Normal form for loop-free programs
(if (x < 0) x=x+1 else x=x); (if (y < 0) y=y+x else y=y);
Without loops, after expressing conditionals using  we obtain
c ::= x=T | assume(F) | c  c | c ; c
Each is of form for some , where each is assignment or assume. Each corresponds to one of the finitely paths from beginning to end of the acyclic control-flow graph for loop-free program.
Length of normal form with sequences of if-then-else.
We want to show:
Verifying Each Path Separately
By normal form this is
which is equivalent to
Note: the rule also applies to infinite union of paths (e.g. generated by loops).
Three Approaches to Generate Verification Conditions
Three equivalent formulations of Hoare triple give us three approaches:
- compute meaning of as a formula, then check Hoare triple (compositional approach for verification-condition generation)
- compute as a formula, then check entailment (forward symbolic execution)
- compute as a formula, then check (backward symbolic execution)