(* Title: HOLCF/cont_proc.ML
ID: $Id$
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 *)
val is_closed_term =
let
fun bound_less i (t $ u) =
bound_less i t andalso bound_less i u
| bound_less i (Abs (_, _, t)) = bound_less (i+1) t
| bound_less i (Bound n) = n < i
| bound_less i _ = true; (* Const, Free, and Var are OK *)
in bound_less 0 end;
(* checks whether a term is written entirely in the LCF sublanguage *)
fun is_lcf_term (Const ("Cfun.Rep_CFun", _) $ t $ u) =
is_lcf_term t andalso is_lcf_term u
| is_lcf_term (Const ("Cfun.Abs_CFun", _) $ Abs (_, _, t)) = is_lcf_term t
| is_lcf_term (Const ("Cfun.Abs_CFun", _) $ _) = false
| 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 "standard" for thms that are used multiple times *)
(* it seems to allow for sharing in explicit proof objects *)
val x' = standard (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 ("Cfun.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 ("Cfun.Abs_CFun", _) $ Abs (_, _, t)) =
let
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.
*)
local
val rules = [cont_K, cont_I, cont_R, cont_A, cont_L];
val prev_cont_thms : thm list ref = ref [];
fun old_cont_tac i thm =
case !prev_cont_thms of
[] => no_tac thm
| (c::cs) => (prev_cont_thms := cs; rtac c i thm);
fun new_cont_tac f' i thm =
case all_cont_thms f' of
[] => no_tac thm
| (c::cs) => (prev_cont_thms := cs; rtac c i thm);
fun cont_tac_of_term (Const ("Cont.cont", _) $ f) =
let
val f' = Const ("Cfun.Abs_CFun", dummyT) $ f;
in
if is_lcf_term f'
then old_cont_tac ORELSE' new_cont_tac f'
else REPEAT_ALL_NEW (resolve_tac rules)
end
| cont_tac_of_term _ = K no_tac;
in
val cont_tac =
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;
val setup =
(fn thy =>
(Simplifier.change_simpset_of thy
(fn ss => ss addsimprocs [cont_proc thy]); thy));
end;