A Note on Interactive Theorem Proving with Theorem Continuation Functions

A simple technique for using theorem continuation functions interactively with HOL's sub-goal package is presented. An interesting aspect of the technique is that it hinges on the existence of assignable variables in ML. Suppose we wish to prove a /\ b ==> b /\ a using HOL's subgoal package 1]: 1 #g "a /\ b ==> b /\ a" ;; "a /\ b ==> b /\ a" The natural proof is to assume the antecedent a /\ b to be true and then deduce the succedent b /\ a from the assumed antecedent, which is called an assumption. In HOL there are, broadly speaking, two methods by which assumptions are manipulated. The rst method is to add the assumption to the assumption list of the goal: 2 #expand(DISCH_TAC);; OK.. "b /\ a" "a /\ b" ] and then prove the the conclusion of the goal using the assumption list: 3 #expand(ASM_REWRITE_TAC ]);; OK.. goal proved. |-b /\ a |-a /\ b ==> b /\ a