--- a/src/HOLCF/Tools/adm_tac.ML Mon Mar 22 15:42:07 2010 -0700
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,160 +0,0 @@
-(* Title: HOLCF/Tools/adm_tac.ML
- Author: Stefan Berghofer, TU Muenchen
-
-Admissibility tactic.
-
-Checks whether adm_subst theorem is applicable to the current proof
-state:
-
- cont t ==> adm P ==> adm (%x. P (t x))
-
-"t" is instantiated with a term of chain-finite type, so that
-adm_chfin can be applied:
-
- adm (P::'a::{chfin,pcpo} => bool)
-*)
-
-signature ADM =
-sig
- val adm_tac: Proof.context -> (int -> tactic) -> int -> tactic
-end;
-
-structure Adm : ADM =
-struct
-
-
-(*** find_subterms t 0 []
- returns lists of terms with the following properties:
- 1. all terms in the list are disjoint subterms of t
- 2. all terms contain the variable which is bound at level 0
- 3. all occurences of the variable which is bound at level 0
- are "covered" by a term in the list
- a list of integers is associated with every term which describes
- the "path" leading to the subterm (required for instantiation of
- the adm_subst theorem (see functions mk_term, inst_adm_subst_thm))
-***)
-
-fun find_subterms (Bound i) lev path =
- if i = lev then [[(Bound 0, path)]]
- else []
- | find_subterms (t as (Abs (_, _, t2))) lev path =
- if filter (fn x => x <= lev) (add_loose_bnos (t, 0, [])) = [lev]
- then
- [(incr_bv (~lev, 0, t), path)] ::
- (find_subterms t2 (lev+1) (0::path))
- else find_subterms t2 (lev+1) (0::path)
- | find_subterms (t as (t1 $ t2)) lev path =
- let val ts1 = find_subterms t1 lev (0::path);
- val ts2 = find_subterms t2 lev (1::path);
- fun combine [] y = []
- | combine (x::xs) ys = map (fn z => x @ z) ys @ combine xs ys
- in
- (if filter (fn x => x <= lev) (add_loose_bnos (t, 0, [])) = [lev]
- then [[(incr_bv (~lev, 0, t), path)]]
- else []) @
- (if ts1 = [] then ts2
- else if ts2 = [] then ts1
- else combine ts1 ts2)
- end
- | find_subterms _ _ _ = [];
-
-
-(*** make term for instantiation of predicate "P" in adm_subst theorem ***)
-
-fun make_term t path paths lev =
- if member (op =) paths path then Bound lev
- else case t of
- (Abs (s, T, t1)) => Abs (s, T, make_term t1 (0::path) paths (lev+1))
- | (t1 $ t2) => (make_term t1 (0::path) paths lev) $
- (make_term t2 (1::path) paths lev)
- | t1 => t1;
-
-
-(*** check whether all terms in list are equal ***)
-
-fun eq_terms [] = true
- | eq_terms (ts as (t, _) :: _) = forall (fn (t2, _) => t2 aconv t) ts;
-
-
-(*** check whether type of terms in list is chain finite ***)
-
-fun is_chfin thy T params ((t, _)::_) =
- let val parTs = map snd (rev params)
- in Sign.of_sort thy (fastype_of1 (T::parTs, t), @{sort "{chfin,pcpo}"}) end;
-
-
-(*** try to prove that terms in list are continuous
- if successful, add continuity theorem to list l ***)
-
-fun prove_cont ctxt tac s T prems params (ts as ((t, _)::_)) l = (* FIXME proper context *)
- let val parTs = map snd (rev params);
- val contT = (T --> (fastype_of1 (T::parTs, t))) --> HOLogic.boolT;
- fun mk_all [] t = t
- | mk_all ((a,T)::Ts) t = Term.all T $ (Abs (a, T, mk_all Ts t));
- val t = HOLogic.mk_Trueprop (Const (@{const_name cont}, contT) $ Abs (s, T, t));
- val t' = mk_all params (Logic.list_implies (prems, t));
- val thm = Goal.prove ctxt [] [] t' (K (tac 1));
- in (ts, thm)::l end
- handle ERROR _ => l;
-
-
-(*** instantiation of adm_subst theorem (a bit tricky) ***)
-
-fun inst_adm_subst_thm state i params s T subt t paths =
- let
- val thy = Thm.theory_of_thm state;
- val j = Thm.maxidx_of state + 1;
- val parTs = map snd (rev params);
- val rule = Thm.lift_rule (Thm.cprem_of state i) @{thm adm_subst};
- val types = the o fst (Drule.types_sorts rule);
- val tT = types ("t", j);
- val PT = types ("P", j);
- fun mk_abs [] t = t
- | mk_abs ((a,T)::Ts) t = Abs (a, T, mk_abs Ts t);
- val tt = cterm_of thy (mk_abs (params @ [(s, T)]) subt);
- val Pt = cterm_of thy (mk_abs (params @ [(s, fastype_of1 (T::parTs, subt))])
- (make_term t [] paths 0));
- val tye = Sign.typ_match thy (tT, #T (rep_cterm tt)) Vartab.empty;
- val tye' = Sign.typ_match thy (PT, #T (rep_cterm Pt)) tye;
- val ctye = map (fn (ixn, (S, T)) =>
- (ctyp_of thy (TVar (ixn, S)), ctyp_of thy T)) (Vartab.dest tye');
- val tv = cterm_of thy (Var (("t", j), Envir.subst_type tye' tT));
- val Pv = cterm_of thy (Var (("P", j), Envir.subst_type tye' PT));
- val rule' = instantiate (ctye, [(tv, tt), (Pv, Pt)]) rule
- in rule' end;
-
-
-(*** the admissibility tactic ***)
-
-fun try_dest_adm (Const _ $ (Const (@{const_name adm}, _) $ Abs abs)) = SOME abs
- | try_dest_adm _ = NONE;
-
-fun adm_tac ctxt tac i state = (i, state) |-> SUBGOAL (fn (goali, _) =>
- (case try_dest_adm (Logic.strip_assums_concl goali) of
- NONE => no_tac
- | SOME (s, T, t) =>
- let
- val thy = ProofContext.theory_of ctxt;
- val prems = Logic.strip_assums_hyp goali;
- val params = Logic.strip_params goali;
- val ts = find_subterms t 0 [];
- val ts' = filter eq_terms ts;
- val ts'' = filter (is_chfin thy T params) ts';
- val thms = fold (prove_cont ctxt tac s T prems params) ts'' [];
- in
- (case thms of
- ((ts as ((t', _)::_), cont_thm) :: _) =>
- let
- val paths = map snd ts;
- val rule = inst_adm_subst_thm state i params s T t' t paths;
- in
- compose_tac (false, rule, 2) i THEN
- resolve_tac [cont_thm] i THEN
- REPEAT (assume_tac i) THEN
- resolve_tac [@{thm adm_chfin}] i
- end
- | [] => no_tac)
- end));
-
-end;
-