author  blanchet 
Mon, 26 Nov 2012 13:35:05 +0100  
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parent 49971  8b50286c36d3 
child 51658  21c10672633b 
permissions  rwrr 
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(* Title: Tools/Code/code_preproc.ML 
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Author: Florian Haftmann, TU Muenchen 
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Preprocessing code equations into a wellsorted system 
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in a graph with explicit dependencies. 
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*) 
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signature CODE_PREPROC = 
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sig 
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val map_pre: (simpset > simpset) > theory > theory 
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val map_post: (simpset > simpset) > theory > theory 
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val add_unfold: thm > theory > theory 
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val add_functrans: string * (theory > (thm * bool) list > (thm * bool) list option) > theory > theory 
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val del_functrans: string > theory > theory 
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val simple_functrans: (theory > thm list > thm list option) 
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> theory > (thm * bool) list > (thm * bool) list option 
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val print_codeproc: theory > unit 
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type code_algebra 
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type code_graph 

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val cert: code_graph > string > Code.cert 
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val sortargs: code_graph > string > sort list 
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val all: code_graph > string list 
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val pretty: theory > code_graph > Pretty.T 

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val obtain: bool > theory > string list > term list > code_algebra * code_graph 
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val dynamic_conv: theory 
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> (code_algebra > code_graph > (string * sort) list > term > conv) > conv 
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val dynamic_value: theory > ((term > term) > 'a > 'a) 
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> (code_algebra > code_graph > (string * sort) list > term > 'a) > term > 'a 
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val static_conv: theory > string list 
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> (code_algebra > code_graph > (string * sort) list > term > conv) > conv 
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val static_value: theory > ((term > term) > 'a > 'a) > string list 
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> (code_algebra > code_graph > (string * sort) list > term > 'a) > term > 'a 
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val setup: theory > theory 
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end 
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structure Code_Preproc : CODE_PREPROC = 
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struct 
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(** preprocessor administration **) 
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(* theory data *) 
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datatype thmproc = Thmproc of { 
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pre: simpset, 
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post: simpset, 
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functrans: (string * (serial * (theory > (thm * bool) list > (thm * bool) list option))) list 
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}; 
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fun make_thmproc ((pre, post), functrans) = 
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Thmproc { pre = pre, post = post, functrans = functrans }; 
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fun map_thmproc f (Thmproc { pre, post, functrans }) = 
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make_thmproc (f ((pre, post), functrans)); 
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fun merge_thmproc (Thmproc { pre = pre1, post = post1, functrans = functrans1 }, 
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Thmproc { pre = pre2, post = post2, functrans = functrans2 }) = 
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let 
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val pre = Simplifier.merge_ss (pre1, pre2); 
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val post = Simplifier.merge_ss (post1, post2); 
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val functrans = AList.merge (op =) (eq_fst (op =)) (functrans1, functrans2) 
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handle AList.DUP => error ("Duplicate function transformer"); 
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in make_thmproc ((pre, post), functrans) end; 
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structure Code_Preproc_Data = Theory_Data 
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( 
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type T = thmproc; 
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val empty = make_thmproc ((Simplifier.empty_ss, Simplifier.empty_ss), []); 
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val extend = I; 
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val merge = merge_thmproc; 

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); 
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fun the_thmproc thy = case Code_Preproc_Data.get thy 
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of Thmproc x => x; 
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fun delete_force msg key xs = 
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if AList.defined (op =) xs key then AList.delete (op =) key xs 
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else error ("No such " ^ msg ^ ": " ^ quote key); 
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val map_data = Code_Preproc_Data.map o map_thmproc; 
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val map_pre_post = map_data o apfst; 
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val map_pre = map_pre_post o apfst; 

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val map_post = map_pre_post o apsnd; 

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val add_unfold = map_pre o Simplifier.add_simp; 
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val del_unfold = map_pre o Simplifier.del_simp; 

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val add_post = map_post o Simplifier.add_simp; 

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val del_post = map_post o Simplifier.del_simp; 

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fun add_code_abbrev raw_thm thy = 
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let 
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val thm = Local_Defs.meta_rewrite_rule (Proof_Context.init_global thy) raw_thm; 
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val thm_sym = Thm.symmetric thm; 
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in 

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thy > map_pre_post (fn (pre, post) => 

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(pre > Simplifier.add_simp thm_sym, post > Simplifier.add_simp thm)) 
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end; 
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fun add_functrans (name, f) = (map_data o apsnd) 
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(AList.update (op =) (name, (serial (), f))); 
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fun del_functrans name = (map_data o apsnd) 
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(delete_force "function transformer" name); 
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(* post and preprocessing *) 
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fun no_variables_conv conv ct = 
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let 
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val cert = Thm.cterm_of (Thm.theory_of_cterm ct); 
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val all_vars = fold_aterms (fn t as Free _ => insert (op aconvc) (cert t) 
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 t as Var _ => insert (op aconvc) (cert t) 
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 _ => I) (Thm.term_of ct) []; 
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fun apply_beta var thm = Thm.combination thm (Thm.reflexive var) 
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> Conv.fconv_rule (Conv.arg_conv (Conv.try_conv (Thm.beta_conversion false))) 
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> Conv.fconv_rule (Conv.arg1_conv (Thm.beta_conversion false)); 
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in 
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ct 
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> fold_rev Thm.lambda all_vars 
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> conv 
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> fold apply_beta all_vars 
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end; 
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fun trans_conv_rule conv thm = Thm.transitive thm ((conv o Thm.rhs_of) thm); 
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fun term_of_conv thy conv = 
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Thm.cterm_of thy 
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#> conv 
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#> Thm.prop_of 
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#> Logic.dest_equals 
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#> snd; 
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fun term_of_conv_resubst thy conv t = 
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let 

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val all_vars = fold_aterms (fn t as Free _ => insert (op aconv) t 

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 t as Var _ => insert (op aconv) t 

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 _ => I) t []; 

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val resubst = curry (Term.betapplys o swap) all_vars; 

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in (resubst, term_of_conv thy conv (fold_rev lambda all_vars t)) end; 

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fun preprocess_conv thy = 

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let 
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val pre = (Simplifier.global_context thy o #pre o the_thmproc) thy; 
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in 
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Simplifier.rewrite pre 
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#> trans_conv_rule (AxClass.unoverload_conv thy) 

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end; 
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fun preprocess_term thy = term_of_conv_resubst thy (preprocess_conv thy); 
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fun postprocess_conv thy = 
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let 
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val post = (Simplifier.global_context thy o #post o the_thmproc) thy; 
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in 
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AxClass.overload_conv thy 
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#> trans_conv_rule (Simplifier.rewrite post) 

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end; 
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fun postprocess_term thy = term_of_conv thy (postprocess_conv thy); 
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fun print_codeproc thy = 
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let 
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val ctxt = Proof_Context.init_global thy; 
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val pre = (#pre o the_thmproc) thy; 
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val post = (#post o the_thmproc) thy; 
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val functrans = (map fst o #functrans o the_thmproc) thy; 
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in 
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(Pretty.writeln o Pretty.chunks) [ 
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Pretty.block [ 
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Pretty.str "preprocessing simpset:", 
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Pretty.fbrk, 
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Simplifier.pretty_ss ctxt pre 
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], 
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Pretty.block [ 
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Pretty.str "postprocessing simpset:", 
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Pretty.fbrk, 
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Simplifier.pretty_ss ctxt post 
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], 
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Pretty.block ( 
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Pretty.str "function transformers:" 
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:: Pretty.fbrk 
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:: (Pretty.fbreaks o map Pretty.str) functrans 
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) 
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] 
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end; 
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fun simple_functrans f thy eqns = case f thy (map fst eqns) 
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of SOME thms' => SOME (map (rpair (forall snd eqns)) thms') 
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 NONE => NONE; 
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(** sort algebra and code equation graph types **) 
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type code_algebra = (sort > sort) * Sorts.algebra; 
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type code_graph = ((string * sort) list * Code.cert) Graph.T; 
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fun get_node eqngr const = Graph.get_node eqngr const 
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handle Graph.UNDEF _ => error ("No such constant in code equation graph: " ^ quote const); 
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fun cert eqngr = snd o get_node eqngr; 
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fun sortargs eqngr = map snd o fst o 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.string_of_const thy) 
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> sort (string_ord o pairself fst) 
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> map (fn (s, cert) => (Pretty.block o Pretty.fbreaks) (Pretty.str s :: Code.pretty_cert thy cert)) 
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> Pretty.chunks; 
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(** the Waisenhaus algorithm **) 
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(* auxiliary *) 
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fun is_proper_class thy = can (AxClass.get_info thy); 
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fun complete_proper_sort thy = 
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Sign.complete_sort thy #> filter (is_proper_class thy); 
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30029  221 
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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(* 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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Graph(type key = var val ord = prod_ord const_ord int_ord); 
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30054  241 
datatype styp = Tyco of string * styp list  Var of var  Free; 
242 

243 
fun styp_of c_lhs (Type (tyco, tys)) = Tyco (tyco, map (styp_of c_lhs) tys) 

244 
 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) 

246 
 NONE => Free; 

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30054  248 
type vardeps_data = ((string * styp list) list * class list) Vargraph.T 
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* (((string * sort) list * Code.cert) Symtab.table 
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* (class * string) list); 
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30054  252 
val empty_vardeps_data : vardeps_data = 
253 
(Vargraph.empty, (Symtab.empty, [])); 

254 

30876  255 

30054  256 
(* 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, cert) => ((lhs, []), cert) 
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 NONE => let 
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val functrans = (map (fn (_, (_, f)) => f thy) 
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o #functrans o the_thmproc) thy; 
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val pre = (Simplifier.global_context thy o #pre o the_thmproc) thy; 
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val cert = Code.get_cert thy { functrans = functrans, ss = pre } c; 
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val (lhs, rhss) = Code.typargs_deps_of_cert thy cert; 
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in ((lhs, rhss), cert) 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 super_classes = 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, (super_classes, inst_params)) end; 
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30054  280 

281 
(* computing instantiations *) 

282 

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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.immediate_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 (ensure_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 new_tyco_styps vardeps_data = 
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let 
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val (old_tyco_stypss, classes) = Vargraph.get_node (fst vardeps_data) c_k; 
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in if member (op =) old_tyco_stypss new_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 new_tyco_styps) 
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> fold (ensure_typmatch_inst thy arities eqngr new_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 ensure_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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> ensure_inst thy arities eqngr (class, tyco) 
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> fold_index (fn (k, styp) => 
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ensure_typmatch thy arities eqngr styp (Inst (class, tyco), k)) styps 
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else vardeps_data (*permissive!*) 
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and ensure_inst thy arities eqngr (inst as (class, tyco)) (vardeps_data as (_, (_, insts))) = 
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if member (op =) insts inst then vardeps_data 
322 
else let 

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val (classess, (super_classes, inst_params)) = 
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obtain_instance thy arities inst; 
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in 
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vardeps_data 
30054  327 
> (apsnd o apsnd) (insert (op =) inst) 
30083  328 
> fold_index (fn (k, _) => 
329 
apfst (Vargraph.new_node ((Inst (class, tyco), k), ([] ,[])))) classess 

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> fold (fn super_class => ensure_inst thy arities eqngr (super_class, tyco)) super_classes 
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> fold (ensure_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 super_class => 
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add_dep thy arities eqngr (Inst (super_class, tyco), k) 
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(Inst (class, tyco), k)) super_classes 
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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 ensure_typmatch thy arities eqngr (Tyco tyco_styps) c_k vardeps_data = 
30054  344 
vardeps_data 
345 
> add_styp thy arities eqngr c_k tyco_styps 

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 ensure_typmatch thy arities eqngr (Var c_k') c_k vardeps_data = 
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vardeps_data 
348 
> add_dep thy arities eqngr c_k c_k' 

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 ensure_typmatch thy arities eqngr Free c_k vardeps_data = 
30054  350 
vardeps_data 
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and ensure_rhs thy arities eqngr (c', styps) vardeps_data = 
30054  352 
vardeps_data 
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> ensure_fun thy arities eqngr c' 
30054  354 
> fold_index (fn (k, styp) => 
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ensure_typmatch thy arities eqngr styp (Fun c', k)) styps 
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356 
and ensure_fun thy arities eqngr c (vardeps_data as (_, (eqntab, _))) = 
30054  357 
if Symtab.defined eqntab c then vardeps_data 
358 
else let 

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val ((lhs, rhss), eqns) = obtain_eqns thy eqngr c; 
30054  360 
val rhss' = (map o apsnd o map) (styp_of (SOME (c, lhs))) rhss; 
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361 
in 
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vardeps_data 
30054  363 
> (apsnd o apfst) (Symtab.update_new (c, (lhs, eqns))) 
30083  364 
> fold_index (fn (k, _) => 
365 
apfst (Vargraph.new_node ((Fun c, k), ([] ,[])))) lhs 

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> fold_index (fn (k, (_, sort)) => 
30083  367 
add_classes thy arities eqngr (Fun c, k) (complete_proper_sort thy sort)) lhs 
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> fold (ensure_rhs thy arities eqngr) rhss' 
30054  369 
end; 
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370 

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371 

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372 
(* applying instantiations *) 
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373 

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374 
fun dicts_of thy (proj_sort, algebra) (T, sort) = 
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375 
let 
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376 
fun class_relation (x, _) _ = x; 
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377 
fun type_constructor (tyco, _) xs class = 
30054  378 
inst_params thy tyco (Sorts.complete_sort algebra [class]) 
379 
@ (maps o maps) fst xs; 

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fun type_variable (TFree (_, sort)) = map (pair []) (proj_sort sort); 
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381 
in 
32795  382 
flat (Sorts.of_sort_derivation algebra 
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383 
{ class_relation = K 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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386 
end; 
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387 

30054  388 
fun add_arity thy vardeps (class, tyco) = 
33063  389 
AList.default (op =) ((class, tyco), 
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map_range (fn k => (snd o Vargraph.get_node vardeps) (Inst (class, tyco), k)) 
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391 
(Sign.arity_number thy tyco)); 
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392 

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fun add_cert thy vardeps (c, (proto_lhs, proto_cert)) (rhss, eqngr) = 
30058  394 
if can (Graph.get_node eqngr) c then (rhss, eqngr) 
395 
else let 

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396 
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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398 
val cert = proto_cert 
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399 
> Code.constrain_cert thy (map (Sign.minimize_sort thy o snd) lhs) 
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400 
> Code.conclude_cert; 
35224  401 
val (vs, rhss') = Code.typargs_deps_of_cert thy cert; 
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val eqngr' = Graph.new_node (c, (vs, cert)) eqngr; 
30054  403 
in (map (pair c) rhss' @ rhss, eqngr') end; 
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404 

32873  405 
fun extend_arities_eqngr thy cs ts (arities, (eqngr : code_graph)) = 
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406 
let 
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407 
val cs_rhss = (fold o fold_aterms) (fn Const (c_ty as (c, _)) => 
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408 
insert (op =) (c, (map (styp_of NONE) o Sign.const_typargs thy) c_ty)  _ => I) ts []; 
30054  409 
val (vardeps, (eqntab, insts)) = empty_vardeps_data 
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410 
> fold (ensure_fun thy arities eqngr) cs 
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411 
> fold (ensure_rhs thy arities eqngr) cs_rhss; 
30054  412 
val arities' = fold (add_arity thy vardeps) insts arities; 
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413 
val algebra = Sorts.subalgebra (Context.pretty_global thy) (is_proper_class thy) 
30064  414 
(AList.lookup (op =) arities') (Sign.classes_of thy); 
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415 
val (rhss, eqngr') = Symtab.fold (add_cert thy vardeps) eqntab ([], eqngr); 
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416 
fun deps_of (c, rhs) = c :: maps (dicts_of thy algebra) 
32873  417 
(rhs ~~ sortargs eqngr' c); 
30054  418 
val eqngr'' = fold (fn (c, rhs) => fold 
419 
(curry Graph.add_edge c) (deps_of rhs)) rhss eqngr'; 

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420 
in (algebra, (arities', eqngr'')) end; 
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421 

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422 

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423 
(** store for preprocessed arities and code equations **) 
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424 

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425 
structure Wellsorted = Code_Data 
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426 
( 
30947  427 
type T = ((string * class) * sort list) list * code_graph; 
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428 
val empty = ([], Graph.empty); 
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429 
); 
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430 

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431 

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432 
(** retrieval and evaluation interfaces **) 
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433 

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434 
fun obtain ignore_cache thy consts ts = apsnd snd 
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435 
(Wellsorted.change_yield (if ignore_cache then NONE else SOME thy) (extend_arities_eqngr thy consts ts)); 
38670  436 

437 
fun dest_cterm ct = let val t = Thm.term_of ct in (Term.add_tfrees t [], t) end; 

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438 

41184  439 
fun dynamic_conv thy conv = no_variables_conv (fn ct => 
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440 
let 
39475  441 
val thm1 = preprocess_conv thy ct; 
442 
val ct' = Thm.rhs_of thm1; 

38670  443 
val (vs', t') = dest_cterm ct'; 
30947  444 
val consts = fold_aterms 
445 
(fn Const (c, _) => insert (op =) c  _ => I) t' []; 

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446 
val (algebra', eqngr') = obtain false thy consts [t']; 
39475  447 
val thm2 = conv algebra' eqngr' vs' t' ct'; 
448 
val thm3 = postprocess_conv thy (Thm.rhs_of thm2); 

449 
in 

450 
Thm.transitive thm1 (Thm.transitive thm2 thm3) handle THM _ => 

451 
error ("could not construct evaluation proof:\n" 

452 
^ (cat_lines o map (Display.string_of_thm_global thy)) [thm1, thm2, thm3]) 

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453 
end); 
30947  454 

41184  455 
fun dynamic_value thy postproc evaluator t = 
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456 
let 
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457 
val (resubst, t') = preprocess_term thy t; 
39475  458 
val vs' = Term.add_tfrees t' []; 
459 
val consts = fold_aterms 

460 
(fn Const (c, _) => insert (op =) c  _ => I) t' []; 

461 
val (algebra', eqngr') = obtain false thy consts [t']; 

462 
in 

40176  463 
t' 
464 
> evaluator algebra' eqngr' vs' 

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465 
> postproc (postprocess_term thy o resubst) 
39475  466 
end; 
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467 

41184  468 
fun static_conv thy consts conv = 
38670  469 
let 
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470 
val (algebra, eqngr) = obtain true thy consts []; 
41346  471 
val conv' = conv algebra eqngr; 
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472 
in 
41189  473 
no_variables_conv ((preprocess_conv thy) 
474 
then_conv (fn ct => uncurry conv' (dest_cterm ct) ct) 

475 
then_conv (postprocess_conv thy)) 

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476 
end; 
38670  477 

41184  478 
fun static_value thy postproc consts evaluator = 
39475  479 
let 
480 
val (algebra, eqngr) = obtain true thy consts []; 

481 
val evaluator' = evaluator algebra eqngr; 

41189  482 
in 
483 
preprocess_term thy 

484 
#> (fn resubst => fn t => t 

41346  485 
> evaluator' (Term.add_tfrees t []) 
41189  486 
> postproc (postprocess_term thy o resubst)) 
39475  487 
end; 
488 

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489 

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490 
(** setup **) 
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491 

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492 
val setup = 
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493 
let 
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494 
fun mk_attribute f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I); 
32072  495 
fun add_del_attribute_parser add del = 
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496 
Attrib.add_del (mk_attribute add) (mk_attribute del); 
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497 
in 
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498 
Attrib.setup @{binding code_unfold} (add_del_attribute_parser add_unfold del_unfold) 
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499 
"preprocessing equations for code generator" 
32072  500 
#> Attrib.setup @{binding code_post} (add_del_attribute_parser add_post del_post) 
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501 
"postprocessing equations for code generator" 
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502 
#> Attrib.setup @{binding code_abbrev} (Scan.succeed (mk_attribute add_code_abbrev)) 
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503 
"post and preprocessing equations for code generator" 
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504 
end; 
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505 

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506 
val _ = 
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507 
Outer_Syntax.improper_command @{command_spec "print_codeproc"} "print code preprocessor setup" 
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508 
(Scan.succeed 
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509 
(Toplevel.no_timing o Toplevel.unknown_theory o Toplevel.keep 
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510 
(print_codeproc o Toplevel.theory_of))); 
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511 

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512 
end; (*struct*) 