author | wenzelm |
Thu, 28 May 1998 11:08:45 +0200 | |
changeset 4974 | 45b7a51342a1 |
parent 4713 | bea2ab2e360b |
child 5081 | 7274f7d101ee |
permissions | -rw-r--r-- |
3302 | 1 |
(* Title: TFL/rules |
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ID: $Id$ |
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Author: Konrad Slind, Cambridge University Computer Laboratory |
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Copyright 1997 University of Cambridge |
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Emulation of HOL inference rules for TFL |
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*) |
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structure Rules : Rules_sig = |
2112 | 10 |
struct |
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open Utils; |
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structure USyntax = USyntax; |
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structure S = USyntax; |
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structure U = Utils; |
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structure D = Dcterm; |
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fun RULES_ERR{func,mesg} = Utils.ERR{module = "Rules",func=func,mesg=mesg}; |
2112 | 21 |
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fun cconcl thm = D.drop_prop(#prop(crep_thm thm)); |
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fun chyps thm = map D.drop_prop(#hyps(crep_thm thm)); |
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fun dest_thm thm = |
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let val {prop,hyps,...} = rep_thm thm |
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in (map HOLogic.dest_Trueprop hyps, HOLogic.dest_Trueprop prop) |
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end; |
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(* Inference rules *) |
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(*--------------------------------------------------------------------------- |
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* Equality (one step) |
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*---------------------------------------------------------------------------*) |
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fun REFL tm = Thm.reflexive tm RS meta_eq_to_obj_eq; |
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fun SYM thm = thm RS sym; |
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fun ALPHA thm ctm1 = |
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let val ctm2 = cprop_of thm |
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val ctm2_eq = reflexive ctm2 |
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val ctm1_eq = reflexive ctm1 |
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in equal_elim (transitive ctm2_eq ctm1_eq) thm |
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end; |
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(*---------------------------------------------------------------------------- |
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* typ instantiation |
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*---------------------------------------------------------------------------*) |
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fun INST_TYPE blist thm = |
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let val {sign,...} = rep_thm thm |
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val blist' = map (fn (TVar(idx,_), B) => (idx, ctyp_of sign B)) blist |
2112 | 55 |
in Thm.instantiate (blist',[]) thm |
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end |
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handle _ => raise RULES_ERR{func = "INST_TYPE", mesg = ""}; |
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(*---------------------------------------------------------------------------- |
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* Implication and the assumption list |
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* |
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* Assumptions get stuck on the meta-language assumption list. Implications |
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* are in the object language, so discharging an assumption "A" from theorem |
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* "B" results in something that looks like "A --> B". |
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*---------------------------------------------------------------------------*) |
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fun ASSUME ctm = Thm.assume (D.mk_prop ctm); |
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(*--------------------------------------------------------------------------- |
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* Implication in TFL is -->. Meta-language implication (==>) is only used |
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* in the implementation of some of the inference rules below. |
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*---------------------------------------------------------------------------*) |
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fun MP th1 th2 = th2 RS (th1 RS mp); |
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fun DISCH tm thm = Thm.implies_intr (D.mk_prop tm) thm COMP impI; |
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fun DISCH_ALL thm = Utils.itlist DISCH (#hyps (crep_thm thm)) thm; |
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fun FILTER_DISCH_ALL P thm = |
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let fun check tm = U.holds P (#t(rep_cterm tm)) |
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in foldr (fn (tm,th) => if (check tm) then DISCH tm th else th) |
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(chyps thm, thm) |
2112 | 85 |
end; |
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(* freezeT expensive! *) |
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fun UNDISCH thm = |
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let val tm = D.mk_prop(#1(D.dest_imp(cconcl (freezeT thm)))) |
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in implies_elim (thm RS mp) (ASSUME tm) |
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end |
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handle _ => raise RULES_ERR{func = "UNDISCH", mesg = ""}; |
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fun PROVE_HYP ath bth = MP (DISCH (cconcl ath) bth) ath; |
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local val [p1,p2] = goal HOL.thy "(A-->B) ==> (B --> C) ==> (A-->C)" |
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val dummy = by (rtac impI 1) |
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val dummy = by (rtac (p2 RS mp) 1) |
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val dummy = by (rtac (p1 RS mp) 1) |
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val dummy = by (assume_tac 1) |
2112 | 101 |
val imp_trans = result() |
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in |
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fun IMP_TRANS th1 th2 = th2 RS (th1 RS imp_trans) |
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end; |
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(*---------------------------------------------------------------------------- |
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* Conjunction |
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*---------------------------------------------------------------------------*) |
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fun CONJUNCT1 thm = (thm RS conjunct1) |
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fun CONJUNCT2 thm = (thm RS conjunct2); |
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fun CONJUNCTS th = (CONJUNCTS (CONJUNCT1 th) @ CONJUNCTS (CONJUNCT2 th)) |
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handle _ => [th]; |
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fun LIST_CONJ [] = raise RULES_ERR{func = "LIST_CONJ", mesg = "empty list"} |
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| LIST_CONJ [th] = th |
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| LIST_CONJ (th::rst) = MP(MP(conjI COMP (impI RS impI)) th) (LIST_CONJ rst); |
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(*---------------------------------------------------------------------------- |
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* Disjunction |
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*---------------------------------------------------------------------------*) |
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local val {prop,sign,...} = rep_thm disjI1 |
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val [P,Q] = term_vars prop |
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val disj1 = forall_intr (cterm_of sign Q) disjI1 |
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in |
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fun DISJ1 thm tm = thm RS (forall_elim (D.drop_prop tm) disj1) |
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end; |
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local val {prop,sign,...} = rep_thm disjI2 |
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val [P,Q] = term_vars prop |
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val disj2 = forall_intr (cterm_of sign P) disjI2 |
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in |
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fun DISJ2 tm thm = thm RS (forall_elim (D.drop_prop tm) disj2) |
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end; |
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(*---------------------------------------------------------------------------- |
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* |
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* A1 |- M1, ..., An |- Mn |
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* --------------------------------------------------- |
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* [A1 |- M1 \/ ... \/ Mn, ..., An |- M1 \/ ... \/ Mn] |
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* |
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*---------------------------------------------------------------------------*) |
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fun EVEN_ORS thms = |
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let fun blue ldisjs [] _ = [] |
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| blue ldisjs (th::rst) rdisjs = |
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let val tail = tl rdisjs |
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val rdisj_tl = D.list_mk_disj tail |
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in itlist DISJ2 ldisjs (DISJ1 th rdisj_tl) |
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:: blue (ldisjs@[cconcl th]) rst tail |
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end handle _ => [itlist DISJ2 ldisjs th] |
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in |
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blue [] thms (map cconcl thms) |
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end; |
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(*---------------------------------------------------------------------------- |
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* |
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* A |- P \/ Q B,P |- R C,Q |- R |
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* --------------------------------------------------- |
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* A U B U C |- R |
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* |
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*---------------------------------------------------------------------------*) |
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local val [p1,p2,p3] = goal HOL.thy "(P | Q) ==> (P --> R) ==> (Q --> R) ==> R" |
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val dummy = by (rtac (p1 RS disjE) 1) |
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val dummy = by (rtac (p2 RS mp) 1) |
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val dummy = by (assume_tac 1) |
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val dummy = by (rtac (p3 RS mp) 1) |
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val dummy = by (assume_tac 1) |
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val tfl_exE = result() |
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in |
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fun DISJ_CASES th1 th2 th3 = |
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let val c = D.drop_prop(cconcl th1) |
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val (disj1,disj2) = D.dest_disj c |
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val th2' = DISCH disj1 th2 |
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val th3' = DISCH disj2 th3 |
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in |
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th3' RS (th2' RS (th1 RS tfl_exE)) |
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end |
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end; |
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(*----------------------------------------------------------------------------- |
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* |
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* |- A1 \/ ... \/ An [A1 |- M, ..., An |- M] |
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* --------------------------------------------------- |
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* |- M |
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* |
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* Note. The list of theorems may be all jumbled up, so we have to |
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* first organize it to align with the first argument (the disjunctive |
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* theorem). |
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*---------------------------------------------------------------------------*) |
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fun organize eq = (* a bit slow - analogous to insertion sort *) |
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let fun extract a alist = |
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let fun ex (_,[]) = raise RULES_ERR{func = "organize", |
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mesg = "not a permutation.1"} |
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| ex(left,h::t) = if (eq h a) then (h,rev left@t) else ex(h::left,t) |
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in ex ([],alist) |
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end |
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fun place [] [] = [] |
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| place (a::rst) alist = |
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let val (item,next) = extract a alist |
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in item::place rst next |
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end |
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| place _ _ = raise RULES_ERR{func = "organize", |
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mesg = "not a permutation.2"} |
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in place |
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end; |
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(* freezeT expensive! *) |
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fun DISJ_CASESL disjth thl = |
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let val c = cconcl disjth |
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fun eq th atm = exists (fn t => HOLogic.dest_Trueprop t |
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aconv term_of atm) |
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(#hyps(rep_thm th)) |
2112 | 218 |
val tml = D.strip_disj c |
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fun DL th [] = raise RULES_ERR{func="DISJ_CASESL",mesg="no cases"} |
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| DL th [th1] = PROVE_HYP th th1 |
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| DL th [th1,th2] = DISJ_CASES th th1 th2 |
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| DL th (th1::rst) = |
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let val tm = #2(D.dest_disj(D.drop_prop(cconcl th))) |
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in DISJ_CASES th th1 (DL (ASSUME tm) rst) end |
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in DL (freezeT disjth) (organize eq tml thl) |
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end; |
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(*---------------------------------------------------------------------------- |
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* Universals |
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*---------------------------------------------------------------------------*) |
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local (* this is fragile *) |
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val {prop,sign,...} = rep_thm spec |
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val x = hd (tl (term_vars prop)) |
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val (TVar (indx,_)) = type_of x |
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val gspec = forall_intr (cterm_of sign x) spec |
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in |
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fun SPEC tm thm = |
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let val {sign,T,...} = rep_cterm tm |
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val gspec' = instantiate([(indx,ctyp_of sign T)],[]) gspec |
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in thm RS (forall_elim tm gspec') |
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end |
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end; |
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fun SPEC_ALL thm = rev_itlist SPEC (#1(D.strip_forall(cconcl thm))) thm; |
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val ISPEC = SPEC |
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val ISPECL = rev_itlist ISPEC; |
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(* Not optimized! Too complicated. *) |
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local val {prop,sign,...} = rep_thm allI |
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val [P] = add_term_vars (prop, []) |
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fun cty_theta s = map (fn (i,ty) => (i, ctyp_of s ty)) |
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fun ctm_theta s = map (fn (i,tm2) => |
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let val ctm2 = cterm_of s tm2 |
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in (cterm_of s (Var(i,#T(rep_cterm ctm2))), ctm2) |
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end) |
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fun certify s (ty_theta,tm_theta) = (cty_theta s ty_theta, |
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ctm_theta s tm_theta) |
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in |
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fun GEN v th = |
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let val gth = forall_intr v th |
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val {prop=Const("all",_)$Abs(x,ty,rst),sign,...} = rep_thm gth |
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val P' = Abs(x,ty, HOLogic.dest_Trueprop rst) (* get rid of trueprop *) |
2112 | 265 |
val tsig = #tsig(Sign.rep_sg sign) |
266 |
val theta = Pattern.match tsig (P,P') |
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val allI2 = instantiate (certify sign theta) allI |
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val thm = implies_elim allI2 gth |
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val {prop = tp $ (A $ Abs(_,_,M)),sign,...} = rep_thm thm |
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val prop' = tp $ (A $ Abs(x,ty,M)) |
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in ALPHA thm (cterm_of sign prop') |
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end |
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273 |
end; |
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val GENL = itlist GEN; |
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fun GEN_ALL thm = |
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let val {prop,sign,...} = rep_thm thm |
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val tycheck = cterm_of sign |
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val vlist = map tycheck (add_term_vars (prop, [])) |
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in GENL vlist thm |
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end; |
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283 |
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284 |
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285 |
fun MATCH_MP th1 th2 = |
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286 |
if (D.is_forall (D.drop_prop(cconcl th1))) |
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then MATCH_MP (th1 RS spec) th2 |
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else MP th1 th2; |
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289 |
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290 |
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291 |
(*---------------------------------------------------------------------------- |
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292 |
* Existentials |
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293 |
*---------------------------------------------------------------------------*) |
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294 |
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295 |
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296 |
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297 |
(*--------------------------------------------------------------------------- |
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298 |
* Existential elimination |
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299 |
* |
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300 |
* A1 |- ?x.t[x] , A2, "t[v]" |- t' |
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301 |
* ------------------------------------ (variable v occurs nowhere) |
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302 |
* A1 u A2 |- t' |
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303 |
* |
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304 |
*---------------------------------------------------------------------------*) |
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305 |
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306 |
local val [p1,p2] = goal HOL.thy "(? x. P x) ==> (!x. P x --> Q) ==> Q" |
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307 |
val dummy = by (rtac (p1 RS exE) 1) |
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changeset
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308 |
val dummy = by (rtac ((p2 RS allE) RS mp) 1) |
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val dummy = by (assume_tac 2) |
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parents:
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changeset
|
310 |
val dummy = by (assume_tac 1) |
2112 | 311 |
val choose_thm = result() |
312 |
in |
|
313 |
fun CHOOSE(fvar,exth) fact = |
|
314 |
let val lam = #2(dest_comb(D.drop_prop(cconcl exth))) |
|
315 |
val redex = capply lam fvar |
|
3405 | 316 |
val {sign, t = t$u,...} = rep_cterm redex |
317 |
val residue = cterm_of sign (betapply(t,u)) |
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2112 | 318 |
in GEN fvar (DISCH residue fact) RS (exth RS choose_thm) |
319 |
end |
|
320 |
end; |
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321 |
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322 |
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323 |
local val {prop,sign,...} = rep_thm exI |
|
324 |
val [P,x] = term_vars prop |
|
325 |
in |
|
326 |
fun EXISTS (template,witness) thm = |
|
327 |
let val {prop,sign,...} = rep_thm thm |
|
328 |
val P' = cterm_of sign P |
|
329 |
val x' = cterm_of sign x |
|
330 |
val abstr = #2(dest_comb template) |
|
331 |
in |
|
332 |
thm RS (cterm_instantiate[(P',abstr), (x',witness)] exI) |
|
333 |
end |
|
334 |
end; |
|
335 |
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336 |
(*---------------------------------------------------------------------------- |
|
337 |
* |
|
338 |
* A |- M |
|
339 |
* ------------------- [v_1,...,v_n] |
|
340 |
* A |- ?v1...v_n. M |
|
341 |
* |
|
342 |
*---------------------------------------------------------------------------*) |
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343 |
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344 |
fun EXISTL vlist th = |
|
345 |
U.itlist (fn v => fn thm => EXISTS(D.mk_exists(v,cconcl thm), v) thm) |
|
346 |
vlist th; |
|
347 |
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348 |
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349 |
(*---------------------------------------------------------------------------- |
|
350 |
* |
|
351 |
* A |- M[x_1,...,x_n] |
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352 |
* ---------------------------- [(x |-> y)_1,...,(x |-> y)_n] |
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353 |
* A |- ?y_1...y_n. M |
|
354 |
* |
|
355 |
*---------------------------------------------------------------------------*) |
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3353
9112a2efb9a3
Removal of module Mask and datatype binding with its constructor |->
paulson
parents:
3332
diff
changeset
|
356 |
(* Could be improved, but needs "subst_free" for certified terms *) |
2112 | 357 |
|
358 |
fun IT_EXISTS blist th = |
|
359 |
let val {sign,...} = rep_thm th |
|
360 |
val tych = cterm_of sign |
|
361 |
val detype = #t o rep_cterm |
|
3353
9112a2efb9a3
Removal of module Mask and datatype binding with its constructor |->
paulson
parents:
3332
diff
changeset
|
362 |
val blist' = map (fn (x,y) => (detype x, detype y)) blist |
2112 | 363 |
fun ?v M = cterm_of sign (S.mk_exists{Bvar=v,Body = M}) |
364 |
||
365 |
in |
|
3353
9112a2efb9a3
Removal of module Mask and datatype binding with its constructor |->
paulson
parents:
3332
diff
changeset
|
366 |
U.itlist (fn (b as (r1,r2)) => fn thm => |
9112a2efb9a3
Removal of module Mask and datatype binding with its constructor |->
paulson
parents:
3332
diff
changeset
|
367 |
EXISTS(?r2(subst_free[b] |
9112a2efb9a3
Removal of module Mask and datatype binding with its constructor |->
paulson
parents:
3332
diff
changeset
|
368 |
(HOLogic.dest_Trueprop(#prop(rep_thm thm)))), tych r1) |
2112 | 369 |
thm) |
370 |
blist' th |
|
371 |
end; |
|
372 |
||
373 |
(*--------------------------------------------------------------------------- |
|
374 |
* Faster version, that fails for some as yet unknown reason |
|
375 |
* fun IT_EXISTS blist th = |
|
376 |
* let val {sign,...} = rep_thm th |
|
377 |
* val tych = cterm_of sign |
|
3353
9112a2efb9a3
Removal of module Mask and datatype binding with its constructor |->
paulson
parents:
3332
diff
changeset
|
378 |
* fun detype (x,y) = ((#t o rep_cterm) x, (#t o rep_cterm) y) |
2112 | 379 |
* in |
3353
9112a2efb9a3
Removal of module Mask and datatype binding with its constructor |->
paulson
parents:
3332
diff
changeset
|
380 |
* fold (fn (b as (r1,r2), thm) => |
9112a2efb9a3
Removal of module Mask and datatype binding with its constructor |->
paulson
parents:
3332
diff
changeset
|
381 |
* EXISTS(D.mk_exists(r2, tych(subst_free[detype b](#t(rep_cterm(cconcl thm))))), |
2112 | 382 |
* r1) thm) blist th |
383 |
* end; |
|
384 |
*---------------------------------------------------------------------------*) |
|
385 |
||
386 |
(*---------------------------------------------------------------------------- |
|
387 |
* Rewriting |
|
388 |
*---------------------------------------------------------------------------*) |
|
389 |
||
390 |
fun SUBS thl = |
|
391 |
rewrite_rule (map (fn th => (th RS eq_reflection) handle _ => th) thl); |
|
392 |
||
4713 | 393 |
local fun rew_conv mss = rewrite_cterm (true,false,false) mss (K(K None)) |
2112 | 394 |
in |
3405 | 395 |
fun simpl_conv ss thl ctm = |
3556 | 396 |
rew_conv (Thm.mss_of (#simps (Thm.dest_mss (#mss (rep_ss ss))) @ thl)) ctm |
2112 | 397 |
RS meta_eq_to_obj_eq |
398 |
end; |
|
399 |
||
400 |
local fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]) |
|
401 |
in |
|
402 |
val RIGHT_ASSOC = rewrite_rule [prover"((a|b)|c) = (a|(b|c))" RS eq_reflection] |
|
403 |
val ASM = refl RS iffD1 |
|
404 |
end; |
|
405 |
||
406 |
||
407 |
||
408 |
||
409 |
(*--------------------------------------------------------------------------- |
|
410 |
* TERMINATION CONDITION EXTRACTION |
|
411 |
*---------------------------------------------------------------------------*) |
|
412 |
||
413 |
||
414 |
(* Object language quantifier, i.e., "!" *) |
|
415 |
fun Forall v M = S.mk_forall{Bvar=v, Body=M}; |
|
416 |
||
417 |
||
418 |
(* Fragile: it's a cong if it is not "R y x ==> cut f R x y = f y" *) |
|
419 |
fun is_cong thm = |
|
420 |
let val {prop, ...} = rep_thm thm |
|
421 |
in case prop |
|
422 |
of (Const("==>",_)$(Const("Trueprop",_)$ _) $ |
|
423 |
(Const("==",_) $ (Const ("cut",_) $ f $ R $ a $ x) $ _)) => false |
|
424 |
| _ => true |
|
425 |
end; |
|
426 |
||
427 |
||
428 |
||
429 |
fun dest_equal(Const ("==",_) $ |
|
3379
7091ffa99c93
Simplified the calling sequence of CONTEXT_REWRITE_RULE
paulson
parents:
3353
diff
changeset
|
430 |
(Const ("Trueprop",_) $ lhs) |
7091ffa99c93
Simplified the calling sequence of CONTEXT_REWRITE_RULE
paulson
parents:
3353
diff
changeset
|
431 |
$ (Const ("Trueprop",_) $ rhs)) = {lhs=lhs, rhs=rhs} |
2112 | 432 |
| dest_equal(Const ("==",_) $ lhs $ rhs) = {lhs=lhs, rhs=rhs} |
433 |
| dest_equal tm = S.dest_eq tm; |
|
434 |
||
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
435 |
fun get_lhs tm = #lhs(dest_equal (HOLogic.dest_Trueprop tm)); |
2112 | 436 |
|
437 |
fun dest_all(Const("all",_) $ (a as Abs _)) = S.dest_abs a |
|
438 |
| dest_all _ = raise RULES_ERR{func = "dest_all", mesg = "not a !!"}; |
|
439 |
||
440 |
val is_all = Utils.can dest_all; |
|
441 |
||
442 |
fun strip_all fm = |
|
443 |
if (is_all fm) |
|
444 |
then let val {Bvar,Body} = dest_all fm |
|
445 |
val (bvs,core) = strip_all Body |
|
446 |
in ((Bvar::bvs), core) |
|
447 |
end |
|
448 |
else ([],fm); |
|
449 |
||
450 |
fun break_all(Const("all",_) $ Abs (_,_,body)) = body |
|
451 |
| break_all _ = raise RULES_ERR{func = "break_all", mesg = "not a !!"}; |
|
452 |
||
453 |
fun list_break_all(Const("all",_) $ Abs (s,ty,body)) = |
|
454 |
let val (L,core) = list_break_all body |
|
455 |
in ((s,ty)::L, core) |
|
456 |
end |
|
457 |
| list_break_all tm = ([],tm); |
|
458 |
||
459 |
(*--------------------------------------------------------------------------- |
|
460 |
* Rename a term of the form |
|
461 |
* |
|
462 |
* !!x1 ...xn. x1=M1 ==> ... ==> xn=Mn |
|
463 |
* ==> ((%v1...vn. Q) x1 ... xn = g x1 ... xn. |
|
464 |
* to one of |
|
465 |
* |
|
466 |
* !!v1 ... vn. v1=M1 ==> ... ==> vn=Mn |
|
467 |
* ==> ((%v1...vn. Q) v1 ... vn = g v1 ... vn. |
|
468 |
* |
|
469 |
* This prevents name problems in extraction, and helps the result to read |
|
470 |
* better. There is a problem with varstructs, since they can introduce more |
|
471 |
* than n variables, and some extra reasoning needs to be done. |
|
472 |
*---------------------------------------------------------------------------*) |
|
473 |
||
474 |
fun get ([],_,L) = rev L |
|
475 |
| get (ant::rst,n,L) = |
|
476 |
case (list_break_all ant) |
|
477 |
of ([],_) => get (rst, n+1,L) |
|
478 |
| (vlist,body) => |
|
479 |
let val eq = Logic.strip_imp_concl body |
|
480 |
val (f,args) = S.strip_comb (get_lhs eq) |
|
481 |
val (vstrl,_) = S.strip_abs f |
|
3405 | 482 |
val names = variantlist (map (#1 o dest_Free) vstrl, |
483 |
add_term_names(body, [])) |
|
2112 | 484 |
in get (rst, n+1, (names,n)::L) |
485 |
end handle _ => get (rst, n+1, L); |
|
486 |
||
487 |
(* Note: rename_params_rule counts from 1, not 0 *) |
|
488 |
fun rename thm = |
|
489 |
let val {prop,sign,...} = rep_thm thm |
|
490 |
val tych = cterm_of sign |
|
491 |
val ants = Logic.strip_imp_prems prop |
|
492 |
val news = get (ants,1,[]) |
|
493 |
in |
|
494 |
U.rev_itlist rename_params_rule news thm |
|
495 |
end; |
|
496 |
||
497 |
||
498 |
(*--------------------------------------------------------------------------- |
|
499 |
* Beta-conversion to the rhs of an equation (taken from hol90/drule.sml) |
|
500 |
*---------------------------------------------------------------------------*) |
|
501 |
||
502 |
fun list_beta_conv tm = |
|
503 |
let fun rbeta th = transitive th (beta_conversion(#2(D.dest_eq(cconcl th)))) |
|
504 |
fun iter [] = reflexive tm |
|
505 |
| iter (v::rst) = rbeta (combination(iter rst) (reflexive v)) |
|
506 |
in iter end; |
|
507 |
||
508 |
||
509 |
(*--------------------------------------------------------------------------- |
|
510 |
* Trace information for the rewriter |
|
511 |
*---------------------------------------------------------------------------*) |
|
512 |
val term_ref = ref[] : term list ref |
|
513 |
val mss_ref = ref [] : meta_simpset list ref; |
|
514 |
val thm_ref = ref [] : thm list ref; |
|
515 |
val tracing = ref false; |
|
516 |
||
3629 | 517 |
fun say s = if !tracing then prs s else (); |
2112 | 518 |
|
519 |
fun print_thms s L = |
|
520 |
(say s; |
|
521 |
map (fn th => say (string_of_thm th ^"\n")) L; |
|
522 |
say"\n"); |
|
523 |
||
524 |
fun print_cterms s L = |
|
525 |
(say s; |
|
526 |
map (fn th => say (string_of_cterm th ^"\n")) L; |
|
527 |
say"\n"); |
|
528 |
||
529 |
(*--------------------------------------------------------------------------- |
|
530 |
* General abstraction handlers, should probably go in USyntax. |
|
531 |
*---------------------------------------------------------------------------*) |
|
532 |
fun mk_aabs(vstr,body) = S.mk_abs{Bvar=vstr,Body=body} |
|
533 |
handle _ => S.mk_pabs{varstruct = vstr, body = body}; |
|
534 |
||
535 |
fun list_mk_aabs (vstrl,tm) = |
|
536 |
U.itlist (fn vstr => fn tm => mk_aabs(vstr,tm)) vstrl tm; |
|
537 |
||
538 |
fun dest_aabs tm = |
|
539 |
let val {Bvar,Body} = S.dest_abs tm |
|
540 |
in (Bvar,Body) |
|
541 |
end handle _ => let val {varstruct,body} = S.dest_pabs tm |
|
542 |
in (varstruct,body) |
|
543 |
end; |
|
544 |
||
545 |
fun strip_aabs tm = |
|
546 |
let val (vstr,body) = dest_aabs tm |
|
547 |
val (bvs, core) = strip_aabs body |
|
548 |
in (vstr::bvs, core) |
|
549 |
end |
|
550 |
handle _ => ([],tm); |
|
551 |
||
552 |
fun dest_combn tm 0 = (tm,[]) |
|
553 |
| dest_combn tm n = |
|
554 |
let val {Rator,Rand} = S.dest_comb tm |
|
555 |
val (f,rands) = dest_combn Rator (n-1) |
|
556 |
in (f,Rand::rands) |
|
557 |
end; |
|
558 |
||
559 |
||
560 |
||
561 |
||
562 |
local fun dest_pair M = let val {fst,snd} = S.dest_pair M in (fst,snd) end |
|
563 |
fun mk_fst tm = |
|
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
564 |
let val ty as Type("*", [fty,sty]) = type_of tm |
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
565 |
in Const ("fst", ty --> fty) $ tm end |
2112 | 566 |
fun mk_snd tm = |
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
567 |
let val ty as Type("*", [fty,sty]) = type_of tm |
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
568 |
in Const ("snd", ty --> sty) $ tm end |
2112 | 569 |
in |
570 |
fun XFILL tych x vstruct = |
|
571 |
let fun traverse p xocc L = |
|
3332 | 572 |
if (is_Free p) |
2112 | 573 |
then tych xocc::L |
574 |
else let val (p1,p2) = dest_pair p |
|
575 |
in traverse p1 (mk_fst xocc) (traverse p2 (mk_snd xocc) L) |
|
576 |
end |
|
577 |
in |
|
578 |
traverse vstruct x [] |
|
579 |
end end; |
|
580 |
||
581 |
(*--------------------------------------------------------------------------- |
|
582 |
* Replace a free tuple (vstr) by a universally quantified variable (a). |
|
583 |
* Note that the notion of "freeness" for a tuple is different than for a |
|
584 |
* variable: if variables in the tuple also occur in any other place than |
|
585 |
* an occurrences of the tuple, they aren't "free" (which is thus probably |
|
586 |
* the wrong word to use). |
|
587 |
*---------------------------------------------------------------------------*) |
|
588 |
||
589 |
fun VSTRUCT_ELIM tych a vstr th = |
|
590 |
let val L = S.free_vars_lr vstr |
|
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
591 |
val bind1 = tych (HOLogic.mk_Trueprop (HOLogic.mk_eq(a,vstr))) |
2112 | 592 |
val thm1 = implies_intr bind1 (SUBS [SYM(assume bind1)] th) |
593 |
val thm2 = forall_intr_list (map tych L) thm1 |
|
594 |
val thm3 = forall_elim_list (XFILL tych a vstr) thm2 |
|
595 |
in refl RS |
|
596 |
rewrite_rule[symmetric (surjective_pairing RS eq_reflection)] thm3 |
|
597 |
end; |
|
598 |
||
599 |
fun PGEN tych a vstr th = |
|
600 |
let val a1 = tych a |
|
601 |
val vstr1 = tych vstr |
|
602 |
in |
|
603 |
forall_intr a1 |
|
3332 | 604 |
(if (is_Free vstr) |
2112 | 605 |
then cterm_instantiate [(vstr1,a1)] th |
606 |
else VSTRUCT_ELIM tych a vstr th) |
|
607 |
end; |
|
608 |
||
609 |
||
610 |
(*--------------------------------------------------------------------------- |
|
611 |
* Takes apart a paired beta-redex, looking like "(\(x,y).N) vstr", into |
|
612 |
* |
|
613 |
* (([x,y],N),vstr) |
|
614 |
*---------------------------------------------------------------------------*) |
|
615 |
fun dest_pbeta_redex M n = |
|
616 |
let val (f,args) = dest_combn M n |
|
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
617 |
val dummy = dest_aabs f |
2112 | 618 |
in (strip_aabs f,args) |
619 |
end; |
|
620 |
||
621 |
fun pbeta_redex M n = U.can (U.C dest_pbeta_redex n) M; |
|
622 |
||
623 |
fun dest_impl tm = |
|
624 |
let val ants = Logic.strip_imp_prems tm |
|
625 |
val eq = Logic.strip_imp_concl tm |
|
626 |
in (ants,get_lhs eq) |
|
627 |
end; |
|
628 |
||
3405 | 629 |
fun restricted t = is_some (S.find_term |
630 |
(fn (Const("cut",_)) =>true | _ => false) |
|
631 |
t) |
|
2112 | 632 |
|
3405 | 633 |
fun CONTEXT_REWRITE_RULE (ss, func, R, cut_lemma, congs) th = |
634 |
let val pbeta_reduce = simpl_conv ss [split RS eq_reflection]; |
|
635 |
val tc_list = ref[]: term list ref |
|
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
636 |
val dummy = term_ref := [] |
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
637 |
val dummy = thm_ref := [] |
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
638 |
val dummy = mss_ref := [] |
2112 | 639 |
val cut_lemma' = (cut_lemma RS mp) RS eq_reflection |
640 |
fun prover mss thm = |
|
641 |
let fun cong_prover mss thm = |
|
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
642 |
let val dummy = say "cong_prover:\n" |
2112 | 643 |
val cntxt = prems_of_mss mss |
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
644 |
val dummy = print_thms "cntxt:\n" cntxt |
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
645 |
val dummy = say "cong rule:\n" |
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
646 |
val dummy = say (string_of_thm thm^"\n") |
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
647 |
val dummy = thm_ref := (thm :: !thm_ref) |
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
648 |
val dummy = mss_ref := (mss :: !mss_ref) |
2112 | 649 |
(* Unquantified eliminate *) |
650 |
fun uq_eliminate (thm,imp,sign) = |
|
651 |
let val tych = cterm_of sign |
|
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
652 |
val dummy = print_cterms "To eliminate:\n" [tych imp] |
2112 | 653 |
val ants = map tych (Logic.strip_imp_prems imp) |
654 |
val eq = Logic.strip_imp_concl imp |
|
655 |
val lhs = tych(get_lhs eq) |
|
656 |
val mss' = add_prems(mss, map ASSUME ants) |
|
4713 | 657 |
val lhs_eq_lhs1 = rewrite_cterm(false,true,false)mss' prover lhs |
2112 | 658 |
handle _ => reflexive lhs |
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
659 |
val dummy = print_thms "proven:\n" [lhs_eq_lhs1] |
2112 | 660 |
val lhs_eq_lhs2 = implies_intr_list ants lhs_eq_lhs1 |
661 |
val lhs_eeq_lhs2 = lhs_eq_lhs2 RS meta_eq_to_obj_eq |
|
662 |
in |
|
663 |
lhs_eeq_lhs2 COMP thm |
|
664 |
end |
|
665 |
fun pq_eliminate (thm,sign,vlist,imp_body,lhs_eq) = |
|
666 |
let val ((vstrl,_),args) = dest_pbeta_redex lhs_eq(length vlist) |
|
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
667 |
val dummy = assert (forall (op aconv) |
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
668 |
(ListPair.zip (vlist, args))) |
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
669 |
"assertion failed in CONTEXT_REWRITE_RULE" |
3353
9112a2efb9a3
Removal of module Mask and datatype binding with its constructor |->
paulson
parents:
3332
diff
changeset
|
670 |
val imp_body1 = subst_free (ListPair.zip (args, vstrl)) |
9112a2efb9a3
Removal of module Mask and datatype binding with its constructor |->
paulson
parents:
3332
diff
changeset
|
671 |
imp_body |
2112 | 672 |
val tych = cterm_of sign |
673 |
val ants1 = map tych (Logic.strip_imp_prems imp_body1) |
|
674 |
val eq1 = Logic.strip_imp_concl imp_body1 |
|
675 |
val Q = get_lhs eq1 |
|
676 |
val QeqQ1 = pbeta_reduce (tych Q) |
|
677 |
val Q1 = #2(D.dest_eq(cconcl QeqQ1)) |
|
678 |
val mss' = add_prems(mss, map ASSUME ants1) |
|
4713 | 679 |
val Q1eeqQ2 = rewrite_cterm (false,true,false) mss' prover Q1 |
2112 | 680 |
handle _ => reflexive Q1 |
3379
7091ffa99c93
Simplified the calling sequence of CONTEXT_REWRITE_RULE
paulson
parents:
3353
diff
changeset
|
681 |
val Q2 = #2 (Logic.dest_equals (#prop(rep_thm Q1eeqQ2))) |
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
682 |
val Q3 = tych(list_comb(list_mk_aabs(vstrl,Q2),vstrl)) |
2112 | 683 |
val Q2eeqQ3 = symmetric(pbeta_reduce Q3 RS eq_reflection) |
684 |
val thA = transitive(QeqQ1 RS eq_reflection) Q1eeqQ2 |
|
685 |
val QeeqQ3 = transitive thA Q2eeqQ3 handle _ => |
|
686 |
((Q2eeqQ3 RS meta_eq_to_obj_eq) |
|
687 |
RS ((thA RS meta_eq_to_obj_eq) RS trans)) |
|
688 |
RS eq_reflection |
|
689 |
val impth = implies_intr_list ants1 QeeqQ3 |
|
690 |
val impth1 = impth RS meta_eq_to_obj_eq |
|
691 |
(* Need to abstract *) |
|
692 |
val ant_th = U.itlist2 (PGEN tych) args vstrl impth1 |
|
693 |
in ant_th COMP thm |
|
694 |
end |
|
695 |
fun q_eliminate (thm,imp,sign) = |
|
696 |
let val (vlist,imp_body) = strip_all imp |
|
697 |
val (ants,Q) = dest_impl imp_body |
|
698 |
in if (pbeta_redex Q) (length vlist) |
|
699 |
then pq_eliminate (thm,sign,vlist,imp_body,Q) |
|
700 |
else |
|
701 |
let val tych = cterm_of sign |
|
702 |
val ants1 = map tych ants |
|
703 |
val mss' = add_prems(mss, map ASSUME ants1) |
|
4713 | 704 |
val Q_eeq_Q1 = rewrite_cterm(false,true,false) mss' |
2112 | 705 |
prover (tych Q) |
706 |
handle _ => reflexive (tych Q) |
|
707 |
val lhs_eeq_lhs2 = implies_intr_list ants1 Q_eeq_Q1 |
|
708 |
val lhs_eq_lhs2 = lhs_eeq_lhs2 RS meta_eq_to_obj_eq |
|
709 |
val ant_th = forall_intr_list(map tych vlist)lhs_eq_lhs2 |
|
710 |
in |
|
711 |
ant_th COMP thm |
|
712 |
end end |
|
713 |
||
714 |
fun eliminate thm = |
|
715 |
case (rep_thm thm) |
|
716 |
of {prop = (Const("==>",_) $ imp $ _), sign, ...} => |
|
717 |
eliminate |
|
718 |
(if not(is_all imp) |
|
719 |
then uq_eliminate (thm,imp,sign) |
|
720 |
else q_eliminate (thm,imp,sign)) |
|
721 |
(* Assume that the leading constant is ==, *) |
|
722 |
| _ => thm (* if it is not a ==> *) |
|
723 |
in Some(eliminate (rename thm)) |
|
724 |
end handle _ => None |
|
725 |
||
726 |
fun restrict_prover mss thm = |
|
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
727 |
let val dummy = say "restrict_prover:\n" |
2112 | 728 |
val cntxt = rev(prems_of_mss mss) |
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
729 |
val dummy = print_thms "cntxt:\n" cntxt |
2112 | 730 |
val {prop = Const("==>",_) $ (Const("Trueprop",_) $ A) $ _, |
731 |
sign,...} = rep_thm thm |
|
3391
5e45dd3b64e9
More de-HOLification: using Free, Const, etc. instead of mk_var, mk_const
paulson
parents:
3379
diff
changeset
|
732 |
fun genl tm = let val vlist = gen_rems (op aconv) |
5e45dd3b64e9
More de-HOLification: using Free, Const, etc. instead of mk_var, mk_const
paulson
parents:
3379
diff
changeset
|
733 |
(add_term_frees(tm,[]), [func,R]) |
2112 | 734 |
in U.itlist Forall vlist tm |
735 |
end |
|
736 |
(*-------------------------------------------------------------- |
|
737 |
* This actually isn't quite right, since it will think that |
|
738 |
* not-fully applied occs. of "f" in the context mean that the |
|
739 |
* current call is nested. The real solution is to pass in a |
|
740 |
* term "f v1..vn" which is a pattern that any full application |
|
741 |
* of "f" will match. |
|
742 |
*-------------------------------------------------------------*) |
|
3405 | 743 |
val func_name = #1(dest_Const func) |
744 |
fun is_func (Const (name,_)) = (name = func_name) |
|
745 |
| is_func _ = false |
|
2112 | 746 |
val rcontext = rev cntxt |
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
747 |
val cncl = HOLogic.dest_Trueprop o #prop o rep_thm |
2112 | 748 |
val antl = case rcontext of [] => [] |
749 |
| _ => [S.list_mk_conj(map cncl rcontext)] |
|
750 |
val TC = genl(S.list_mk_imp(antl, A)) |
|
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
751 |
val dummy = print_cterms "func:\n" [cterm_of sign func] |
3379
7091ffa99c93
Simplified the calling sequence of CONTEXT_REWRITE_RULE
paulson
parents:
3353
diff
changeset
|
752 |
val dummy = print_cterms "TC:\n" |
7091ffa99c93
Simplified the calling sequence of CONTEXT_REWRITE_RULE
paulson
parents:
3353
diff
changeset
|
753 |
[cterm_of sign (HOLogic.mk_Trueprop TC)] |
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
754 |
val dummy = tc_list := (TC :: !tc_list) |
3405 | 755 |
val nestedp = is_some (S.find_term is_func TC) |
3379
7091ffa99c93
Simplified the calling sequence of CONTEXT_REWRITE_RULE
paulson
parents:
3353
diff
changeset
|
756 |
val dummy = if nestedp then say"nested\n" else say"not_nested\n" |
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
757 |
val dummy = term_ref := ([func,TC]@(!term_ref)) |
2112 | 758 |
val th' = if nestedp then raise RULES_ERR{func = "solver", |
759 |
mesg = "nested function"} |
|
3379
7091ffa99c93
Simplified the calling sequence of CONTEXT_REWRITE_RULE
paulson
parents:
3353
diff
changeset
|
760 |
else let val cTC = cterm_of sign |
7091ffa99c93
Simplified the calling sequence of CONTEXT_REWRITE_RULE
paulson
parents:
3353
diff
changeset
|
761 |
(HOLogic.mk_Trueprop TC) |
2112 | 762 |
in case rcontext of |
763 |
[] => SPEC_ALL(ASSUME cTC) |
|
764 |
| _ => MP (SPEC_ALL (ASSUME cTC)) |
|
765 |
(LIST_CONJ rcontext) |
|
766 |
end |
|
767 |
val th'' = th' RS thm |
|
768 |
in Some (th'') |
|
769 |
end handle _ => None |
|
770 |
in |
|
771 |
(if (is_cong thm) then cong_prover else restrict_prover) mss thm |
|
772 |
end |
|
773 |
val ctm = cprop_of th |
|
4713 | 774 |
val th1 = rewrite_cterm(false,true,false) (add_congs(mss_of [cut_lemma'], congs)) |
2112 | 775 |
prover ctm |
776 |
val th2 = equal_elim th1 th |
|
777 |
in |
|
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset
|
778 |
(th2, filter (not o restricted) (!tc_list)) |
2112 | 779 |
end; |
780 |
||
781 |
||
782 |
||
3405 | 783 |
fun prove (ptm,tac) = |
784 |
#1 (freeze_thaw (prove_goalw_cterm [] ptm (fn _ => [tac]))); |
|
2112 | 785 |
|
786 |
||
787 |
end; (* Rules *) |