author  haftmann 
Fri, 20 Feb 2009 10:14:32 +0100  
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child 30024  5e9d471afef3 
permissions  rwrr 
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(* Title: Tools/code/code_wellsorted.ML 
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Author: Florian Haftmann, TU Muenchen 
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Retrieving, wellsorting and structuring code equations in graph 
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with explicit dependencies  the Waisenhaus algorithm. 
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*) 
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signature CODE_FUNCGR = 
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sig 
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type T 
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val eqns: T > string > (thm * bool) list 
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val typ: T > string > (string * sort) list * typ 
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val all: T > string list 
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val pretty: theory > T > Pretty.T 
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val make: theory > string list 
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> ((sort > sort) * Sorts.algebra) * T 
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val eval_conv: theory 
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> (term > term * (((sort > sort) * Sorts.algebra) > T > thm)) > cterm > thm 
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val eval_term: theory 
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> (term > term * (((sort > sort) * Sorts.algebra) > T > 'a)) > term > 'a 
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end 
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structure Code_Funcgr : CODE_FUNCGR = 
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struct 
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(** the equation graph type **) 
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type T = (((string * sort) list * typ) * (thm * bool) list) Graph.T; 
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fun eqns eqngr = these o Option.map snd o try (Graph.get_node eqngr); 
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fun typ eqngr = fst o Graph.get_node eqngr; 
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fun all eqngr = Graph.keys eqngr; 
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fun pretty thy eqngr = 
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AList.make (snd o Graph.get_node eqngr) (Graph.keys eqngr) 
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> (map o apfst) (Code_Unit.string_of_const thy) 
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> sort (string_ord o pairself fst) 
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> map (fn (s, thms) => 
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(Pretty.block o Pretty.fbreaks) ( 
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Pretty.str s 
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:: map (Display.pretty_thm o fst) thms 
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)) 
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> Pretty.chunks; 
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(** the Waisenhaus algorithm **) 
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(* auxiliary *) 
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fun complete_proper_sort thy = 
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Sign.complete_sort thy #> filter (can (AxClass.get_info thy)); 
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fun inst_params thy tyco class = 
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map (fn (c, _) => AxClass.param_of_inst thy (c, tyco)) 
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((#params o AxClass.get_info thy) class); 
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fun consts_of thy eqns = [] > (fold o fold o fold_aterms) 
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(fn Const (c, ty) => insert (op =) (c, Sign.const_typargs thy (c, Logic.unvarifyT ty))  _ => I) 
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(map (op :: o swap o apfst (snd o strip_comb) o Logic.dest_equals o Thm.plain_prop_of o fst) eqns); 
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fun tyscm_rhss_of thy c eqns = 
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let 
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val tyscm = case eqns of [] => Code.default_typscheme thy c 
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 ((thm, _) :: _) => (snd o Code_Unit.head_eqn thy) thm; 
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val rhss = consts_of thy eqns; 
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in (tyscm, rhss) end; 
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(* data structures *) 
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datatype const = Fun of string  Inst of class * string; 
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fun const_ord (Fun c1, Fun c2) = fast_string_ord (c1, c2) 
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 const_ord (Inst class_tyco1, Inst class_tyco2) = 
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prod_ord fast_string_ord fast_string_ord (class_tyco1, class_tyco2) 
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 const_ord (Fun _, Inst _) = LESS 
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 const_ord (Inst _, Fun _) = GREATER; 
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type var = const * int; 
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structure Vargraph = 
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GraphFun(type key = var val ord = prod_ord const_ord int_ord); 
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datatype styp = Tyco of string * styp list  Var of var; 
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(* computing instantiations *) 
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fun obtain_eqns thy eqngr c = 
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case try (Graph.get_node eqngr) c 
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of SOME ((lhs, _), eqns) => ((lhs, []), eqns) 
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 NONE => let 
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val eqns = Code.these_eqns thy c 
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> burrow_fst (Code_Unit.norm_args thy) 
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> burrow_fst (Code_Unit.norm_varnames thy Code_Name.purify_tvar Code_Name.purify_var); 
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val ((lhs, _), rhss) = tyscm_rhss_of thy c eqns; 
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in ((lhs, rhss), eqns) end; 
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fun obtain_instance thy arities (inst as (class, tyco)) = 
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case AList.lookup (op =) arities inst 
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of SOME classess => (classess, ([], [])) 
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 NONE => let 
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val classess = map (complete_proper_sort thy) 
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(Sign.arity_sorts thy tyco [class]); 
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val superclasses = [class] 
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> complete_proper_sort thy 
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> remove (op =) class; 
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val inst_params = inst_params thy tyco class; 
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in (classess, (superclasses, inst_params)) end; 
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fun add_classes thy arities eqngr c_k new_classes vardeps_data = 
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let 
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val (styps, old_classes) = Vargraph.get_node (fst vardeps_data) c_k; 
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val diff_classes = new_classes > subtract (op =) old_classes; 
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in if null diff_classes then vardeps_data 
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else let 
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val c_ks = Vargraph.imm_succs (fst vardeps_data) c_k > insert (op =) c_k; 
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in 
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vardeps_data 
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> (apfst o Vargraph.map_node c_k o apsnd) (append diff_classes) 
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> fold (fn styp => fold (add_typmatch_inst thy arities eqngr styp) new_classes) styps 
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> fold (fn c_k => add_classes thy arities eqngr c_k diff_classes) c_ks 
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end end 
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and add_styp thy arities eqngr c_k tyco_styps vardeps_data = 
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let 
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val (old_styps, classes) = Vargraph.get_node (fst vardeps_data) c_k; 
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in if member (op =) old_styps tyco_styps then vardeps_data 
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else 
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vardeps_data 
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> (apfst o Vargraph.map_node c_k o apfst) (cons tyco_styps) 
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> fold (add_typmatch_inst thy arities eqngr tyco_styps) classes 
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end 
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and add_dep thy arities eqngr c_k c_k' vardeps_data = 
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let 
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val (_, classes) = Vargraph.get_node (fst vardeps_data) c_k; 
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in 
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vardeps_data 
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> add_classes thy arities eqngr c_k' classes 
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> apfst (Vargraph.add_edge (c_k, c_k')) 
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end 
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and add_typmatch_inst thy arities eqngr (tyco, styps) class vardeps_data = 
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if can (Sign.arity_sorts thy tyco) [class] 
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then vardeps_data 
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> assert thy arities eqngr (Inst (class, tyco)) 
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> fold_index (fn (k, styp) => 
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add_typmatch thy arities eqngr styp (Inst (class, tyco), k)) styps 
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else vardeps_data (*permissive!*) 
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and add_typmatch thy arities eqngr (Var c_k') c_k vardeps_data = 
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vardeps_data 
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> add_dep thy arities eqngr c_k c_k' 
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 add_typmatch thy arities eqngr (Tyco tyco_styps) c_k vardeps_data = 
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vardeps_data 
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> add_styp thy arities eqngr c_k tyco_styps 
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and add_inst thy arities eqngr (inst as (class, tyco)) vardeps_data = 
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let 
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val (classess, (superclasses, inst_params)) = 
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obtain_instance thy arities inst; 
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in 
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vardeps_data 
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> fold (fn superclass => assert thy arities eqngr (Inst (superclass, tyco))) superclasses 
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> fold (assert thy arities eqngr o Fun) inst_params 
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> fold_index (fn (k, classes) => 
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apfst (Vargraph.new_node ((Inst (class, tyco), k), ([] ,[]))) 
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#> add_classes thy arities eqngr (Inst (class, tyco), k) classes 
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#> fold (fn superclass => 
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add_dep thy arities eqngr (Inst (superclass, tyco), k) 
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(Inst (class, tyco), k)) superclasses 
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#> fold (fn inst_param => 
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add_dep thy arities eqngr (Fun inst_param, k) 
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(Inst (class, tyco), k) 
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) inst_params 
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) classess 
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end 
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and add_const thy arities eqngr c vardeps_data = 
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let 
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val ((lhs, rhss), eqns) = obtain_eqns thy eqngr c; 
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fun styp_of (Type (tyco, tys)) = Tyco (tyco, map styp_of tys) 
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 styp_of (TFree (v, _)) = Var (Fun c, find_index (fn (v', _) => v = v') lhs); 
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val rhss' = (map o apsnd o map) styp_of rhss; 
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in 
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vardeps_data 
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> (apsnd o apsnd) (Symtab.update_new (c, (lhs, eqns))) 
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> fold_index (fn (k, (_, sort)) => 
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apfst (Vargraph.new_node ((Fun c, k), ([] ,[]))) 
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#> add_classes thy arities eqngr (Fun c, k) (complete_proper_sort thy sort)) lhs 
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> fold (assert thy arities eqngr o Fun o fst) rhss' 
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> fold (fn (c', styps) => fold_index (fn (k', styp) => 
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add_typmatch thy arities eqngr styp (Fun c', k')) styps) rhss' 
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end 
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and assert thy arities eqngr c vardeps_data = 
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if member (op =) ((fst o snd) vardeps_data) c then vardeps_data 
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else case c 
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of Fun const => vardeps_data > (apsnd o apfst) (cons c) > add_const thy arities eqngr const 
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 Inst inst => vardeps_data > (apsnd o apfst) (cons c) > add_inst thy arities eqngr inst; 
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(* applying instantiations *) 
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fun build_algebra thy arities = 
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let 
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val pp = Syntax.pp_global thy; 
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val thy_algebra = Sign.classes_of thy; 
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val is_proper = can (AxClass.get_info thy); 
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val classrels = Sorts.classrels_of thy_algebra 
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> filter (is_proper o fst) 
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> (map o apsnd) (filter is_proper); 
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val instances = Sorts.instances_of thy_algebra 
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> filter (is_proper o snd); 
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fun add_class (class, superclasses) algebra = 
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Sorts.add_class pp (class, Sorts.minimize_sort algebra superclasses) algebra; 
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fun add_arity (tyco, class) algebra = 
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case AList.lookup (op =) arities (tyco, class) 
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of SOME sorts => Sorts.add_arities pp 
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(tyco, [(class, map (Sorts.minimize_sort algebra) sorts)]) algebra 
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 NONE => if Sign.arity_number thy tyco = 0 
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then Sorts.add_arities pp (tyco, [(class, [])]) algebra 
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else algebra; 
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in 
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Sorts.empty_algebra 
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> fold add_class classrels 
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> fold add_arity instances 
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end; 
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fun dicts_of thy (proj_sort, algebra) (T, sort) = 
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let 
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fun class_relation (x, _) _ = x; 
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fun type_constructor tyco xs class = 
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inst_params thy tyco class @ (maps o maps) fst xs; 
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fun type_variable (TFree (_, sort)) = map (pair []) (proj_sort sort); 
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in 
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flat (Sorts.of_sort_derivation (Syntax.pp_global thy) algebra 
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{ class_relation = class_relation, type_constructor = type_constructor, 
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type_variable = type_variable } (T, proj_sort sort) 
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handle Sorts.CLASS_ERROR _ => [] (*permissive!*)) 
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end; 
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fun add_arities thy vardeps = Vargraph.fold (fn ((Fun _, _), _) => I 
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 ((Inst (class, tyco), k), ((_, classes), _)) => 
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AList.map_default (op =) 
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((tyco, class), replicate (Sign.arity_number thy tyco) []) 
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(nth_map k (K classes))) vardeps; 
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fun add_eqs thy (proj_sort, algebra) eqntab vardeps c gr = 
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let 
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val (proto_lhs, proto_eqns) = (the o Symtab.lookup eqntab) c; 
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val lhs = map_index (fn (k, (v, _)) => 
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(v, snd (Vargraph.get_node vardeps (Fun c, k)))) proto_lhs; 
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val inst_tab = Vartab.empty > fold (fn (v, sort) => 
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Vartab.update ((v, 0), sort)) lhs; 
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val eqns = proto_eqns 
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> (map o apfst) (Code_Unit.inst_thm thy inst_tab); 
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val (tyscm, rhss) = tyscm_rhss_of thy c eqns; 
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in 
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gr 
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> Graph.new_node (c, (tyscm, eqns)) 
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> fold (fn (c', Ts) => ensure_eqs_dep thy (proj_sort, algebra) eqntab vardeps c c' 
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#> (fn (vs, _) => 
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fold2 (ensure_match thy (proj_sort, algebra) eqntab vardeps c) Ts (map snd vs))) rhss 
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> pair tyscm 
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end 
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and ensure_match thy (proj_sort, algebra) eqntab vardeps c T sort gr = 
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gr 
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> fold (fn c' => ensure_eqs_dep thy (proj_sort, algebra) eqntab vardeps c c' #> snd) 
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(dicts_of thy (proj_sort, algebra) (T, proj_sort sort)) 
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and ensure_eqs_dep thy (proj_sort, algebra) eqntab vardeps c c' gr = 
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gr 
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> ensure_eqs thy (proj_sort, algebra) eqntab vardeps c' 
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> Graph.add_edge (c, c') 
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and ensure_eqs thy (proj_sort, algebra) eqntab vardeps c gr = 
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case try (Graph.get_node gr) c 
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of SOME (tyscm, _) => (tyscm, gr) 
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 NONE => add_eqs thy (proj_sort, algebra) eqntab vardeps c gr; 
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fun extend_arities_eqngr thy cs (arities, eqngr) = 
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let 
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val (vardeps, (_, eqntab)) = fold (assert thy arities eqngr o Fun) 
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cs (Vargraph.empty, ([], Symtab.empty)); 
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val arities' = add_arities thy vardeps arities; 
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val algebra = build_algebra thy arities'; 
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val proj_sort = complete_proper_sort thy #> Sorts.minimize_sort algebra; 
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val (_, eqngr') = fold_map (ensure_eqs thy (proj_sort, algebra) eqntab vardeps) cs eqngr; 
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in ((proj_sort, algebra), (arities', eqngr')) end; 
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(** retrieval interfaces **) 
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fun proto_eval thy cterm_of evaluator_lift evaluator proto_ct arities_eqngr = 
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let 
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val ct = cterm_of proto_ct; 
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val _ = Sign.no_vars (Syntax.pp_global thy) (Thm.term_of ct); 
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val _ = Term.fold_types (Type.no_tvars #> K I) (Thm.term_of ct) (); 
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fun consts_of t = 
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fold_aterms (fn Const c_ty => cons c_ty  _ => I) t []; 
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val thm = Code.preprocess_conv thy ct; 
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val ct' = Thm.rhs_of thm; 
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val t' = Thm.term_of ct'; 
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val consts = map fst (consts_of t'); 
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val (algebra', arities_eqngr') = extend_arities_eqngr thy consts arities_eqngr; 
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val (t'', evaluator_eqngr) = evaluator t'; 
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val consts' = consts_of t''; 
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val const_matches = fold (fn (c, ty) => 
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insert (op =) (Sign.const_typargs thy (c, Logic.unvarifyT ty), c)) consts' []; 
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val typ_matches = maps (fn (tys, c) => 
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tys ~~ map snd (fst (fst (Graph.get_node (snd arities_eqngr') c)))) 
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const_matches; 
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val dicts = maps (dicts_of thy algebra') typ_matches; 
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val (algebra'', arities_eqngr'') = extend_arities_eqngr thy dicts arities_eqngr'; 
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in (evaluator_lift (evaluator_eqngr algebra'') thm (snd arities_eqngr''), arities_eqngr'') end; 
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fun proto_eval_conv thy = 
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let 
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fun evaluator_lift evaluator thm1 eqngr = 
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let 
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val thm2 = evaluator eqngr; 
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val thm3 = Code.postprocess_conv thy (Thm.rhs_of thm2); 
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in 
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Thm.transitive thm1 (Thm.transitive thm2 thm3) handle THM _ => 
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error ("could not construct evaluation proof:\n" 
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^ (cat_lines o map Display.string_of_thm) [thm1, thm2, thm3]) 
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end; 
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in proto_eval thy I evaluator_lift end; 
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fun proto_eval_term thy = 
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let 
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fun evaluator_lift evaluator _ eqngr = evaluator eqngr; 
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in proto_eval thy (Thm.cterm_of thy) evaluator_lift end; 
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structure Wellsorted = CodeDataFun 
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( 
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type T = ((string * class) * sort list) list * T; 
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val empty = ([], Graph.empty); 
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fun purge thy cs (arities, eqngr) = 
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let 
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val del_cs = ((Graph.all_preds eqngr 
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o filter (can (Graph.get_node eqngr))) cs); 
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val del_arities = 
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map_filter (AxClass.inst_of_param thy) del_cs; 
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val arities' = fold (AList.delete (op =)) del_arities arities; 
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val eqngr' = Graph.del_nodes del_cs eqngr; 
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in (arities', eqngr') end; 
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); 
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fun make thy = apsnd snd 
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o Wellsorted.change_yield thy o extend_arities_eqngr thy; 
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fun eval_conv thy f = 
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fst o Wellsorted.change_yield thy o proto_eval_conv thy f; 
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fun eval_term thy f = 
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fst o Wellsorted.change_yield thy o proto_eval_term thy f; 
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(** diagnostic commands **) 
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fun code_depgr thy consts = 
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let 
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val (_, eqngr) = make thy consts; 
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val select = Graph.all_succs eqngr consts; 
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in 
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eqngr 
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> not (null consts) ? Graph.subgraph (member (op =) select) 
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> Graph.map_nodes ((apsnd o map o apfst) (AxClass.overload thy)) 
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end; 
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fun code_thms thy = Pretty.writeln o pretty thy o code_depgr thy; 
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fun code_deps thy consts = 
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let 
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val eqngr = code_depgr thy consts; 
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fun mk_entry (const, (_, (_, parents))) = 
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let 
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val name = Code_Unit.string_of_const thy const; 
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val nameparents = map (Code_Unit.string_of_const thy) parents; 
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in { name = name, ID = name, dir = "", unfold = true, 
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path = "", parents = nameparents } 
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end; 
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val prgr = Graph.fold ((fn x => fn xs => xs @ [x]) o mk_entry) eqngr []; 
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in Present.display_graph prgr end; 
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local 
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structure P = OuterParse 
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and K = OuterKeyword 
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fun code_thms_cmd thy = code_thms thy o op @ o Code_Name.read_const_exprs thy; 
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fun code_deps_cmd thy = code_deps thy o op @ o Code_Name.read_const_exprs thy; 
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in 
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val _ = 
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OuterSyntax.improper_command "code_thms" "print system of defining equations for code" OuterKeyword.diag 
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(Scan.repeat P.term_group 
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>> (fn cs => Toplevel.no_timing o Toplevel.unknown_theory 
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o Toplevel.keep ((fn thy => code_thms_cmd thy cs) o Toplevel.theory_of))); 
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val _ = 
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OuterSyntax.improper_command "code_deps" "visualize dependencies of defining equations for code" OuterKeyword.diag 
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(Scan.repeat P.term_group 
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>> (fn cs => Toplevel.no_timing o Toplevel.unknown_theory 
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o Toplevel.keep ((fn thy => code_deps_cmd thy cs) o Toplevel.theory_of))); 
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end; 
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end; (*struct*) 