# Program equivalence with Structural induction

I recently attended my first lecture on structural induction and the professor stated that structural induction can be used to to prove that two programming languages are equivalent.

I am new to structural induction, however from what i have read so far, structural induction is used to prove properties $P$ like arithmetic or boolean expression of a particular language are deterministic. But these deterministic properties allows to define determinacy of a particular language .

How is structural induction used to prove that two languages are equivalent?

• What exactly is your notion of equivalence? – adrianN Jul 21 '16 at 7:39
• @adrianN, If the two languages have commands (for sake of simplicity lets consider boolean commands only). If Commands $C_1$ of language 1 and $C_2$ of language 2 both execute a boolean expression (if else), and if i have to show that the commands are equivalent – anil keshav Jul 21 '16 at 9:22