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TFL/post.ML

author | skalberg |

Thu, 03 Mar 2005 12:43:01 +0100 | |

changeset 15570 | 8d8c70b41bab |

parent 15531 | 08c8dad8e399 |

child 15574 | b1d1b5bfc464 |

permissions | -rw-r--r-- |

Move towards standard functions.

(* Title: TFL/post.ML ID: $Id$ Author: Konrad Slind, Cambridge University Computer Laboratory Copyright 1997 University of Cambridge Second part of main module (postprocessing of TFL definitions). *) signature TFL = sig val trace: bool ref val quiet_mode: bool ref val message: string -> unit val tgoalw: theory -> thm list -> thm list -> thm list val tgoal: theory -> thm list -> thm list val define_i: bool -> theory -> claset -> simpset -> thm list -> thm list -> xstring -> term -> term list -> theory * {rules: (thm * int) list, induct: thm, tcs: term list} val define: bool -> theory -> claset -> simpset -> thm list -> thm list -> xstring -> string -> string list -> theory * {rules: (thm * int) list, induct: thm, tcs: term list} val defer_i: theory -> thm list -> xstring -> term list -> theory * thm val defer: theory -> thm list -> xstring -> string list -> theory * thm end; structure Tfl: TFL = struct structure S = USyntax (* messages *) val trace = Prim.trace val quiet_mode = ref false; fun message s = if ! quiet_mode then () else writeln s; (* misc *) val read_term = Thm.term_of oo (HOLogic.read_cterm o Theory.sign_of); (*--------------------------------------------------------------------------- * Extract termination goals so that they can be put it into a goalstack, or * have a tactic directly applied to them. *--------------------------------------------------------------------------*) fun termination_goals rules = map (#1 o Type.freeze_thaw o HOLogic.dest_Trueprop) (Library.foldr (fn (th,A) => union_term (prems_of th, A)) (rules, [])); (*--------------------------------------------------------------------------- * Finds the termination conditions in (highly massaged) definition and * puts them into a goalstack. *--------------------------------------------------------------------------*) fun tgoalw thy defs rules = case termination_goals rules of [] => error "tgoalw: no termination conditions to prove" | L => goalw_cterm defs (Thm.cterm_of (Theory.sign_of thy) (HOLogic.mk_Trueprop(USyntax.list_mk_conj L))); fun tgoal thy = tgoalw thy []; (*--------------------------------------------------------------------------- * Three postprocessors are applied to the definition. It * attempts to prove wellfoundedness of the given relation, simplifies the * non-proved termination conditions, and finally attempts to prove the * simplified termination conditions. *--------------------------------------------------------------------------*) fun std_postprocessor strict cs ss wfs = Prim.postprocess strict {wf_tac = REPEAT (ares_tac wfs 1), terminator = asm_simp_tac ss 1 THEN TRY (silent_arith_tac 1 ORELSE fast_tac (cs addSDs [not0_implies_Suc] addss ss) 1), simplifier = Rules.simpl_conv ss []}; val concl = #2 o Rules.dest_thm; (*--------------------------------------------------------------------------- * Postprocess a definition made by "define". This is a separate stage of * processing from the definition stage. *---------------------------------------------------------------------------*) local structure R = Rules structure U = Utils (* The rest of these local definitions are for the tricky nested case *) val solved = not o can S.dest_eq o #2 o S.strip_forall o concl fun id_thm th = let val {lhs,rhs} = S.dest_eq (#2 (S.strip_forall (#2 (R.dest_thm th)))); in lhs aconv rhs end handle U.ERR _ => false; fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]); val P_imp_P_iff_True = prover "P --> (P= True)" RS mp; val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection; fun mk_meta_eq r = case concl_of r of Const("==",_)$_$_ => r | _ $(Const("op =",_)$_$_) => r RS eq_reflection | _ => r RS P_imp_P_eq_True (*Is this the best way to invoke the simplifier??*) fun rewrite L = rewrite_rule (map mk_meta_eq (List.filter(not o id_thm) L)) fun join_assums th = let val {sign,...} = rep_thm th val tych = cterm_of sign val {lhs,rhs} = S.dest_eq(#2 (S.strip_forall (concl th))) val cntxtl = (#1 o S.strip_imp) lhs (* cntxtl should = cntxtr *) val cntxtr = (#1 o S.strip_imp) rhs (* but union is solider *) val cntxt = gen_union (op aconv) (cntxtl, cntxtr) in R.GEN_ALL (R.DISCH_ALL (rewrite (map (R.ASSUME o tych) cntxt) (R.SPEC_ALL th))) end val gen_all = S.gen_all in fun proof_stage strict cs ss wfs theory {f, R, rules, full_pats_TCs, TCs} = let val _ = message "Proving induction theorem ..." val ind = Prim.mk_induction theory {fconst=f, R=R, SV=[], pat_TCs_list=full_pats_TCs} val _ = message "Postprocessing ..."; val {rules, induction, nested_tcs} = std_postprocessor strict cs ss wfs theory {rules=rules, induction=ind, TCs=TCs} in case nested_tcs of [] => {induction=induction, rules=rules,tcs=[]} | L => let val dummy = message "Simplifying nested TCs ..." val (solved,simplified,stubborn) = U.itlist (fn th => fn (So,Si,St) => if (id_thm th) then (So, Si, th::St) else if (solved th) then (th::So, Si, St) else (So, th::Si, St)) nested_tcs ([],[],[]) val simplified' = map join_assums simplified val dummy = (Prim.trace_thms "solved =" solved; Prim.trace_thms "simplified' =" simplified') val rewr = full_simplify (ss addsimps (solved @ simplified')); val dummy = Prim.trace_thms "Simplifying the induction rule..." [induction] val induction' = rewr induction val dummy = Prim.trace_thms "Simplifying the recursion rules..." [rules] val rules' = rewr rules val _ = message "... Postprocessing finished"; in {induction = induction', rules = rules', tcs = map (gen_all o S.rhs o #2 o S.strip_forall o concl) (simplified@stubborn)} end end; (*lcp: curry the predicate of the induction rule*) fun curry_rule rl = SplitRule.split_rule_var (Term.head_of (HOLogic.dest_Trueprop (concl_of rl)), rl); (*lcp: put a theorem into Isabelle form, using meta-level connectives*) val meta_outer = curry_rule o standard o rule_by_tactic (REPEAT (FIRSTGOAL (resolve_tac [allI, impI, conjI] ORELSE' etac conjE))); (*Strip off the outer !P*) val spec'= read_instantiate [("x","P::?'b=>bool")] spec; fun tracing true _ = () | tracing false msg = writeln msg; fun simplify_defn strict thy cs ss congs wfs id pats def0 = let val def = freezeT def0 RS meta_eq_to_obj_eq val {theory,rules,rows,TCs,full_pats_TCs} = Prim.post_definition congs (thy, (def,pats)) val {lhs=f,rhs} = S.dest_eq (concl def) val (_,[R,_]) = S.strip_comb rhs val dummy = Prim.trace_thms "congs =" congs (*the next step has caused simplifier looping in some cases*) val {induction, rules, tcs} = proof_stage strict cs ss wfs theory {f = f, R = R, rules = rules, full_pats_TCs = full_pats_TCs, TCs = TCs} val rules' = map (standard o ObjectLogic.rulify_no_asm) (R.CONJUNCTS rules) in {induct = meta_outer (ObjectLogic.rulify_no_asm (induction RS spec')), rules = ListPair.zip(rules', rows), tcs = (termination_goals rules') @ tcs} end handle U.ERR {mesg,func,module} => error (mesg ^ "\n (In TFL function " ^ module ^ "." ^ func ^ ")"); (* Derive the initial equations from the case-split rules to meet the users specification of the recursive function. Note: We don't do this if the wf conditions fail to be solved, as each case may have a different wf condition. We could group the conditions together and say that they must be true to solve the general case, but that would hide from the user which sub-case they were related to. Probably this is not important, and it would work fine, but, for now, I prefer leaving more fine-grain control to the user. -- Lucas Dixon, Aug 2004 *) local fun get_related_thms i = List.mapPartial ((fn (r,x) => if x = i then SOME r else NONE)); fun solve_eq (th, [], i) = raise ERROR_MESSAGE "derive_init_eqs: missing rules" | solve_eq (th, [a], i) = [(a, i)] | solve_eq (th, splitths as (_ :: _), i) = (writeln "Proving unsplit equation..."; [((standard o ObjectLogic.rulify_no_asm) (CaseSplit.splitto splitths th), i)]) (* if there's an error, pretend nothing happened with this definition We should probably print something out so that the user knows...? *) handle ERROR_MESSAGE s => (writeln ("WARNING:post.ML:solve_eq: " ^ s); map (fn x => (x,i)) splitths); in fun derive_init_eqs sgn rules eqs = let val eqths = map (Thm.trivial o (Thm.cterm_of sgn) o HOLogic.mk_Trueprop) eqs fun countlist l = (rev o snd o (Library.foldl (fn ((i,L), e) => (i + 1,(e,i) :: L)))) ((0,[]), l) in List.concat (map (fn (e,i) => solve_eq (e, (get_related_thms i rules), i)) (countlist eqths)) end; end; (*--------------------------------------------------------------------------- * Defining a function with an associated termination relation. *---------------------------------------------------------------------------*) fun define_i strict thy cs ss congs wfs fid R eqs = let val {functional,pats} = Prim.mk_functional thy eqs val (thy, def) = Prim.wfrec_definition0 thy (Sign.base_name fid) R functional val {induct, rules, tcs} = simplify_defn strict thy cs ss congs wfs fid pats def val rules' = if strict then derive_init_eqs (Theory.sign_of thy) rules eqs else rules in (thy, {rules = rules', induct = induct, tcs = tcs}) end; fun define strict thy cs ss congs wfs fid R seqs = define_i strict thy cs ss congs wfs fid (read_term thy R) (map (read_term thy) seqs) handle U.ERR {mesg,...} => error mesg; (*--------------------------------------------------------------------------- * * Definitions with synthesized termination relation * *---------------------------------------------------------------------------*) fun func_of_cond_eqn tm = #1 (S.strip_comb (#lhs (S.dest_eq (#2 (S.strip_forall (#2 (S.strip_imp tm))))))); fun defer_i thy congs fid eqs = let val {rules,R,theory,full_pats_TCs,SV,...} = Prim.lazyR_def thy (Sign.base_name fid) congs eqs val f = func_of_cond_eqn (concl (R.CONJUNCT1 rules handle U.ERR _ => rules)); val dummy = message "Proving induction theorem ..."; val induction = Prim.mk_induction theory {fconst=f, R=R, SV=SV, pat_TCs_list=full_pats_TCs} in (theory, (*return the conjoined induction rule and recursion equations, with assumptions remaining to discharge*) standard (induction RS (rules RS conjI))) end fun defer thy congs fid seqs = defer_i thy congs fid (map (read_term thy) seqs) handle U.ERR {mesg,...} => error mesg; end; end;