diff -r 8939b8fd8603 -r 069d525f8f1d CookBook/Package/simple_inductive_package.ML --- a/CookBook/Package/simple_inductive_package.ML Wed Mar 18 23:52:51 2009 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,243 +0,0 @@ -(* @chunk SIMPLE_INDUCTIVE_PACKAGE *) -signature SIMPLE_INDUCTIVE_PACKAGE = -sig - val add_inductive_i: - ((Binding.binding * typ) * mixfix) list -> (*{predicates}*) - (Binding.binding * typ) list -> (*{parameters}*) - (Attrib.binding * term) list -> (*{rules}*) - local_theory -> local_theory - - val add_inductive: - (Binding.binding * string option * mixfix) list -> (*{predicates}*) - (Binding.binding * string option * mixfix) list -> (*{parameters}*) - (Attrib.binding * string) list -> (*{rules}*) - local_theory -> local_theory -end; -(* @end *) - -structure SimpleInductivePackage: SIMPLE_INDUCTIVE_PACKAGE = -struct - -(* @chunk make_definitions *) -fun make_defs ((binding, syn), trm) lthy = -let - val arg = ((binding, syn), (Attrib.empty_binding, trm)) - val ((_, (_ , thm)), lthy) = LocalTheory.define Thm.internalK arg lthy -in - (thm, lthy) -end -(* @end *) - -(* @chunk definitions_aux *) -fun defs_aux lthy orules preds params (pred, arg_types) = -let - fun mk_all x P = HOLogic.all_const (fastype_of x) $ lambda x P - - val fresh_args = - arg_types - |> map (pair "z") - |> Variable.variant_frees lthy orules - |> map Free -in - list_comb (pred, fresh_args) - |> fold_rev (curry HOLogic.mk_imp) orules - |> fold_rev mk_all preds - |> fold_rev lambda (params @ fresh_args) -end -(* @end *) - -(* @chunk definitions *) -fun definitions rules params preds prednames syns arg_typess lthy = -let - val thy = ProofContext.theory_of lthy - val orules = map (ObjectLogic.atomize_term thy) rules - val defs = - map (defs_aux lthy orules preds params) (preds ~~ arg_typess) -in - fold_map make_defs (prednames ~~ syns ~~ defs) lthy -end -(* @end *) - -fun inst_spec ct = - Drule.instantiate' [SOME (ctyp_of_term ct)] [NONE, SOME ct] @{thm spec}; - -(* @chunk induction_tac *) -fun induction_tac defs prems insts = - EVERY1 [ObjectLogic.full_atomize_tac, - cut_facts_tac prems, - K (rewrite_goals_tac defs), - EVERY' (map (dtac o inst_spec) insts), - assume_tac] -(* @end *) - -(* @chunk induction_rules *) -fun inductions rules defs parnames preds Tss lthy1 = -let - val (_, lthy2) = Variable.add_fixes parnames lthy1 - - val Ps = replicate (length preds) "P" - val (newprednames, lthy3) = Variable.variant_fixes Ps lthy2 - - val thy = ProofContext.theory_of lthy3 - - val Tss' = map (fn Ts => Ts ---> HOLogic.boolT) Tss - val newpreds = map Free (newprednames ~~ Tss') - val cnewpreds = map (cterm_of thy) newpreds - val rules' = map (subst_free (preds ~~ newpreds)) rules - - fun prove_induction ((pred, newpred), Ts) = - let - val (newargnames, lthy4) = - Variable.variant_fixes (replicate (length Ts) "z") lthy3; - val newargs = map Free (newargnames ~~ Ts) - - val prem = HOLogic.mk_Trueprop (list_comb (pred, newargs)) - val goal = Logic.list_implies - (rules', HOLogic.mk_Trueprop (list_comb (newpred, newargs))) - in - Goal.prove lthy4 [] [prem] goal - (fn {prems, ...} => induction_tac defs prems cnewpreds) - |> singleton (ProofContext.export lthy4 lthy1) - end -in - map prove_induction (preds ~~ newpreds ~~ Tss) -end -(* @end *) - -val all_elims = fold (fn ct => fn th => th RS inst_spec ct); -val imp_elims = fold (fn th => fn th' => [th', th] MRS @{thm mp}); - - -(* @chunk subproof1 *) -fun subproof2 prem params2 prems2 = - SUBPROOF (fn {prems, ...} => - let - val prem' = prems MRS prem; - val prem'' = - case prop_of prem' of - _ $ (Const (@{const_name All}, _) $ _) => - prem' |> all_elims params2 - |> imp_elims prems2 - | _ => prem'; - in - rtac prem'' 1 - end) -(* @end *) - -(* @chunk subproof2 *) -fun subproof1 rules preds i = - SUBPROOF (fn {params, prems, context = ctxt', ...} => - let - val (prems1, prems2) = chop (length prems - length rules) prems; - val (params1, params2) = chop (length params - length preds) params; - in - rtac (ObjectLogic.rulify (all_elims params1 (nth prems2 i))) 1 - THEN - EVERY1 (map (fn prem => subproof2 prem params2 prems2 ctxt') prems1) - end) -(* @end *) - -fun introductions_tac defs rules preds i ctxt = - EVERY1 [ObjectLogic.rulify_tac, - K (rewrite_goals_tac defs), - REPEAT o (resolve_tac [@{thm allI},@{thm impI}]), - subproof1 rules preds i ctxt] - - -(* @chunk intro_rules *) -fun introductions rules parnames preds defs lthy1 = -let - val (_, lthy2) = Variable.add_fixes parnames lthy1 - - fun prove_intro (i, goal) = - Goal.prove lthy2 [] [] goal - (fn {context, ...} => introductions_tac defs rules preds i context) - |> singleton (ProofContext.export lthy2 lthy1) -in - map_index prove_intro rules -end -(* @end *) - -(* @chunk add_inductive_i *) -fun add_inductive_i preds params specs lthy = -let - val params' = map (fn (p, T) => Free (Binding.name_of p, T)) params; - val preds' = map (fn ((R, T), _) => list_comb (Free (Binding.name_of R, T), params')) preds; - val Tss = map (binder_types o fastype_of) preds'; - val (ass, rules) = split_list specs; (* FIXME: ass not used? *) - - val prednames = map (fst o fst) preds - val syns = map snd preds - val parnames = map (Binding.name_of o fst) params - - val (defs, lthy1) = definitions rules params' preds' prednames syns Tss lthy; - - val inducts = inductions rules defs parnames preds' Tss lthy1 - - val intros = introductions rules parnames preds' defs lthy1 - - val mut_name = space_implode "_" (map (Binding.name_of o fst o fst) preds); - val case_names = map (Binding.name_of o fst o fst) specs -in - lthy1 - |> LocalTheory.notes Thm.theoremK (map (fn (((a, atts), _), th) => - ((Binding.qualify false mut_name a, atts), [([th], [])])) (specs ~~ intros)) - |-> (fn intross => LocalTheory.note Thm.theoremK - ((Binding.qualify false mut_name (Binding.name "intros"), []), maps snd intross)) - |>> snd - ||>> (LocalTheory.notes Thm.theoremK (map (fn (((R, _), _), th) => - ((Binding.qualify false (Binding.name_of R) (Binding.name "induct"), - [Attrib.internal (K (RuleCases.case_names case_names)), - Attrib.internal (K (RuleCases.consumes 1)), - Attrib.internal (K (Induct.induct_pred ""))]), [([th], [])])) - (preds ~~ inducts)) #>> maps snd) - |> snd -end -(* @end *) - -(* @chunk read_specification *) -fun read_specification' vars specs lthy = -let - val specs' = map (fn (a, s) => (a, [s])) specs - val ((varst, specst), _) = - Specification.read_specification vars specs' lthy - val specst' = map (apsnd the_single) specst -in - (varst, specst') -end -(* @end *) - -(* @chunk add_inductive *) -fun add_inductive preds params specs lthy = -let - val (vars, specs') = read_specification' (preds @ params) specs lthy; - val (preds', params') = chop (length preds) vars; - val params'' = map fst params' -in - add_inductive_i preds' params'' specs' lthy -end; -(* @end *) - -(* @chunk parser *) -val spec_parser = - OuterParse.opt_target -- - OuterParse.fixes -- - OuterParse.for_fixes -- - Scan.optional - (OuterParse.$$$ "where" |-- - OuterParse.!!! - (OuterParse.enum1 "|" - (SpecParse.opt_thm_name ":" -- OuterParse.prop))) [] -(* @end *) - -(* @chunk syntax *) -val specification = - spec_parser >> - (fn (((loc, preds), params), specs) => - Toplevel.local_theory loc (add_inductive preds params specs)) - -val _ = OuterSyntax.command "simple_inductive" "define inductive predicates" - OuterKeyword.thy_decl specification -(* @end *) - -end;