%%% Assignment 10 %%% Out: Mon 3 Dec %%% Due: Mon 10 Dec % % This assignment is to be submitted on paper. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % 1. Structural Induction on Lists. % % Prove the following propositions using structural induction. % In each case, give an informal proof and then a proof term. % You may make use of lemmas already proved. % % A. !l: t-list .!k: t-list . l = k => k = l % % B. !k: t-list .!l: t-list . !m: t-list . % rev (rev k l) m = rev l (app k m) % % % 2. Generalizing the Induction Hypothesis. % % Using previously proved problems and lemmas, % give a formal proof of the following: % % !l: t-list . reverse(reverse l) = l . % % % 3. Dependent Types. % % [to be posted Wednesday 5 December] % % % %%%