author  wenzelm 
Sun, 15 Nov 2009 19:44:29 +0100  
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parent 33522  737589bb9bb8 
child 33942  6a03c894fef8 
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 eqns: code_graph > string > (thm * bool) list 

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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: theory > string list > term list > code_algebra * code_graph 

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val eval_conv: theory 
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> (code_algebra > code_graph > (string * sort) list > term > cterm > thm) > cterm > thm 
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val eval: 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 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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(* FIXME handle AList.DUP (!?) *) 
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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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fun map_data f = Code.purge_data 
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#> (Code_Preproc_Data.map o map_thmproc) f; 

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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 MetaSimplifier.add_simp; 
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val del_unfold = map_pre o MetaSimplifier.del_simp; 

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val add_post = map_post o MetaSimplifier.add_simp; 
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val del_post = map_post o MetaSimplifier.del_simp; 
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fun add_unfold_post raw_thm thy = 

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let 

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val thm = LocalDefs.meta_rewrite_rule (ProofContext.init 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 > MetaSimplifier.add_simp thm, post > MetaSimplifier.del_simp thm_sym)) 

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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 apply_functrans thy c _ [] = [] 
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 apply_functrans thy c [] eqns = eqns 
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 apply_functrans thy c functrans eqns = eqns 
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> perhaps (perhaps_loop (perhaps_apply functrans)) 
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> Code.assert_eqns_const thy c 
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(*FIXME in future, the check here should be more accurate wrt. type schemes 

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 perhaps by means of upcoming code certificates with a corresponding 

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preprocessor protocol*); 

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fun rhs_conv conv thm = Thm.transitive thm ((conv o Thm.rhs_of) thm); 
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fun eqn_conv conv = 
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let 

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fun lhs_conv ct = if can Thm.dest_comb ct 

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then Conv.combination_conv lhs_conv conv ct 

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else Conv.all_conv ct; 

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in Conv.combination_conv (Conv.arg_conv lhs_conv) conv end; 

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val rewrite_eqn = Conv.fconv_rule o eqn_conv o Simplifier.rewrite; 

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fun term_of_conv thy f = 
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Thm.cterm_of thy 
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#> f 
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#> Thm.prop_of 
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#> Logic.dest_equals 
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#> snd; 
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fun preprocess thy c eqns = 
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let 
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val pre = (Simplifier.theory_context thy o #pre o the_thmproc) thy; 
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val functrans = (map (fn (_, (_, f)) => f thy) o #functrans 
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o the_thmproc) thy; 
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in 
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eqns 
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> apply_functrans thy c functrans 
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> (map o apfst) (rewrite_eqn pre) 
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> (map o apfst) (AxClass.unoverload thy) 
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> map (Code.assert_eqn thy) 
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end; 
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fun preprocess_conv thy ct = 
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let 
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val pre = (Simplifier.theory_context thy o #pre o the_thmproc) thy; 
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in 
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ct 
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> Simplifier.rewrite pre 
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> rhs_conv (AxClass.unoverload_conv thy) 
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end; 
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fun postprocess_conv thy ct = 
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let 
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val post = (Simplifier.theory_context thy o #post o the_thmproc) thy; 
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in 
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ct 
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> AxClass.overload_conv thy 
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> rhs_conv (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 = ProofContext.init 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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30947  198 
type code_algebra = (sort > sort) * Sorts.algebra; 
32873  199 
type code_graph = ((string * sort) list * (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 sortargs eqngr = map snd o 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.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_global thy 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 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  226 
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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32873  230 
fun typscheme_rhss thy c eqns = 
231 
let 

232 
val tyscm = Code.typscheme_eqns thy c (map fst eqns); 

233 
val rhss = [] > (fold o fold o fold_aterms) 

234 
(fn Const (c, ty) => insert (op =) (c, Sign.const_typargs thy (c, Logic.unvarifyT ty))  _ => I) 

235 
(map (op :: o swap o apfst (snd o strip_comb) o Logic.dest_equals o Thm.plain_prop_of o fst) eqns); 

236 
in (tyscm, rhss) end; 

237 

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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  254 
datatype styp = Tyco of string * styp list  Var of var  Free; 
255 

256 
fun styp_of c_lhs (Type (tyco, tys)) = Tyco (tyco, map (styp_of c_lhs) tys) 

257 
 styp_of c_lhs (TFree (v, _)) = case c_lhs 

258 
of SOME (c, lhs) => Var (Fun c, find_index (fn (v', _) => v = v') lhs) 

259 
 NONE => Free; 

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30054  261 
type vardeps_data = ((string * styp list) list * class list) Vargraph.T 
262 
* (((string * sort) list * (thm * bool) list) Symtab.table 

263 
* (class * string) list); 

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30054  265 
val empty_vardeps_data : vardeps_data = 
266 
(Vargraph.empty, (Symtab.empty, [])); 

267 

30876  268 

30054  269 
(* 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 
32873  273 
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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> preprocess thy c; 
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val ((lhs, _), rhss) = typscheme_rhss 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]; 
285 
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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30054  291 

292 
(* computing instantiations *) 

293 

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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 (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 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 (ensure_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 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))) = 
30054  332 
if member (op =) insts inst then vardeps_data 
333 
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 
30054  338 
> (apsnd o apsnd) (insert (op =) inst) 
30083  339 
> fold_index (fn (k, _) => 
340 
apfst (Vargraph.new_node ((Inst (class, tyco), k), ([] ,[])))) classess 

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> fold (fn superclass => ensure_inst thy arities eqngr (superclass, tyco)) superclasses 
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> fold (ensure_fun thy arities eqngr) inst_params 
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> fold_index (fn (k, classes) => 
30075  344 
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 ensure_typmatch thy arities eqngr (Tyco tyco_styps) c_k vardeps_data = 
30054  355 
vardeps_data 
356 
> 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 = 
30054  358 
vardeps_data 
359 
> add_dep thy arities eqngr c_k c_k' 

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 ensure_typmatch thy arities eqngr Free c_k vardeps_data = 
30054  361 
vardeps_data 
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and ensure_rhs thy arities eqngr (c', styps) vardeps_data = 
30054  363 
vardeps_data 
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> ensure_fun thy arities eqngr c' 
30054  365 
> fold_index (fn (k, styp) => 
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ensure_typmatch thy arities eqngr styp (Fun c', k)) styps 
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and ensure_fun thy arities eqngr c (vardeps_data as (_, (eqntab, _))) = 
30054  368 
if Symtab.defined eqntab c then vardeps_data 
369 
else let 

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val ((lhs, rhss), eqns) = obtain_eqns thy eqngr c; 
30054  371 
val rhss' = (map o apsnd o map) (styp_of (SOME (c, lhs))) rhss; 
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in 
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vardeps_data 
30054  374 
> (apsnd o apfst) (Symtab.update_new (c, (lhs, eqns))) 
30083  375 
> fold_index (fn (k, _) => 
376 
apfst (Vargraph.new_node ((Fun c, k), ([] ,[])))) lhs 

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> fold_index (fn (k, (_, sort)) => 
30083  378 
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  380 
end; 
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381 

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382 

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383 
(* applying instantiations *) 
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384 

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fun dicts_of thy (proj_sort, algebra) (T, sort) = 
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386 
let 
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fun class_relation (x, _) _ = x; 
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fun type_constructor tyco xs class = 
30054  389 
inst_params thy tyco (Sorts.complete_sort algebra [class]) 
390 
@ (maps o maps) fst xs; 

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fun type_variable (TFree (_, sort)) = map (pair []) (proj_sort sort); 
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in 
32795  393 
flat (Sorts.of_sort_derivation 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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397 
end; 
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398 

31957  399 
fun inst_thm thy tvars' thm = 
400 
let 

401 
val tvars = (Term.add_tvars o Thm.prop_of) thm []; 

402 
val inter_sort = Sorts.inter_sort (Sign.classes_of thy); 

403 
fun mk_inst (tvar as (v, sort)) = case Vartab.lookup tvars' v 

404 
of SOME sort' => SOME (pairself (Thm.ctyp_of thy o TVar) 

405 
(tvar, (v, inter_sort (sort, sort')))) 

406 
 NONE => NONE; 

407 
val insts = map_filter mk_inst tvars; 

408 
in Thm.instantiate (insts, []) thm end; 

409 

30054  410 
fun add_arity thy vardeps (class, tyco) = 
33063  411 
AList.default (op =) ((class, tyco), 
412 
map_range (fn k => (snd o Vargraph.get_node vardeps) (Inst (class, tyco), k)) (Sign.arity_number thy tyco)); 

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413 

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fun add_eqs thy vardeps (c, (proto_lhs, proto_eqns)) (rhss, eqngr) = 
30058  415 
if can (Graph.get_node eqngr) c then (rhss, eqngr) 
416 
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 
31957  422 
> (map o apfst) (inst_thm thy inst_tab); 
32873  423 
val ((vs, _), rhss') = typscheme_rhss thy c eqns; 
424 
val eqngr' = Graph.new_node (c, (vs, eqns)) eqngr; 

30054  425 
in (map (pair c) rhss' @ rhss, eqngr') end; 
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426 

32873  427 
fun extend_arities_eqngr thy cs ts (arities, (eqngr : code_graph)) = 
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428 
let 
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val cs_rhss = (fold o fold_aterms) (fn Const (c_ty as (c, _)) => 
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insert (op =) (c, (map (styp_of NONE) o Sign.const_typargs thy) c_ty)  _ => I) ts []; 
30054  431 
val (vardeps, (eqntab, insts)) = empty_vardeps_data 
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> fold (ensure_fun thy arities eqngr) cs 
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> fold (ensure_rhs thy arities eqngr) cs_rhss; 
30054  434 
val arities' = fold (add_arity thy vardeps) insts arities; 
30064  435 
val pp = Syntax.pp_global thy; 
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val algebra = Sorts.subalgebra pp (is_proper_class thy) 
30064  437 
(AList.lookup (op =) arities') (Sign.classes_of thy); 
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val (rhss, eqngr') = Symtab.fold (add_eqs thy vardeps) eqntab ([], eqngr); 
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fun deps_of (c, rhs) = c :: maps (dicts_of thy algebra) 
32873  440 
(rhs ~~ sortargs eqngr' c); 
30054  441 
val eqngr'' = fold (fn (c, rhs) => fold 
442 
(curry Graph.add_edge c) (deps_of rhs)) rhss eqngr'; 

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in (algebra, (arities', eqngr'')) end; 
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444 

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445 

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446 
(** store for preprocessed arities and code equations **) 
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447 

31962  448 
structure Wellsorted = Code_Data_Fun 
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( 
30947  450 
type T = ((string * class) * sort list) list * code_graph; 
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451 
val empty = ([], Graph.empty); 
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452 
fun purge thy cs (arities, eqngr) = 
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453 
let 
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454 
val del_cs = ((Graph.all_preds eqngr 
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455 
o filter (can (Graph.get_node eqngr))) cs); 
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456 
val del_arities = del_cs 
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457 
> map_filter (AxClass.inst_of_param thy) 
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458 
> maps (fn (c, tyco) => 
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(map (rpair tyco) o Sign.complete_sort thy o the_list 
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460 
o AxClass.class_of_param thy) c); 
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val arities' = fold (AList.delete (op =)) del_arities arities; 
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462 
val eqngr' = Graph.del_nodes del_cs eqngr; 
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463 
in (arities', eqngr') end; 
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464 
); 
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465 

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466 

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467 
(** retrieval and evaluation interfaces **) 
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468 

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469 
fun obtain thy cs ts = apsnd snd 
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470 
(Wellsorted.change_yield thy (extend_arities_eqngr thy cs ts)); 
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471 

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472 
fun gen_eval thy cterm_of conclude_evaluation evaluator proto_ct = 
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473 
let 
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474 
val pp = Syntax.pp_global thy; 
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475 
val ct = cterm_of proto_ct; 
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476 
val _ = (Sign.no_frees pp o map_types (K dummyT) o Sign.no_vars pp) 
30947  477 
(Thm.term_of ct); 
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val thm = preprocess_conv thy ct; 
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479 
val ct' = Thm.rhs_of thm; 
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480 
val t' = Thm.term_of ct'; 
30947  481 
val vs = Term.add_tfrees t' []; 
482 
val consts = fold_aterms 

483 
(fn Const (c, _) => insert (op =) c  _ => I) t' []; 

32544  484 
val (algebra', eqngr') = obtain thy consts [t']; 
485 
in conclude_evaluation (evaluator algebra' eqngr' vs t' ct') thm end; 

30947  486 

487 
fun simple_evaluator evaluator algebra eqngr vs t ct = 

488 
evaluator algebra eqngr vs t; 

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489 

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490 
fun eval_conv thy = 
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491 
let 
30947  492 
fun conclude_evaluation thm2 thm1 = 
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493 
let 
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494 
val thm3 = postprocess_conv thy (Thm.rhs_of thm2); 
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495 
in 
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496 
Thm.transitive thm1 (Thm.transitive thm2 thm3) handle THM _ => 
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497 
error ("could not construct evaluation proof:\n" 
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498 
^ (cat_lines o map (Display.string_of_thm_global thy)) [thm1, thm2, thm3]) 
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499 
end; 
30947  500 
in gen_eval thy I conclude_evaluation end; 
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501 

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502 
fun eval thy postproc evaluator = gen_eval thy (Thm.cterm_of thy) 
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503 
(K o postproc (postprocess_term thy)) (simple_evaluator evaluator); 
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504 

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505 

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506 
(** setup **) 
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507 

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508 
val setup = 
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509 
let 
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510 
fun mk_attribute f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I); 
32072  511 
fun add_del_attribute_parser add del = 
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512 
Attrib.add_del (mk_attribute add) (mk_attribute del); 
32072  513 
fun both f g thm = f thm #> g thm; 
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514 
in 
32072  515 
Attrib.setup @{binding code_unfold} (add_del_attribute_parser 
516 
(both Codegen.add_unfold add_unfold) (both Codegen.del_unfold del_unfold)) 

517 
"preprocessing equations for code generators" 

518 
#> Attrib.setup @{binding code_inline} (add_del_attribute_parser add_unfold del_unfold) 

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519 
"preprocessing equations for code generator" 
32072  520 
#> Attrib.setup @{binding code_post} (add_del_attribute_parser add_post del_post) 
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521 
"postprocessing equations for code generator" 
32072  522 
#> Attrib.setup @{binding code_unfold_post} (Scan.succeed (mk_attribute add_unfold_post)) 
523 
"pre and postprocessing equations for code generator" 

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524 
end; 
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525 

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526 
val _ = 
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527 
OuterSyntax.improper_command "print_codeproc" "print code preprocessor setup" 
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528 
OuterKeyword.diag (Scan.succeed 
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529 
(Toplevel.no_timing o Toplevel.unknown_theory o Toplevel.keep 
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530 
(print_codeproc o Toplevel.theory_of))); 
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531 

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532 
end; (*struct*) 