CIS 301: Lecture Notes on Induction

These notes are written as a supplement to [1, Sect. 16.1&16.3], but can be read independently. 1 Demystifying Induction Consider a loop of the form while B do C od, and assume that we know 1 ψ is established by the preamble of the loop (1) if with B true, ψ holds prior to C, then ψ also holds after C (2) Then we can infer that ψ is an invariant of the loop. (3) That is, each time control reaches B, ψ holds. (1) and (2) below being valid assertions. {ψ} (1) while B do {ψ ∧ B} WhileTrue C {ψ} (2) od