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(* Title: Tools/code/code_wellsorted.ML 
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Author: Florian Haftmann, TU Muenchen 
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Producing wellsorted systems of code equations in a graph 
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with explicit dependencies  the Waisenhaus algorithm. 
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*) 
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signature CODE_WELLSORTED = 
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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_Wellsorted : CODE_WELLSORTED = 
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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 = 
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map (fn (c, _) => AxClass.param_of_inst thy (c, tyco)) 
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o maps (#params o AxClass.get_info thy); 
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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  Free; 
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fun styp_of c_lhs (Type (tyco, tys)) = Tyco (tyco, map (styp_of c_lhs) tys) 

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 styp_of c_lhs (TFree (v, _)) = case c_lhs 

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of SOME (c, lhs) => Var (Fun c, find_index (fn (v', _) => v = v') lhs) 

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 NONE => Free; 

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type vardeps_data = ((string * styp list) list * class list) Vargraph.T 
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* (((string * sort) list * (thm * bool) list) Symtab.table 

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* (class * string) list); 

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val empty_vardeps_data : vardeps_data = 
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(Vargraph.empty, (Symtab.empty, [])); 

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(* retrieving equations and instances from the background context *) 
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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, []), []) 
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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 all_classes = complete_proper_sort thy [class]; 
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val superclasses = remove (op =) class all_classes 

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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 inst_params = inst_params thy tyco all_classes; 
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in (classess, (superclasses, inst_params)) end; 
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(* computing instantiations *) 

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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 (assert_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 (assert_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 assert_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_inst thy arities eqngr (class, tyco) 
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> fold_index (fn (k, styp) => 
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assert_typmatch thy arities eqngr styp (Inst (class, tyco), k)) styps 
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else vardeps_data (*permissive!*) 
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and assert_inst thy arities eqngr (inst as (class, tyco)) (vardeps_data as (_, (_, insts))) = 
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if member (op =) insts inst then vardeps_data 

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else 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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> (apsnd o apsnd) (insert (op =) inst) 
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> fold_index (fn (k, _) => 
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apfst (Vargraph.new_node ((Inst (class, tyco), k), ([] ,[])))) classess 

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> fold (fn superclass => assert_inst thy arities eqngr (superclass, tyco)) superclasses 
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> fold (assert_fun thy arities eqngr) inst_params 

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> fold_index (fn (k, classes) => 
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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 assert_typmatch thy arities eqngr (Tyco tyco_styps) c_k vardeps_data = 
186 
vardeps_data 

187 
> add_styp thy arities eqngr c_k tyco_styps 

188 
 assert_typmatch thy arities eqngr (Var c_k') c_k vardeps_data = 

189 
vardeps_data 

190 
> add_dep thy arities eqngr c_k c_k' 

191 
 assert_typmatch thy arities eqngr Free c_k vardeps_data = 

192 
vardeps_data 

193 
and assert_rhs thy arities eqngr (c', styps) vardeps_data = 

194 
vardeps_data 

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> assert_fun thy arities eqngr c' 

196 
> fold_index (fn (k, styp) => 

197 
assert_typmatch thy arities eqngr styp (Fun c', k)) styps 

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and assert_fun thy arities eqngr c (vardeps_data as (_, (eqntab, _))) = 

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if Symtab.defined eqntab c then vardeps_data 

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else let 

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val ((lhs, rhss), eqns) = obtain_eqns thy eqngr c; 
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val rhss' = (map o apsnd o map) (styp_of (SOME (c, lhs))) rhss; 
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in 
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vardeps_data 
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> (apsnd o apfst) (Symtab.update_new (c, (lhs, eqns))) 
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> fold_index (fn (k, _) => 
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apfst (Vargraph.new_node ((Fun c, k), ([] ,[])))) lhs 

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> fold_index (fn (k, (_, sort)) => 
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add_classes thy arities eqngr (Fun c, k) (complete_proper_sort thy sort)) lhs 
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> fold (assert_rhs thy arities eqngr) rhss' 
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end; 

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(* applying instantiations *) 
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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 (Sorts.complete_sort algebra [class]) 
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@ (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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30054  230 
fun add_arity thy vardeps (class, tyco) = 
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AList.default (op =) 
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((class, tyco), map (fn k => (snd o Vargraph.get_node vardeps) (Inst (class, tyco), k)) 
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(0 upto Sign.arity_number thy tyco  1)); 

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fun add_eqs thy (proj_sort, algebra) vardeps 
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(c, (proto_lhs, proto_eqns)) (rhss, eqngr) = 

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if can (Graph.get_node eqngr) c then (rhss, eqngr) 
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else let 

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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; 
246 
val eqngr' = Graph.new_node (c, (tyscm, eqns)) eqngr; 

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in (map (pair c) rhss' @ rhss, eqngr') end; 

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30054  249 
fun extend_arities_eqngr thy cs cs_rhss (arities, eqngr) = 
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let 
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val cs_rhss' = (map o apsnd o map) (styp_of NONE) cs_rhss; 
252 
val (vardeps, (eqntab, insts)) = empty_vardeps_data 

253 
> fold (assert_fun thy arities eqngr) cs 

254 
> fold (assert_rhs thy arities eqngr) cs_rhss'; 

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val arities' = fold (add_arity thy vardeps) insts arities; 

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val pp = Syntax.pp_global thy; 
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val is_proper_class = can (AxClass.get_info thy); 

258 
val (proj_sort, algebra) = Sorts.subalgebra pp is_proper_class 

259 
(AList.lookup (op =) arities') (Sign.classes_of thy); 

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val (rhss, eqngr') = Symtab.fold 
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(add_eqs thy (proj_sort, algebra) vardeps) eqntab ([], eqngr); 

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fun deps_of (c, rhs) = c :: 

263 
maps (dicts_of thy (proj_sort, algebra)) 

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(rhs ~~ (map snd o fst o fst o Graph.get_node eqngr') c); 

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val eqngr'' = fold (fn (c, rhs) => fold 

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(curry Graph.add_edge c) (deps_of rhs)) rhss 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 (t'', evaluator_eqngr) = evaluator t'; 
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val consts = map fst (consts_of 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 =) (c, Sign.const_typargs thy (c, ty))) consts' []; 
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val (algebra', arities_eqngr') = 
288 
extend_arities_eqngr thy consts const_matches' arities_eqngr; 

289 
in 

290 
(evaluator_lift (evaluator_eqngr algebra') thm (snd arities_eqngr'), 

291 
arities_eqngr') 

292 
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 = del_cs 
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> map_filter (AxClass.inst_of_param thy) 
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> maps (fn (c, tyco) => 
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(map (rpair tyco) o Sign.complete_sort thy o the_list 
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o AxClass.class_of_param thy) c); 
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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 cs = apsnd snd 
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(Wellsorted.change_yield thy (extend_arities_eqngr thy cs [])); 
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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; 
30769  357 
val constss = Graph.strong_conn eqngr; 
358 
val mapping = Symtab.empty > fold (fn consts => fold (fn const => 

359 
Symtab.update (const, consts)) consts) constss; 

360 
fun succs consts = consts 

361 
> maps (Graph.imm_succs eqngr) 

362 
> subtract (op =) consts 

363 
> map (the o Symtab.lookup mapping) 

364 
> distinct (op =); 

365 
val conn = [] > fold (fn consts => cons (consts, succs consts)) constss; 

366 
fun namify consts = map (Code_Unit.string_of_const thy) consts 

367 
> commas; 

368 
val prgr = map (fn (consts, constss) => 

369 
{ name = namify consts, ID = namify consts, dir = "", unfold = true, 

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path = "", parents = map namify constss }) conn; 

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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 code 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 code 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*) 