(* search_mu t searches for Mu terms in term t. In the case of nested Mu's,
it yields innermost one. If no Mu term is present, search_mu yields None
*)
(* extended for treatment of nu (TH) *)
fun search_mu ((Const("MuCalculus.mu",tp)) $ t2) =
(case (search_mu t2) of
Some t => Some t
| None => Some ((Const("MuCalculus.mu",tp)) $ t2))
| search_mu ((Const("MuCalculus.nu",tp)) $ t2) =
(case (search_mu t2) of
Some t => Some t
| None => Some ((Const("MuCalculus.nu",tp)) $ t2))
| search_mu (t1 $ t2) =
(case (search_mu t1) of
Some t => Some t
| None => search_mu t2)
| search_mu (Abs(_,_,t)) = search_mu t
| search_mu _ = None;
(* seraching a variable in a term. Used in move_mus to extract the
term-rep of var b in hthm *)
fun search_var s t =
case t of
t1 $ t2 => (case (search_var s t1) of
Some tt => Some tt |
None => search_var s t2) |
Abs(_,_,t) => search_var s t |
Var((s1,_),_) => if s = s1 then Some t else None |
_ => None;
(* function move_mus:
Mucke can't deal with nested Mu terms. move_mus i searches for
Mu terms in the subgoal i and replaces Mu terms in the conclusion
by constants and definitions in the premises recursively.
move_thm is the theorem the performs the replacement. To create NEW
names for the Mu terms, the indizes of move_thm are incremented by
max_idx of the subgoal.
*)
local
val move_thm = prove_goal MuckeSyn.thy "[| a = b ==> P a; a = b |] ==> P b"
(fn prems => [cut_facts_tac prems 1, dtac sym 1, hyp_subst_tac 1,
REPEAT (resolve_tac prems 1)]);
val sig_move_thm = #sign (rep_thm move_thm);
val bCterm = cterm_of sig_move_thm (the (search_var "b" (concl_of move_thm)));
val aCterm = cterm_of sig_move_thm (the (search_var "a" (hd(prems_of move_thm))));
in
fun move_mus i state =
let val sign = #sign (rep_thm state);
val (subgoal::_) = drop(i-1,prems_of state);
val concl = Logic.strip_imp_concl subgoal; (* recursive mu's in prems? *)
val redex = search_mu concl;
val idx = let val t = #maxidx (rep_thm state) in
if t < 0 then 1 else t+1 end;
in
case redex of
None => all_tac state |
Some redexterm =>
let val Credex = cterm_of sign redexterm;
val aiCterm =
cterm_of sig_move_thm (Logic.incr_indexes ([],idx) (term_of aCterm));
val inst_move_thm = cterm_instantiate
[(bCterm,Credex),(aCterm,aiCterm)] move_thm;
in
((rtac inst_move_thm i) THEN (dtac eq_reflection i)
THEN (move_mus i)) state
end
end; (* outer let *)
end; (* local *)
(* Type of call_mucke_tac has changed: an argument t of type thy was inserted (TH); *)
(* Normally t can be user-instantiated by the value thy of the Isabelle context *)
fun call_mucke_tac i state =
let val sign = #sign (rep_thm state);
val (subgoal::_) = drop(i-1,prems_of state);
val OraAss = invoke_oracle MuckeSyn.thy "Mucke" (sign,MuckeOracleExn (subgoal));
in
(cut_facts_tac [OraAss] i) state
end;
(* transforming fun-defs into lambda-defs *)
val [eq] = goal CPure.thy "(!! x. f x == g x) ==> f == g";
by (rtac (extensional eq) 1);
qed "ext_rl";
infix cc;
fun None cc xl = xl
| (Some x) cc xl = x::xl;
fun getargs ((x $ y) $ (Var ((z,_),_))) = getargs (x $ y) ^ " " ^z
| getargs (x $ (Var ((y,_),_))) = y;
fun getfun ((x $ y) $ z) = getfun (x $ y)
| getfun (x $ _) = x;
local
fun is_prefix [] s = true
| is_prefix (p::ps) [] = false
| is_prefix (p::ps) (x::xs) = (p=x) andalso (is_prefix ps xs);
fun delete_bold [] = []
| delete_bold (x::xs) = if (is_prefix ("\^["::"["::"0"::"m"::[]) (x::xs))
then (let val (_::_::_::s) = xs in delete_bold s end)
else (if (is_prefix ("\^["::"["::"1"::"m"::[]) (x::xs))
then (let val (_::_::_::s) = xs in delete_bold s end)
else (x::delete_bold xs));
fun delete_bold_string s = implode(delete_bold (explode s));
in
(* extension with removing bold font (TH) *)
fun mk_lam_def (_::_) _ _ = None
| mk_lam_def [] ((Const("==",_) $ (Const _)) $ RHS) t = Some t
| mk_lam_def [] ((Const("==",_) $ LHS) $ RHS) t =
let val tsig = #sign (rep_thm t);
val fnam = Sign.string_of_term tsig (getfun LHS);
val rhs = Sign.string_of_term tsig (freeze_thaw RHS)
val gl = delete_bold_string (fnam ^" == % " ^ (getargs LHS) ^" . " ^ rhs);
in
Some (prove_goal (theory_of_sign tsig) gl (fn prems =>
[(REPEAT (rtac ext_rl 1)), (rtac t 1) ]))
end
| mk_lam_def [] _ t= None;
fun mk_lam_defs ([]:thm list) = ([]: thm list)
| mk_lam_defs (t::l) =
(mk_lam_def (prems_of t) (concl_of t) t) cc (mk_lam_defs l);
end;
(* first simplification, then model checking *)
goalw (theory "Product_Type") [split_def] "(f::'a*'b=>'c) = (%(x, y). f (x, y))";
by (rtac ext 1);
by (stac (surjective_pairing RS sym) 1);
by (rtac refl 1);
qed "pair_eta_expand";
val pair_eta_expand_proc =
Simplifier.simproc (Theory.sign_of (the_context ())) "pair_eta_expand" ["f::'a*'b=>'c"]
(fn _ => fn _ => fn t => case t of Abs _ => Some (mk_meta_eq pair_eta_expand) | _ => None);
val Mucke_ss = simpset() addsimprocs [pair_eta_expand_proc] addsimps [Let_def];
(* the interface *)
fun mc_mucke_tac defs i state =
(case drop (i - 1, Thm.prems_of state) of
[] => PureGeneral.Seq.empty
| subgoal :: _ =>
EVERY [
REPEAT (etac thin_rl i),
cut_facts_tac (mk_lam_defs defs) i,
full_simp_tac (Mucke_ss delsimps [not_iff,split_part]) i,
move_mus i, call_mucke_tac i,atac i,
REPEAT (rtac refl i)] state);
(*check if user has mucke installed*)
fun mucke_enabled () = getenv "MUCKE_HOME" <> "";
fun if_mucke_enabled f x = if mucke_enabled () then f x else ();