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By Prof. Sheila A. Greibach (eds.)

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By Prof. Sheila A. Greibach (eds.)

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Extra info for Theory of Program Structures: Schemes, Semantics, Verification

Sample text

If we placed k' . ,v n) I -< k £ n . ,val(Un,i)) i s k -< n . must have been some test and further we must have i = I*(T)(T) , k. (T)(val(vl,J) .... ,val(vn,J) ) = I(T)(l(val*(Vl, j))(a),... ,l(val*(Vn, j))(a)) = l(T)(l(tl)(a),... ,l(tn)(a--)) = l(T) (l(val*(u l,i) ) (a) .... ,l(val*(Un,i) ) (a)) = l(T) (val(Ul,i) ,... ,val(Un,i)) = 0 which is a contradiction, and hence l(T) since I is supposed to be a legitimate interpretation must be single valued. 3-7 Thus we ~ast have Q(s,T,0) ~ Q(s,T,I) = @ for each test T a legitlmaZe fr~e interpretation with the desired properties, and so I* is m We can rephrase the previous lemma to provide in effect a syntactic definition of what it romans for a path to be an.

We assume that computations always start at statement i and so we did not need a START statement in this model. We define interpretation in this model exactly as in the flow diagram model. However, the timing of computations is now off by ½~ step. computation sequence stage i and £nstruction s , val(u,i) s(i-l) s(i) For this model, in a is the address of the statement to be executed at is the value of variable u before stage We nov give an inductive definition of computation sequence interpretation I.

75 or John Jones or anything else; what matters is that there is some interpretation I under which its value is different from the value of scme other term (although under other interpretations all values might coincide). value If we know that under certain circumstances both f(x,g(y,z)) considering the actual value of f(x,g(y,z)) f and g and and P' halt with under any particular interpretation. If a certain sequence of outcomes of tests leads f(x,g(y,z)) P , then we know that they have identical outputs, without P' with" g(f(x,x),y) would lead to P and P' P to halt with output , then we know that some specification of halting with different outcomes.

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