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sav08:fol_with_update_expressions [2008/04/09 00:16] vkuncak |
sav08:fol_with_update_expressions [2008/04/09 00:23] vkuncak |
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| === Function Update === | === Function Update === | ||
| - | f (a:=b)(x) = ++|ite(x=a,b,f(x))++ | + | f (a:=b)(x) |
| - | f ( (a,b) :=c)(x,y) = ++|ite(x=a & y=b, c,f(x,y))++ | + | f ( (a,b) :=c)(x,y) |
| === Sets === | === Sets === | ||
| Line 33: | Line 33: | ||
| f(a:=b)(x) = ++|ite(x=a,b,f(x))++ | f(a:=b)(x) = ++|ite(x=a,b,f(x))++ | ||
| - | f((a,b):=c)(x,y) = ++|ite(x=a & y=b, c,f(x,y))++ | + | f ( (a,b):=c )(x,y) = ++|ite(x=a & y=b, c,f(x,y))++ |
| z=ite(p,x,y) $\leftrightarrow$ ++| (p & z=x) | (~p & z=y) ++ | z=ite(p,x,y) $\leftrightarrow$ ++| (p & z=x) | (~p & z=y) ++ | ||
| Line 41: | Line 41: | ||
| S1 = S0 Un {a} $\leftrightarrow$ ++| ALL x. S1(x) <-> S0(x) | x=a ++ | S1 = S0 Un {a} $\leftrightarrow$ ++| ALL x. S1(x) <-> S0(x) | x=a ++ | ||
| - | ===== Substituting Function Symbols ===== | + | === Substituting Function Symbols === |
| + | Consider symbolic execution of assignment to local variable | ||
| + | x = e | ||
| + | Evaluate e in current symbolic state, then assign symbolic value of x to result. | ||
| + | |||
| + | Consider | ||
| + | x.f = e; | ||
| + | i.e. | ||
| + | f = f(x:=e) | ||
| + | We need to replace f with f(x:=e). | ||
| + | * do we always get syntactically valid formula in FOL extension above? | ||