(* Title: HOLCF/Tools/cont_proc.ML Author: Brian Huffman *) signature CONT_PROC = sig val is_lcf_term: term -> bool val cont_thms: term -> thm list val all_cont_thms: term -> thm list val cont_tac: int -> tactic val cont_proc: theory -> simproc val setup: theory -> theory end; structure ContProc: CONT_PROC = struct (** theory context references **) val cont_K = @{thm cont_const}; val cont_I = @{thm cont_id}; val cont_A = @{thm cont2cont_Rep_CFun}; val cont_L = @{thm cont2cont_LAM}; val cont_R = @{thm cont_Rep_CFun2}; (* checks whether a term contains no dangling bound variables *) fun is_closed_term t = not (Term.loose_bvar (t, 0)); (* checks whether a term is written entirely in the LCF sublanguage *) fun is_lcf_term (Const (@{const_name Rep_CFun}, _) $ t $ u) = is_lcf_term t andalso is_lcf_term u | is_lcf_term (Const (@{const_name Abs_CFun}, _) $ Abs (_, _, t)) = is_lcf_term t | is_lcf_term (Const (@{const_name Abs_CFun}, _) $ t) = is_lcf_term (Term.incr_boundvars 1 t $ Bound 0) | is_lcf_term (Bound _) = true | is_lcf_term t = is_closed_term t; (* efficiently generates a cont thm for every LAM abstraction in a term, using forward proof and reusing common subgoals *) local fun var 0 = [SOME cont_I] | var n = NONE :: var (n-1); fun k NONE = cont_K | k (SOME x) = x; fun ap NONE NONE = NONE | ap x y = SOME (k y RS (k x RS cont_A)); fun zip [] [] = [] | zip [] (y::ys) = (ap NONE y ) :: zip [] ys | zip (x::xs) [] = (ap x NONE) :: zip xs [] | zip (x::xs) (y::ys) = (ap x y ) :: zip xs ys fun lam [] = ([], cont_K) | lam (x::ys) = let (* should use "close_derivation" for thms that are used multiple times *) (* it seems to allow for sharing in explicit proof objects *) val x' = Thm.close_derivation (k x); val Lx = x' RS cont_L; in (map (fn y => SOME (k y RS Lx)) ys, x') end; (* first list: cont thm for each dangling bound variable *) (* second list: cont thm for each LAM in t *) (* if b = false, only return cont thm for outermost LAMs *) fun cont_thms1 b (Const (@{const_name Rep_CFun}, _) $ f $ t) = let val (cs1,ls1) = cont_thms1 b f; val (cs2,ls2) = cont_thms1 b t; in (zip cs1 cs2, if b then ls1 @ ls2 else []) end | cont_thms1 b (Const (@{const_name Abs_CFun}, _) $ Abs (_, _, t)) = let val (cs, ls) = cont_thms1 b t; val (cs', l) = lam cs; in (cs', l::ls) end | cont_thms1 b (Const (@{const_name Abs_CFun}, _) $ t) = let val t' = Term.incr_boundvars 1 t $ Bound 0; val (cs, ls) = cont_thms1 b t'; val (cs', l) = lam cs; in (cs', l::ls) end | cont_thms1 _ (Bound n) = (var n, []) | cont_thms1 _ _ = ([], []); in (* precondition: is_lcf_term t = true *) fun cont_thms t = snd (cont_thms1 false t); fun all_cont_thms t = snd (cont_thms1 true t); end; (* Given the term "cont f", the procedure tries to construct the theorem "cont f == True". If this theorem cannot be completely solved by the introduction rules, then the procedure returns a conditional rewrite rule with the unsolved subgoals as premises. *) val cont_tac = let val rules = [cont_K, cont_I, cont_R, cont_A, cont_L]; fun new_cont_tac f' i = case all_cont_thms f' of [] => no_tac | (c::cs) => rtac c i; fun cont_tac_of_term (Const (@{const_name cont}, _) $ f) = let val f' = Const (@{const_name Abs_CFun}, dummyT) $ f; in if is_lcf_term f' then new_cont_tac f' else REPEAT_ALL_NEW (resolve_tac rules) end | cont_tac_of_term _ = K no_tac; in SUBGOAL (fn (t, i) => cont_tac_of_term (HOLogic.dest_Trueprop t) i) end; local fun solve_cont thy _ t = let val tr = instantiate' [] [SOME (cterm_of thy t)] Eq_TrueI; in Option.map fst (Seq.pull (cont_tac 1 tr)) end in fun cont_proc thy = Simplifier.simproc thy "cont_proc" ["cont f"] solve_cont; end; fun setup thy = Simplifier.map_simpset (fn ss => ss addsimprocs [cont_proc thy]) thy; end;