(* Title: TFL/rules
ID: $Id$
Author: Konrad Slind, Cambridge University Computer Laboratory
Copyright 1997 University of Cambridge
Emulation of HOL inference rules for TFL
*)
structure Rules : Rules_sig =
struct
open Utils;
structure USyntax = USyntax;
structure S = USyntax;
structure U = Utils;
structure D = Dcterm;
fun RULES_ERR{func,mesg} = Utils.ERR{module = "Rules",func=func,mesg=mesg};
fun cconcl thm = D.drop_prop(#prop(crep_thm thm));
fun chyps thm = map D.drop_prop(#hyps(crep_thm thm));
fun dest_thm thm =
let val {prop,hyps,...} = rep_thm thm
in (map HOLogic.dest_Trueprop hyps, HOLogic.dest_Trueprop prop)
end;
(* Inference rules *)
(*---------------------------------------------------------------------------
* Equality (one step)
*---------------------------------------------------------------------------*)
fun REFL tm = Thm.reflexive tm RS meta_eq_to_obj_eq;
fun SYM thm = thm RS sym;
fun ALPHA thm ctm1 =
let val ctm2 = cprop_of thm
val ctm2_eq = reflexive ctm2
val ctm1_eq = reflexive ctm1
in equal_elim (transitive ctm2_eq ctm1_eq) thm
end;
(*----------------------------------------------------------------------------
* typ instantiation
*---------------------------------------------------------------------------*)
fun INST_TYPE blist thm =
let val {sign,...} = rep_thm thm
val blist' = map (fn (TVar(idx,_), B) => (idx, ctyp_of sign B)) blist
in Thm.instantiate (blist',[]) thm
end
handle _ => raise RULES_ERR{func = "INST_TYPE", mesg = ""};
(*----------------------------------------------------------------------------
* Implication and the assumption list
*
* Assumptions get stuck on the meta-language assumption list. Implications
* are in the object language, so discharging an assumption "A" from theorem
* "B" results in something that looks like "A --> B".
*---------------------------------------------------------------------------*)
fun ASSUME ctm = Thm.assume (D.mk_prop ctm);
(*---------------------------------------------------------------------------
* Implication in TFL is -->. Meta-language implication (==>) is only used
* in the implementation of some of the inference rules below.
*---------------------------------------------------------------------------*)
fun MP th1 th2 = th2 RS (th1 RS mp);
fun DISCH tm thm = Thm.implies_intr (D.mk_prop tm) thm COMP impI;
fun DISCH_ALL thm = Utils.itlist DISCH (#hyps (crep_thm thm)) thm;
fun FILTER_DISCH_ALL P thm =
let fun check tm = U.holds P (#t(rep_cterm tm))
in foldr (fn (tm,th) => if (check tm) then DISCH tm th else th)
(chyps thm, thm)
end;
(* freezeT expensive! *)
fun UNDISCH thm =
let val tm = D.mk_prop(#1(D.dest_imp(cconcl (freezeT thm))))
in implies_elim (thm RS mp) (ASSUME tm)
end
handle _ => raise RULES_ERR{func = "UNDISCH", mesg = ""};
fun PROVE_HYP ath bth = MP (DISCH (cconcl ath) bth) ath;
local val [p1,p2] = goal HOL.thy "(A-->B) ==> (B --> C) ==> (A-->C)"
val dummy = by (rtac impI 1)
val dummy = by (rtac (p2 RS mp) 1)
val dummy = by (rtac (p1 RS mp) 1)
val dummy = by (assume_tac 1)
val imp_trans = result()
in
fun IMP_TRANS th1 th2 = th2 RS (th1 RS imp_trans)
end;
(*----------------------------------------------------------------------------
* Conjunction
*---------------------------------------------------------------------------*)
fun CONJUNCT1 thm = (thm RS conjunct1)
fun CONJUNCT2 thm = (thm RS conjunct2);
fun CONJUNCTS th = (CONJUNCTS (CONJUNCT1 th) @ CONJUNCTS (CONJUNCT2 th))
handle _ => [th];
fun LIST_CONJ [] = raise RULES_ERR{func = "LIST_CONJ", mesg = "empty list"}
| LIST_CONJ [th] = th
| LIST_CONJ (th::rst) = MP(MP(conjI COMP (impI RS impI)) th) (LIST_CONJ rst);
(*----------------------------------------------------------------------------
* Disjunction
*---------------------------------------------------------------------------*)
local val {prop,sign,...} = rep_thm disjI1
val [P,Q] = term_vars prop
val disj1 = forall_intr (cterm_of sign Q) disjI1
in
fun DISJ1 thm tm = thm RS (forall_elim (D.drop_prop tm) disj1)
end;
local val {prop,sign,...} = rep_thm disjI2
val [P,Q] = term_vars prop
val disj2 = forall_intr (cterm_of sign P) disjI2
in
fun DISJ2 tm thm = thm RS (forall_elim (D.drop_prop tm) disj2)
end;
(*----------------------------------------------------------------------------
*
* A1 |- M1, ..., An |- Mn
* ---------------------------------------------------
* [A1 |- M1 \/ ... \/ Mn, ..., An |- M1 \/ ... \/ Mn]
*
*---------------------------------------------------------------------------*)
fun EVEN_ORS thms =
let fun blue ldisjs [] _ = []
| blue ldisjs (th::rst) rdisjs =
let val tail = tl rdisjs
val rdisj_tl = D.list_mk_disj tail
in itlist DISJ2 ldisjs (DISJ1 th rdisj_tl)
:: blue (ldisjs@[cconcl th]) rst tail
end handle _ => [itlist DISJ2 ldisjs th]
in
blue [] thms (map cconcl thms)
end;
(*----------------------------------------------------------------------------
*
* A |- P \/ Q B,P |- R C,Q |- R
* ---------------------------------------------------
* A U B U C |- R
*
*---------------------------------------------------------------------------*)
local val [p1,p2,p3] = goal HOL.thy "(P | Q) ==> (P --> R) ==> (Q --> R) ==> R"
val dummy = by (rtac (p1 RS disjE) 1)
val dummy = by (rtac (p2 RS mp) 1)
val dummy = by (assume_tac 1)
val dummy = by (rtac (p3 RS mp) 1)
val dummy = by (assume_tac 1)
val tfl_exE = result()
in
fun DISJ_CASES th1 th2 th3 =
let val c = D.drop_prop(cconcl th1)
val (disj1,disj2) = D.dest_disj c
val th2' = DISCH disj1 th2
val th3' = DISCH disj2 th3
in
th3' RS (th2' RS (th1 RS tfl_exE))
end
end;
(*-----------------------------------------------------------------------------
*
* |- A1 \/ ... \/ An [A1 |- M, ..., An |- M]
* ---------------------------------------------------
* |- M
*
* Note. The list of theorems may be all jumbled up, so we have to
* first organize it to align with the first argument (the disjunctive
* theorem).
*---------------------------------------------------------------------------*)
fun organize eq = (* a bit slow - analogous to insertion sort *)
let fun extract a alist =
let fun ex (_,[]) = raise RULES_ERR{func = "organize",
mesg = "not a permutation.1"}
| ex(left,h::t) = if (eq h a) then (h,rev left@t) else ex(h::left,t)
in ex ([],alist)
end
fun place [] [] = []
| place (a::rst) alist =
let val (item,next) = extract a alist
in item::place rst next
end
| place _ _ = raise RULES_ERR{func = "organize",
mesg = "not a permutation.2"}
in place
end;
(* freezeT expensive! *)
fun DISJ_CASESL disjth thl =
let val c = cconcl disjth
fun eq th atm = exists (fn t => HOLogic.dest_Trueprop t
aconv term_of atm)
(#hyps(rep_thm th))
val tml = D.strip_disj c
fun DL th [] = raise RULES_ERR{func="DISJ_CASESL",mesg="no cases"}
| DL th [th1] = PROVE_HYP th th1
| DL th [th1,th2] = DISJ_CASES th th1 th2
| DL th (th1::rst) =
let val tm = #2(D.dest_disj(D.drop_prop(cconcl th)))
in DISJ_CASES th th1 (DL (ASSUME tm) rst) end
in DL (freezeT disjth) (organize eq tml thl)
end;
(*----------------------------------------------------------------------------
* Universals
*---------------------------------------------------------------------------*)
local (* this is fragile *)
val {prop,sign,...} = rep_thm spec
val x = hd (tl (term_vars prop))
val (TVar (indx,_)) = type_of x
val gspec = forall_intr (cterm_of sign x) spec
in
fun SPEC tm thm =
let val {sign,T,...} = rep_cterm tm
val gspec' = instantiate([(indx,ctyp_of sign T)],[]) gspec
in thm RS (forall_elim tm gspec')
end
end;
fun SPEC_ALL thm = rev_itlist SPEC (#1(D.strip_forall(cconcl thm))) thm;
val ISPEC = SPEC
val ISPECL = rev_itlist ISPEC;
(* Not optimized! Too complicated. *)
local val {prop,sign,...} = rep_thm allI
val [P] = add_term_vars (prop, [])
fun cty_theta s = map (fn (i,ty) => (i, ctyp_of s ty))
fun ctm_theta s = map (fn (i,tm2) =>
let val ctm2 = cterm_of s tm2
in (cterm_of s (Var(i,#T(rep_cterm ctm2))), ctm2)
end)
fun certify s (ty_theta,tm_theta) = (cty_theta s ty_theta,
ctm_theta s tm_theta)
in
fun GEN v th =
let val gth = forall_intr v th
val {prop=Const("all",_)$Abs(x,ty,rst),sign,...} = rep_thm gth
val P' = Abs(x,ty, HOLogic.dest_Trueprop rst) (* get rid of trueprop *)
val tsig = #tsig(Sign.rep_sg sign)
val theta = Pattern.match tsig (P,P')
val allI2 = instantiate (certify sign theta) allI
val thm = implies_elim allI2 gth
val {prop = tp $ (A $ Abs(_,_,M)),sign,...} = rep_thm thm
val prop' = tp $ (A $ Abs(x,ty,M))
in ALPHA thm (cterm_of sign prop')
end
end;
val GENL = itlist GEN;
fun GEN_ALL thm =
let val {prop,sign,...} = rep_thm thm
val tycheck = cterm_of sign
val vlist = map tycheck (add_term_vars (prop, []))
in GENL vlist thm
end;
fun MATCH_MP th1 th2 =
if (D.is_forall (D.drop_prop(cconcl th1)))
then MATCH_MP (th1 RS spec) th2
else MP th1 th2;
(*----------------------------------------------------------------------------
* Existentials
*---------------------------------------------------------------------------*)
(*---------------------------------------------------------------------------
* Existential elimination
*
* A1 |- ?x.t[x] , A2, "t[v]" |- t'
* ------------------------------------ (variable v occurs nowhere)
* A1 u A2 |- t'
*
*---------------------------------------------------------------------------*)
local val [p1,p2] = goal HOL.thy "(? x. P x) ==> (!x. P x --> Q) ==> Q"
val dummy = by (rtac (p1 RS exE) 1)
val dummy = by (rtac ((p2 RS allE) RS mp) 1)
val dummy = by (assume_tac 2)
val dummy = by (assume_tac 1)
val choose_thm = result()
in
fun CHOOSE(fvar,exth) fact =
let val lam = #2(dest_comb(D.drop_prop(cconcl exth)))
val redex = capply lam fvar
val {sign, t = t$u,...} = rep_cterm redex
val residue = cterm_of sign (betapply(t,u))
in GEN fvar (DISCH residue fact) RS (exth RS choose_thm)
end
end;
local val {prop,sign,...} = rep_thm exI
val [P,x] = term_vars prop
in
fun EXISTS (template,witness) thm =
let val {prop,sign,...} = rep_thm thm
val P' = cterm_of sign P
val x' = cterm_of sign x
val abstr = #2(dest_comb template)
in
thm RS (cterm_instantiate[(P',abstr), (x',witness)] exI)
end
end;
(*----------------------------------------------------------------------------
*
* A |- M
* ------------------- [v_1,...,v_n]
* A |- ?v1...v_n. M
*
*---------------------------------------------------------------------------*)
fun EXISTL vlist th =
U.itlist (fn v => fn thm => EXISTS(D.mk_exists(v,cconcl thm), v) thm)
vlist th;
(*----------------------------------------------------------------------------
*
* A |- M[x_1,...,x_n]
* ---------------------------- [(x |-> y)_1,...,(x |-> y)_n]
* A |- ?y_1...y_n. M
*
*---------------------------------------------------------------------------*)
(* Could be improved, but needs "subst_free" for certified terms *)
fun IT_EXISTS blist th =
let val {sign,...} = rep_thm th
val tych = cterm_of sign
val detype = #t o rep_cterm
val blist' = map (fn (x,y) => (detype x, detype y)) blist
fun ?v M = cterm_of sign (S.mk_exists{Bvar=v,Body = M})
in
U.itlist (fn (b as (r1,r2)) => fn thm =>
EXISTS(?r2(subst_free[b]
(HOLogic.dest_Trueprop(#prop(rep_thm thm)))), tych r1)
thm)
blist' th
end;
(*---------------------------------------------------------------------------
* Faster version, that fails for some as yet unknown reason
* fun IT_EXISTS blist th =
* let val {sign,...} = rep_thm th
* val tych = cterm_of sign
* fun detype (x,y) = ((#t o rep_cterm) x, (#t o rep_cterm) y)
* in
* fold (fn (b as (r1,r2), thm) =>
* EXISTS(D.mk_exists(r2, tych(subst_free[detype b](#t(rep_cterm(cconcl thm))))),
* r1) thm) blist th
* end;
*---------------------------------------------------------------------------*)
(*----------------------------------------------------------------------------
* Rewriting
*---------------------------------------------------------------------------*)
fun SUBS thl =
rewrite_rule (map (fn th => (th RS eq_reflection) handle _ => th) thl);
local fun rew_conv mss = Thm.rewrite_cterm (true,false,false) mss (K(K None))
in
fun simpl_conv ss thl ctm =
rew_conv (Thm.mss_of (#simps (Thm.dest_mss (#mss (rep_ss ss))) @ thl)) ctm
RS meta_eq_to_obj_eq
end;
local fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1])
in
val RIGHT_ASSOC = rewrite_rule [prover"((a|b)|c) = (a|(b|c))" RS eq_reflection]
val ASM = refl RS iffD1
end;
(*---------------------------------------------------------------------------
* TERMINATION CONDITION EXTRACTION
*---------------------------------------------------------------------------*)
(* Object language quantifier, i.e., "!" *)
fun Forall v M = S.mk_forall{Bvar=v, Body=M};
(* Fragile: it's a cong if it is not "R y x ==> cut f R x y = f y" *)
fun is_cong thm =
let val {prop, ...} = rep_thm thm
in case prop
of (Const("==>",_)$(Const("Trueprop",_)$ _) $
(Const("==",_) $ (Const ("cut",_) $ f $ R $ a $ x) $ _)) => false
| _ => true
end;
fun dest_equal(Const ("==",_) $
(Const ("Trueprop",_) $ lhs)
$ (Const ("Trueprop",_) $ rhs)) = {lhs=lhs, rhs=rhs}
| dest_equal(Const ("==",_) $ lhs $ rhs) = {lhs=lhs, rhs=rhs}
| dest_equal tm = S.dest_eq tm;
fun get_lhs tm = #lhs(dest_equal (HOLogic.dest_Trueprop tm));
fun dest_all(Const("all",_) $ (a as Abs _)) = S.dest_abs a
| dest_all _ = raise RULES_ERR{func = "dest_all", mesg = "not a !!"};
val is_all = Utils.can dest_all;
fun strip_all fm =
if (is_all fm)
then let val {Bvar,Body} = dest_all fm
val (bvs,core) = strip_all Body
in ((Bvar::bvs), core)
end
else ([],fm);
fun break_all(Const("all",_) $ Abs (_,_,body)) = body
| break_all _ = raise RULES_ERR{func = "break_all", mesg = "not a !!"};
fun list_break_all(Const("all",_) $ Abs (s,ty,body)) =
let val (L,core) = list_break_all body
in ((s,ty)::L, core)
end
| list_break_all tm = ([],tm);
(*---------------------------------------------------------------------------
* Rename a term of the form
*
* !!x1 ...xn. x1=M1 ==> ... ==> xn=Mn
* ==> ((%v1...vn. Q) x1 ... xn = g x1 ... xn.
* to one of
*
* !!v1 ... vn. v1=M1 ==> ... ==> vn=Mn
* ==> ((%v1...vn. Q) v1 ... vn = g v1 ... vn.
*
* This prevents name problems in extraction, and helps the result to read
* better. There is a problem with varstructs, since they can introduce more
* than n variables, and some extra reasoning needs to be done.
*---------------------------------------------------------------------------*)
fun get ([],_,L) = rev L
| get (ant::rst,n,L) =
case (list_break_all ant)
of ([],_) => get (rst, n+1,L)
| (vlist,body) =>
let val eq = Logic.strip_imp_concl body
val (f,args) = S.strip_comb (get_lhs eq)
val (vstrl,_) = S.strip_abs f
val names = variantlist (map (#1 o dest_Free) vstrl,
add_term_names(body, []))
in get (rst, n+1, (names,n)::L)
end handle _ => get (rst, n+1, L);
(* Note: rename_params_rule counts from 1, not 0 *)
fun rename thm =
let val {prop,sign,...} = rep_thm thm
val tych = cterm_of sign
val ants = Logic.strip_imp_prems prop
val news = get (ants,1,[])
in
U.rev_itlist rename_params_rule news thm
end;
(*---------------------------------------------------------------------------
* Beta-conversion to the rhs of an equation (taken from hol90/drule.sml)
*---------------------------------------------------------------------------*)
fun list_beta_conv tm =
let fun rbeta th = transitive th (beta_conversion(#2(D.dest_eq(cconcl th))))
fun iter [] = reflexive tm
| iter (v::rst) = rbeta (combination(iter rst) (reflexive v))
in iter end;
(*---------------------------------------------------------------------------
* Trace information for the rewriter
*---------------------------------------------------------------------------*)
val term_ref = ref[] : term list ref
val mss_ref = ref [] : meta_simpset list ref;
val thm_ref = ref [] : thm list ref;
val tracing = ref false;
fun say s = if !tracing then prs s else ();
fun print_thms s L =
(say s;
map (fn th => say (string_of_thm th ^"\n")) L;
say"\n");
fun print_cterms s L =
(say s;
map (fn th => say (string_of_cterm th ^"\n")) L;
say"\n");
(*---------------------------------------------------------------------------
* General abstraction handlers, should probably go in USyntax.
*---------------------------------------------------------------------------*)
fun mk_aabs(vstr,body) = S.mk_abs{Bvar=vstr,Body=body}
handle _ => S.mk_pabs{varstruct = vstr, body = body};
fun list_mk_aabs (vstrl,tm) =
U.itlist (fn vstr => fn tm => mk_aabs(vstr,tm)) vstrl tm;
fun dest_aabs tm =
let val {Bvar,Body} = S.dest_abs tm
in (Bvar,Body)
end handle _ => let val {varstruct,body} = S.dest_pabs tm
in (varstruct,body)
end;
fun strip_aabs tm =
let val (vstr,body) = dest_aabs tm
val (bvs, core) = strip_aabs body
in (vstr::bvs, core)
end
handle _ => ([],tm);
fun dest_combn tm 0 = (tm,[])
| dest_combn tm n =
let val {Rator,Rand} = S.dest_comb tm
val (f,rands) = dest_combn Rator (n-1)
in (f,Rand::rands)
end;
local fun dest_pair M = let val {fst,snd} = S.dest_pair M in (fst,snd) end
fun mk_fst tm =
let val ty as Type("*", [fty,sty]) = type_of tm
in Const ("fst", ty --> fty) $ tm end
fun mk_snd tm =
let val ty as Type("*", [fty,sty]) = type_of tm
in Const ("snd", ty --> sty) $ tm end
in
fun XFILL tych x vstruct =
let fun traverse p xocc L =
if (is_Free p)
then tych xocc::L
else let val (p1,p2) = dest_pair p
in traverse p1 (mk_fst xocc) (traverse p2 (mk_snd xocc) L)
end
in
traverse vstruct x []
end end;
(*---------------------------------------------------------------------------
* Replace a free tuple (vstr) by a universally quantified variable (a).
* Note that the notion of "freeness" for a tuple is different than for a
* variable: if variables in the tuple also occur in any other place than
* an occurrences of the tuple, they aren't "free" (which is thus probably
* the wrong word to use).
*---------------------------------------------------------------------------*)
fun VSTRUCT_ELIM tych a vstr th =
let val L = S.free_vars_lr vstr
val bind1 = tych (HOLogic.mk_Trueprop (HOLogic.mk_eq(a,vstr)))
val thm1 = implies_intr bind1 (SUBS [SYM(assume bind1)] th)
val thm2 = forall_intr_list (map tych L) thm1
val thm3 = forall_elim_list (XFILL tych a vstr) thm2
in refl RS
rewrite_rule[symmetric (surjective_pairing RS eq_reflection)] thm3
end;
fun PGEN tych a vstr th =
let val a1 = tych a
val vstr1 = tych vstr
in
forall_intr a1
(if (is_Free vstr)
then cterm_instantiate [(vstr1,a1)] th
else VSTRUCT_ELIM tych a vstr th)
end;
(*---------------------------------------------------------------------------
* Takes apart a paired beta-redex, looking like "(\(x,y).N) vstr", into
*
* (([x,y],N),vstr)
*---------------------------------------------------------------------------*)
fun dest_pbeta_redex M n =
let val (f,args) = dest_combn M n
val dummy = dest_aabs f
in (strip_aabs f,args)
end;
fun pbeta_redex M n = U.can (U.C dest_pbeta_redex n) M;
fun dest_impl tm =
let val ants = Logic.strip_imp_prems tm
val eq = Logic.strip_imp_concl tm
in (ants,get_lhs eq)
end;
fun restricted t = is_some (S.find_term
(fn (Const("cut",_)) =>true | _ => false)
t)
fun CONTEXT_REWRITE_RULE (ss, func, R, cut_lemma, congs) th =
let val pbeta_reduce = simpl_conv ss [split RS eq_reflection];
val tc_list = ref[]: term list ref
val dummy = term_ref := []
val dummy = thm_ref := []
val dummy = mss_ref := []
val cut_lemma' = (cut_lemma RS mp) RS eq_reflection
fun prover mss thm =
let fun cong_prover mss thm =
let val dummy = say "cong_prover:\n"
val cntxt = prems_of_mss mss
val dummy = print_thms "cntxt:\n" cntxt
val dummy = say "cong rule:\n"
val dummy = say (string_of_thm thm^"\n")
val dummy = thm_ref := (thm :: !thm_ref)
val dummy = mss_ref := (mss :: !mss_ref)
(* Unquantified eliminate *)
fun uq_eliminate (thm,imp,sign) =
let val tych = cterm_of sign
val dummy = print_cterms "To eliminate:\n" [tych imp]
val ants = map tych (Logic.strip_imp_prems imp)
val eq = Logic.strip_imp_concl imp
val lhs = tych(get_lhs eq)
val mss' = add_prems(mss, map ASSUME ants)
val lhs_eq_lhs1 = Thm.rewrite_cterm(false,true,false)mss' prover lhs
handle _ => reflexive lhs
val dummy = print_thms "proven:\n" [lhs_eq_lhs1]
val lhs_eq_lhs2 = implies_intr_list ants lhs_eq_lhs1
val lhs_eeq_lhs2 = lhs_eq_lhs2 RS meta_eq_to_obj_eq
in
lhs_eeq_lhs2 COMP thm
end
fun pq_eliminate (thm,sign,vlist,imp_body,lhs_eq) =
let val ((vstrl,_),args) = dest_pbeta_redex lhs_eq(length vlist)
val dummy = assert (forall (op aconv)
(ListPair.zip (vlist, args)))
"assertion failed in CONTEXT_REWRITE_RULE"
val imp_body1 = subst_free (ListPair.zip (args, vstrl))
imp_body
val tych = cterm_of sign
val ants1 = map tych (Logic.strip_imp_prems imp_body1)
val eq1 = Logic.strip_imp_concl imp_body1
val Q = get_lhs eq1
val QeqQ1 = pbeta_reduce (tych Q)
val Q1 = #2(D.dest_eq(cconcl QeqQ1))
val mss' = add_prems(mss, map ASSUME ants1)
val Q1eeqQ2 = Thm.rewrite_cterm (false,true,false) mss' prover Q1
handle _ => reflexive Q1
val Q2 = #2 (Logic.dest_equals (#prop(rep_thm Q1eeqQ2)))
val Q3 = tych(list_comb(list_mk_aabs(vstrl,Q2),vstrl))
val Q2eeqQ3 = symmetric(pbeta_reduce Q3 RS eq_reflection)
val thA = transitive(QeqQ1 RS eq_reflection) Q1eeqQ2
val QeeqQ3 = transitive thA Q2eeqQ3 handle _ =>
((Q2eeqQ3 RS meta_eq_to_obj_eq)
RS ((thA RS meta_eq_to_obj_eq) RS trans))
RS eq_reflection
val impth = implies_intr_list ants1 QeeqQ3
val impth1 = impth RS meta_eq_to_obj_eq
(* Need to abstract *)
val ant_th = U.itlist2 (PGEN tych) args vstrl impth1
in ant_th COMP thm
end
fun q_eliminate (thm,imp,sign) =
let val (vlist,imp_body) = strip_all imp
val (ants,Q) = dest_impl imp_body
in if (pbeta_redex Q) (length vlist)
then pq_eliminate (thm,sign,vlist,imp_body,Q)
else
let val tych = cterm_of sign
val ants1 = map tych ants
val mss' = add_prems(mss, map ASSUME ants1)
val Q_eeq_Q1 = Thm.rewrite_cterm(false,true,false) mss'
prover (tych Q)
handle _ => reflexive (tych Q)
val lhs_eeq_lhs2 = implies_intr_list ants1 Q_eeq_Q1
val lhs_eq_lhs2 = lhs_eeq_lhs2 RS meta_eq_to_obj_eq
val ant_th = forall_intr_list(map tych vlist)lhs_eq_lhs2
in
ant_th COMP thm
end end
fun eliminate thm =
case (rep_thm thm)
of {prop = (Const("==>",_) $ imp $ _), sign, ...} =>
eliminate
(if not(is_all imp)
then uq_eliminate (thm,imp,sign)
else q_eliminate (thm,imp,sign))
(* Assume that the leading constant is ==, *)
| _ => thm (* if it is not a ==> *)
in Some(eliminate (rename thm))
end handle _ => None
fun restrict_prover mss thm =
let val dummy = say "restrict_prover:\n"
val cntxt = rev(prems_of_mss mss)
val dummy = print_thms "cntxt:\n" cntxt
val {prop = Const("==>",_) $ (Const("Trueprop",_) $ A) $ _,
sign,...} = rep_thm thm
fun genl tm = let val vlist = gen_rems (op aconv)
(add_term_frees(tm,[]), [func,R])
in U.itlist Forall vlist tm
end
(*--------------------------------------------------------------
* This actually isn't quite right, since it will think that
* not-fully applied occs. of "f" in the context mean that the
* current call is nested. The real solution is to pass in a
* term "f v1..vn" which is a pattern that any full application
* of "f" will match.
*-------------------------------------------------------------*)
val func_name = #1(dest_Const func)
fun is_func (Const (name,_)) = (name = func_name)
| is_func _ = false
val rcontext = rev cntxt
val cncl = HOLogic.dest_Trueprop o #prop o rep_thm
val antl = case rcontext of [] => []
| _ => [S.list_mk_conj(map cncl rcontext)]
val TC = genl(S.list_mk_imp(antl, A))
val dummy = print_cterms "func:\n" [cterm_of sign func]
val dummy = print_cterms "TC:\n"
[cterm_of sign (HOLogic.mk_Trueprop TC)]
val dummy = tc_list := (TC :: !tc_list)
val nestedp = is_some (S.find_term is_func TC)
val dummy = if nestedp then say"nested\n" else say"not_nested\n"
val dummy = term_ref := ([func,TC]@(!term_ref))
val th' = if nestedp then raise RULES_ERR{func = "solver",
mesg = "nested function"}
else let val cTC = cterm_of sign
(HOLogic.mk_Trueprop TC)
in case rcontext of
[] => SPEC_ALL(ASSUME cTC)
| _ => MP (SPEC_ALL (ASSUME cTC))
(LIST_CONJ rcontext)
end
val th'' = th' RS thm
in Some (th'')
end handle _ => None
in
(if (is_cong thm) then cong_prover else restrict_prover) mss thm
end
val ctm = cprop_of th
val th1 = Thm.rewrite_cterm(false,true,false) (add_congs(mss_of [cut_lemma'], congs))
prover ctm
val th2 = equal_elim th1 th
in
(th2, filter (not o restricted) (!tc_list))
end;
fun prove (ptm,tac) =
#1 (freeze_thaw (prove_goalw_cterm [] ptm (fn _ => [tac])));
end; (* Rules *)