 ∧ ¬C1 ∧ wp(P2 , R) ∨ C1 ∧ C2 ∧ wp(P1 , R) ∧ wp(P2 , R), and thus wp(/ \x > 2; y := 1, / \x > 2; y := 2, y = 1) ≡ F.

6 is not compact. This might not be the making of the original author if there were no restrictions on the syntax of the “if” statements. As shown later in Chapter 7, this program can be rewritten into one that yields a compact set of trace subprograms if the restrictions on syntax are removed. Most programs contain loop constructs, and loop constructs generally expand into a large number of possible execution paths. Ostensibly, the sheer size of possible execution paths would render the present method completely useless.

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