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sav07_lecture_3_skeleton [2007/03/20 14:35] vkuncak |
sav07_lecture_3_skeleton [2007/03/20 14:42] vkuncak |
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| assume true = skip (does nothing) | assume true = skip (does nothing) | ||
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| CR(c1 ; c2) = exists x_1,y_1,error_1. CR(c1)[x:=x_1,y:=y_1,error:=error_1] & CR(c2)[x:=x_1,y:=y_1,error:=error_1] | CR(c1 ; c2) = exists x_1,y_1,error_1. CR(c1)[x:=x_1,y:=y_1,error:=error_1] & CR(c2)[x:=x_1,y:=y_1,error:=error_1] | ||
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| + | otherwise | ||
| + | |||
| + | CR(c)=R(c) (base case) | ||
| + | |||
| + | ==== Accumulation of equalities ==== | ||
| + | |||
| + | This approach generates many variables and many frame conditions. | ||
| + | |||
| + | Ignoring error for the moment: | ||
| + | |||
| + | R(x=3) = (x=3 & y=y_0) | ||
| + | R(y=x+2) = (y=x_0 + 2 & x=x_0) | ||
| + | |||
| + | CR(x=3;y=x+2) = x_1=3 & y_1 = y_0 & y = x_1 + 2 & x = x_1 | ||
| + | |||
| + | But if a variable is equal to another, it can be substituted using the substitution rules | ||
| + | |||
| + | (exists x_1. x_1 = t & F(x_1)) <-> F(t) | ||
| + | (forall x_1. x_1 = t -> F(x_1) <-> F(t) | ||