src/HOL/Tools/Groebner_Basis/normalizer.ML
author haftmann
Thu May 06 16:41:14 2010 +0200 (2010-05-06)
changeset 36703 6e870d7f32e5
parent 36702 b455ebd63799
child 36704 9dd2fe596ace
permissions -rw-r--r--
removed former algebra presimpset from signature
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(*  Title:      HOL/Tools/Groebner_Basis/normalizer.ML
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    Author:     Amine Chaieb, TU Muenchen
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Normalization of expressions in semirings.
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*)
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signature NORMALIZER = 
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sig
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  type entry
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  val get: Proof.context -> (thm * entry) list
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  val match: Proof.context -> cterm -> entry option
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  val del: attribute
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  val add: {semiring: cterm list * thm list, ring: cterm list * thm list, field: cterm list * thm list, idom: thm list, ideal: thm list}
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    -> attribute
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  val funs: thm -> {is_const: morphism -> cterm -> bool,
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    dest_const: morphism -> cterm -> Rat.rat,
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    mk_const: morphism -> ctyp -> Rat.rat -> cterm,
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    conv: morphism -> Proof.context -> cterm -> thm} -> declaration
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  val semiring_normalize_conv : Proof.context -> conv
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  val semiring_normalize_ord_conv : Proof.context -> (cterm -> cterm -> bool) -> conv
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  val semiring_normalize_wrapper :  Proof.context -> entry -> conv
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  val semiring_normalize_ord_wrapper :  Proof.context -> entry ->
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    (cterm -> cterm -> bool) -> conv
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  val semiring_normalizers_conv :
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    cterm list -> cterm list * thm list -> cterm list * thm list -> cterm list * thm list ->
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      (cterm -> bool) * conv * conv * conv -> (cterm -> cterm -> bool) ->
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        {add: conv, mul: conv, neg: conv, main: conv, pow: conv, sub: conv}
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  val semiring_normalizers_ord_wrapper :  
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    Proof.context -> entry -> (cterm -> cterm -> bool) ->
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      {add: conv, mul: conv, neg: conv, main: conv, pow: conv, sub: conv}
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  val setup: theory -> theory
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end
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structure Normalizer: NORMALIZER = 
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struct
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(* data *)
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type entry =
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 {vars: cterm list,
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  semiring: cterm list * thm list,
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  ring: cterm list * thm list,
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  field: cterm list * thm list,
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  idom: thm list,
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  ideal: thm list} *
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 {is_const: cterm -> bool,
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  dest_const: cterm -> Rat.rat,
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  mk_const: ctyp -> Rat.rat -> cterm,
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  conv: Proof.context -> cterm -> thm};
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val eq_key = Thm.eq_thm;
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fun eq_data arg = eq_fst eq_key arg;
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structure Data = Generic_Data
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(
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  type T = simpset * (thm * entry) list;
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  val empty = (HOL_basic_ss, []);
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  val extend = I;
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  fun merge ((ss, e), (ss', e')) : T =
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    (merge_ss (ss, ss'), AList.merge eq_key (K true) (e, e'));
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);
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val get = snd o Data.get o Context.Proof;
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(* match data *)
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fun match ctxt tm =
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  let
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    fun match_inst
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        ({vars, semiring = (sr_ops, sr_rules), 
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          ring = (r_ops, r_rules), field = (f_ops, f_rules), idom, ideal},
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         fns as {is_const, dest_const, mk_const, conv}) pat =
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       let
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        fun h instT =
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          let
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            val substT = Thm.instantiate (instT, []);
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            val substT_cterm = Drule.cterm_rule substT;
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            val vars' = map substT_cterm vars;
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            val semiring' = (map substT_cterm sr_ops, map substT sr_rules);
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            val ring' = (map substT_cterm r_ops, map substT r_rules);
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            val field' = (map substT_cterm f_ops, map substT f_rules);
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            val idom' = map substT idom;
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            val ideal' = map substT ideal;
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            val result = ({vars = vars', semiring = semiring', 
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                           ring = ring', field = field', idom = idom', ideal = ideal'}, fns);
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          in SOME result end
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      in (case try Thm.match (pat, tm) of
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           NONE => NONE
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         | SOME (instT, _) => h instT)
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      end;
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    fun match_struct (_,
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        entry as ({semiring = (sr_ops, _), ring = (r_ops, _), field = (f_ops, _), ...}, _): entry) =
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      get_first (match_inst entry) (sr_ops @ r_ops @ f_ops);
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  in get_first match_struct (snd (get ctxt)) end;
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(* logical content *)
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val semiringN = "semiring";
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val ringN = "ring";
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val idomN = "idom";
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val idealN = "ideal";
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val fieldN = "field";
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fun undefined _ = raise Match;
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fun del_data key = apsnd (remove eq_data (key, []));
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val del = Thm.declaration_attribute (Data.map o del_data);
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fun add {semiring = (sr_ops, sr_rules), ring = (r_ops, r_rules), 
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         field = (f_ops, f_rules), idom, ideal} =
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  Thm.declaration_attribute (fn key => fn context => context |> Data.map
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    let
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      val ctxt = Context.proof_of context;
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      fun check kind name xs n =
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        null xs orelse length xs = n orelse
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        error ("Expected " ^ string_of_int n ^ " " ^ kind ^ " for " ^ name);
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      val check_ops = check "operations";
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      val check_rules = check "rules";
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      val _ =
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        check_ops semiringN sr_ops 5 andalso
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        check_rules semiringN sr_rules 37 andalso
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        check_ops ringN r_ops 2 andalso
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        check_rules ringN r_rules 2 andalso
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        check_ops fieldN f_ops 2 andalso
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        check_rules fieldN f_rules 2 andalso
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        check_rules idomN idom 2;
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      val mk_meta = Local_Defs.meta_rewrite_rule ctxt;
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      val sr_rules' = map mk_meta sr_rules;
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      val r_rules' = map mk_meta r_rules;
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      val f_rules' = map mk_meta f_rules;
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      fun rule i = nth sr_rules' (i - 1);
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      val (cx, cy) = Thm.dest_binop (hd sr_ops);
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      val cz = rule 34 |> Thm.rhs_of |> Thm.dest_arg |> Thm.dest_arg;
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      val cn = rule 36 |> Thm.rhs_of |> Thm.dest_arg |> Thm.dest_arg;
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      val ((clx, crx), (cly, cry)) =
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        rule 13 |> Thm.rhs_of |> Thm.dest_binop |> pairself Thm.dest_binop;
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      val ((ca, cb), (cc, cd)) =
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        rule 20 |> Thm.lhs_of |> Thm.dest_binop |> pairself Thm.dest_binop;
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      val cm = rule 1 |> Thm.rhs_of |> Thm.dest_arg;
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      val (cp, cq) = rule 26 |> Thm.lhs_of |> Thm.dest_binop |> pairself Thm.dest_arg;
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      val vars = [ca, cb, cc, cd, cm, cn, cp, cq, cx, cy, cz, clx, crx, cly, cry];
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      val semiring = (sr_ops, sr_rules');
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      val ring = (r_ops, r_rules');
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      val field = (f_ops, f_rules');
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      val ideal' = map (symmetric o mk_meta) ideal
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    in
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      del_data key #>
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      apsnd (cons (key, ({vars = vars, semiring = semiring, 
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                          ring = ring, field = field, idom = idom, ideal = ideal'},
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             {is_const = undefined, dest_const = undefined, mk_const = undefined,
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             conv = undefined})))
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    end);
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(* extra-logical functions *)
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fun funs raw_key {is_const, dest_const, mk_const, conv} phi = 
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 (Data.map o apsnd) (fn data =>
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  let
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    val key = Morphism.thm phi raw_key;
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    val _ = AList.defined eq_key data key orelse
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      raise THM ("No data entry for structure key", 0, [key]);
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    val fns = {is_const = is_const phi, dest_const = dest_const phi,
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      mk_const = mk_const phi, conv = conv phi};
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  in AList.map_entry eq_key key (apsnd (K fns)) data end);
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(* concrete syntax *)
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local
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fun keyword k = Scan.lift (Args.$$$ k -- Args.colon) >> K ();
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fun keyword2 k1 k2 = Scan.lift (Args.$$$ k1 -- Args.$$$ k2 -- Args.colon) >> K ();
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fun keyword3 k1 k2 k3 =
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  Scan.lift (Args.$$$ k1 -- Args.$$$ k2 -- Args.$$$ k3 -- Args.colon) >> K ();
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val opsN = "ops";
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val rulesN = "rules";
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val normN = "norm";
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val constN = "const";
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val delN = "del";
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val any_keyword =
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  keyword2 semiringN opsN || keyword2 semiringN rulesN ||
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  keyword2 ringN opsN || keyword2 ringN rulesN ||
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  keyword2 fieldN opsN || keyword2 fieldN rulesN ||
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  keyword2 idomN rulesN || keyword2 idealN rulesN;
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val thms = Scan.repeat (Scan.unless any_keyword Attrib.multi_thm) >> flat;
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val terms = thms >> map Drule.dest_term;
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fun optional scan = Scan.optional scan [];
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in
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val normalizer_setup =
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  Attrib.setup @{binding normalizer}
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    (Scan.lift (Args.$$$ delN >> K del) ||
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      ((keyword2 semiringN opsN |-- terms) --
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       (keyword2 semiringN rulesN |-- thms)) --
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      (optional (keyword2 ringN opsN |-- terms) --
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       optional (keyword2 ringN rulesN |-- thms)) --
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      (optional (keyword2 fieldN opsN |-- terms) --
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       optional (keyword2 fieldN rulesN |-- thms)) --
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      optional (keyword2 idomN rulesN |-- thms) --
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      optional (keyword2 idealN rulesN |-- thms)
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      >> (fn ((((sr, r), f), id), idl) => 
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             add {semiring = sr, ring = r, field = f, idom = id, ideal = idl}))
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    "semiring normalizer data";
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end;
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open Conv;
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(* Very basic stuff for terms *)
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fun is_comb ct =
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  (case Thm.term_of ct of
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    _ $ _ => true
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  | _ => false);
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val concl = Thm.cprop_of #> Thm.dest_arg;
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fun is_binop ct ct' =
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  (case Thm.term_of ct' of
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    c $ _ $ _ => term_of ct aconv c
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  | _ => false);
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fun dest_binop ct ct' =
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  if is_binop ct ct' then Thm.dest_binop ct'
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  else raise CTERM ("dest_binop: bad binop", [ct, ct'])
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fun inst_thm inst = Thm.instantiate ([], inst);
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val dest_numeral = term_of #> HOLogic.dest_number #> snd;
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val is_numeral = can dest_numeral;
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val numeral01_conv = Simplifier.rewrite
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                         (HOL_basic_ss addsimps [@{thm numeral_1_eq_1}, @{thm numeral_0_eq_0}]);
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val zero1_numeral_conv = 
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 Simplifier.rewrite (HOL_basic_ss addsimps [@{thm numeral_1_eq_1} RS sym, @{thm numeral_0_eq_0} RS sym]);
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fun zerone_conv cv = zero1_numeral_conv then_conv cv then_conv numeral01_conv;
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val natarith = [@{thm "add_nat_number_of"}, @{thm "diff_nat_number_of"},
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                @{thm "mult_nat_number_of"}, @{thm "eq_nat_number_of"}, 
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                @{thm "less_nat_number_of"}];
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val nat_add_conv = 
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 zerone_conv 
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  (Simplifier.rewrite 
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    (HOL_basic_ss 
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       addsimps @{thms arith_simps} @ natarith @ @{thms rel_simps}
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             @ [@{thm if_False}, @{thm if_True}, @{thm Nat.add_0}, @{thm add_Suc},
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                 @{thm add_number_of_left}, @{thm Suc_eq_plus1}]
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             @ map (fn th => th RS sym) @{thms numerals}));
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val zeron_tm = @{cterm "0::nat"};
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val onen_tm  = @{cterm "1::nat"};
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val true_tm = @{cterm "True"};
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(* The main function! *)
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fun semiring_normalizers_conv vars (sr_ops, sr_rules) (r_ops, r_rules) (f_ops, f_rules)
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  (is_semiring_constant, semiring_add_conv, semiring_mul_conv, semiring_pow_conv) =
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let
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val [pthm_02, pthm_03, pthm_04, pthm_05, pthm_07, pthm_08,
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     pthm_09, pthm_10, pthm_11, pthm_12, pthm_13, pthm_14, pthm_15, pthm_16,
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     pthm_17, pthm_18, pthm_19, pthm_21, pthm_22, pthm_23, pthm_24,
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     pthm_25, pthm_26, pthm_27, pthm_28, pthm_29, pthm_30, pthm_31, pthm_32,
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     pthm_33, pthm_34, pthm_35, pthm_36, pthm_37, pthm_38,pthm_39,pthm_40] = sr_rules;
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val [ca, cb, cc, cd, cm, cn, cp, cq, cx, cy, cz, clx, crx, cly, cry] = vars;
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val [add_pat, mul_pat, pow_pat, zero_tm, one_tm] = sr_ops;
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val [add_tm, mul_tm, pow_tm] = map (Thm.dest_fun o Thm.dest_fun) [add_pat, mul_pat, pow_pat];
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val dest_add = dest_binop add_tm
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val dest_mul = dest_binop mul_tm
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fun dest_pow tm =
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 let val (l,r) = dest_binop pow_tm tm
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 in if is_numeral r then (l,r) else raise CTERM ("dest_pow",[tm])
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 end;
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val is_add = is_binop add_tm
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val is_mul = is_binop mul_tm
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fun is_pow tm = is_binop pow_tm tm andalso is_numeral(Thm.dest_arg tm);
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val (neg_mul,sub_add,sub_tm,neg_tm,dest_sub,is_sub,cx',cy') =
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  (case (r_ops, r_rules) of
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    ([sub_pat, neg_pat], [neg_mul, sub_add]) =>
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      let
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        val sub_tm = Thm.dest_fun (Thm.dest_fun sub_pat)
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        val neg_tm = Thm.dest_fun neg_pat
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        val dest_sub = dest_binop sub_tm
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        val is_sub = is_binop sub_tm
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      in (neg_mul,sub_add,sub_tm,neg_tm,dest_sub,is_sub, neg_mul |> concl |> Thm.dest_arg,
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          sub_add |> concl |> Thm.dest_arg |> Thm.dest_arg)
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      end
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    | _ => (TrueI, TrueI, true_tm, true_tm, (fn t => (t,t)), K false, true_tm, true_tm));
chaieb@30866
   313
chaieb@30866
   314
val (divide_inverse, inverse_divide, divide_tm, inverse_tm, is_divide) = 
chaieb@30866
   315
  (case (f_ops, f_rules) of 
chaieb@30866
   316
   ([divide_pat, inverse_pat], [div_inv, inv_div]) => 
chaieb@30866
   317
     let val div_tm = funpow 2 Thm.dest_fun divide_pat
chaieb@30866
   318
         val inv_tm = Thm.dest_fun inverse_pat
chaieb@30866
   319
     in (div_inv, inv_div, div_tm, inv_tm, is_binop div_tm)
chaieb@30866
   320
     end
chaieb@30866
   321
   | _ => (TrueI, TrueI, true_tm, true_tm, K false));
chaieb@30866
   322
wenzelm@23252
   323
in fn variable_order =>
wenzelm@23252
   324
 let
wenzelm@23252
   325
wenzelm@23252
   326
(* Conversion for "x^n * x^m", with either x^n = x and/or x^m = x possible.  *)
wenzelm@23252
   327
(* Also deals with "const * const", but both terms must involve powers of    *)
wenzelm@23252
   328
(* the same variable, or both be constants, or behaviour may be incorrect.   *)
wenzelm@23252
   329
wenzelm@23252
   330
 fun powvar_mul_conv tm =
wenzelm@23252
   331
  let
wenzelm@23252
   332
  val (l,r) = dest_mul tm
wenzelm@23252
   333
  in if is_semiring_constant l andalso is_semiring_constant r
wenzelm@23252
   334
     then semiring_mul_conv tm
wenzelm@23252
   335
     else
wenzelm@23252
   336
      ((let
wenzelm@23252
   337
         val (lx,ln) = dest_pow l
wenzelm@23252
   338
        in
wenzelm@23252
   339
         ((let val (rx,rn) = dest_pow r
wenzelm@23252
   340
               val th1 = inst_thm [(cx,lx),(cp,ln),(cq,rn)] pthm_29
wenzelm@23252
   341
                val (tm1,tm2) = Thm.dest_comb(concl th1) in
wenzelm@23252
   342
               transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv tm2)) end)
wenzelm@23252
   343
           handle CTERM _ =>
wenzelm@23252
   344
            (let val th1 = inst_thm [(cx,lx),(cq,ln)] pthm_31
wenzelm@23252
   345
                 val (tm1,tm2) = Thm.dest_comb(concl th1) in
wenzelm@23252
   346
               transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv tm2)) end)) end)
wenzelm@23252
   347
       handle CTERM _ =>
wenzelm@23252
   348
           ((let val (rx,rn) = dest_pow r
wenzelm@23252
   349
                val th1 = inst_thm [(cx,rx),(cq,rn)] pthm_30
wenzelm@23252
   350
                val (tm1,tm2) = Thm.dest_comb(concl th1) in
wenzelm@23252
   351
               transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv tm2)) end)
wenzelm@23252
   352
           handle CTERM _ => inst_thm [(cx,l)] pthm_32
wenzelm@23252
   353
wenzelm@23252
   354
))
wenzelm@23252
   355
 end;
wenzelm@23252
   356
wenzelm@23252
   357
(* Remove "1 * m" from a monomial, and just leave m.                         *)
wenzelm@23252
   358
wenzelm@23252
   359
 fun monomial_deone th =
wenzelm@23252
   360
       (let val (l,r) = dest_mul(concl th) in
wenzelm@23252
   361
           if l aconvc one_tm
wenzelm@23252
   362
          then transitive th (inst_thm [(ca,r)] pthm_13)  else th end)
wenzelm@23252
   363
       handle CTERM _ => th;
wenzelm@23252
   364
wenzelm@23252
   365
(* Conversion for "(monomial)^n", where n is a numeral.                      *)
wenzelm@23252
   366
wenzelm@23252
   367
 val monomial_pow_conv =
wenzelm@23252
   368
  let
wenzelm@23252
   369
   fun monomial_pow tm bod ntm =
wenzelm@23252
   370
    if not(is_comb bod)
wenzelm@23252
   371
    then reflexive tm
wenzelm@23252
   372
    else
wenzelm@23252
   373
     if is_semiring_constant bod
wenzelm@23252
   374
     then semiring_pow_conv tm
wenzelm@23252
   375
     else
wenzelm@23252
   376
      let
wenzelm@23252
   377
      val (lopr,r) = Thm.dest_comb bod
wenzelm@23252
   378
      in if not(is_comb lopr)
wenzelm@23252
   379
         then reflexive tm
wenzelm@23252
   380
        else
wenzelm@23252
   381
          let
wenzelm@23252
   382
          val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   383
         in
wenzelm@23252
   384
           if opr aconvc pow_tm andalso is_numeral r
wenzelm@23252
   385
          then
wenzelm@23252
   386
            let val th1 = inst_thm [(cx,l),(cp,r),(cq,ntm)] pthm_34
wenzelm@23252
   387
                val (l,r) = Thm.dest_comb(concl th1)
haftmann@36700
   388
           in transitive th1 (Drule.arg_cong_rule l (nat_add_conv r))
wenzelm@23252
   389
           end
wenzelm@23252
   390
           else
wenzelm@23252
   391
            if opr aconvc mul_tm
wenzelm@23252
   392
            then
wenzelm@23252
   393
             let
wenzelm@23252
   394
              val th1 = inst_thm [(cx,l),(cy,r),(cq,ntm)] pthm_33
wenzelm@23252
   395
             val (xy,z) = Thm.dest_comb(concl th1)
wenzelm@23252
   396
              val (x,y) = Thm.dest_comb xy
wenzelm@23252
   397
              val thl = monomial_pow y l ntm
wenzelm@23252
   398
              val thr = monomial_pow z r ntm
wenzelm@23252
   399
             in transitive th1 (combination (Drule.arg_cong_rule x thl) thr)
wenzelm@23252
   400
             end
wenzelm@23252
   401
             else reflexive tm
wenzelm@23252
   402
          end
wenzelm@23252
   403
      end
wenzelm@23252
   404
  in fn tm =>
wenzelm@23252
   405
   let
wenzelm@23252
   406
    val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   407
    val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   408
   in if not (opr aconvc pow_tm) orelse not(is_numeral r)
wenzelm@23252
   409
      then raise CTERM ("monomial_pow_conv", [tm])
wenzelm@23252
   410
      else if r aconvc zeron_tm
wenzelm@23252
   411
      then inst_thm [(cx,l)] pthm_35
wenzelm@23252
   412
      else if r aconvc onen_tm
wenzelm@23252
   413
      then inst_thm [(cx,l)] pthm_36
wenzelm@23252
   414
      else monomial_deone(monomial_pow tm l r)
wenzelm@23252
   415
   end
wenzelm@23252
   416
  end;
wenzelm@23252
   417
wenzelm@23252
   418
(* Multiplication of canonical monomials.                                    *)
wenzelm@23252
   419
 val monomial_mul_conv =
wenzelm@23252
   420
  let
wenzelm@23252
   421
   fun powvar tm =
wenzelm@23252
   422
    if is_semiring_constant tm then one_tm
wenzelm@23252
   423
    else
wenzelm@23252
   424
     ((let val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   425
           val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   426
       in if opr aconvc pow_tm andalso is_numeral r then l 
wenzelm@23252
   427
          else raise CTERM ("monomial_mul_conv",[tm]) end)
wenzelm@23252
   428
     handle CTERM _ => tm)   (* FIXME !? *)
wenzelm@23252
   429
   fun  vorder x y =
wenzelm@23252
   430
    if x aconvc y then 0
wenzelm@23252
   431
    else
wenzelm@23252
   432
     if x aconvc one_tm then ~1
wenzelm@23252
   433
     else if y aconvc one_tm then 1
wenzelm@23252
   434
      else if variable_order x y then ~1 else 1
wenzelm@23252
   435
   fun monomial_mul tm l r =
wenzelm@23252
   436
    ((let val (lx,ly) = dest_mul l val vl = powvar lx
wenzelm@23252
   437
      in
wenzelm@23252
   438
      ((let
wenzelm@23252
   439
        val (rx,ry) = dest_mul r
wenzelm@23252
   440
         val vr = powvar rx
wenzelm@23252
   441
         val ord = vorder vl vr
wenzelm@23252
   442
        in
wenzelm@23252
   443
         if ord = 0
wenzelm@23252
   444
        then
wenzelm@23252
   445
          let
wenzelm@23252
   446
             val th1 = inst_thm [(clx,lx),(cly,ly),(crx,rx),(cry,ry)] pthm_15
wenzelm@23252
   447
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   448
             val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   449
             val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv tm4)) tm2
wenzelm@23252
   450
             val th3 = transitive th1 th2
wenzelm@23252
   451
              val  (tm5,tm6) = Thm.dest_comb(concl th3)
wenzelm@23252
   452
              val  (tm7,tm8) = Thm.dest_comb tm6
wenzelm@23252
   453
             val  th4 = monomial_mul tm6 (Thm.dest_arg tm7) tm8
wenzelm@23252
   454
         in  transitive th3 (Drule.arg_cong_rule tm5 th4)
wenzelm@23252
   455
         end
wenzelm@23252
   456
         else
wenzelm@23252
   457
          let val th0 = if ord < 0 then pthm_16 else pthm_17
wenzelm@23252
   458
             val th1 = inst_thm [(clx,lx),(cly,ly),(crx,rx),(cry,ry)] th0
wenzelm@23252
   459
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   460
             val (tm3,tm4) = Thm.dest_comb tm2
wenzelm@23252
   461
         in transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4))
wenzelm@23252
   462
         end
wenzelm@23252
   463
        end)
wenzelm@23252
   464
       handle CTERM _ =>
wenzelm@23252
   465
        (let val vr = powvar r val ord = vorder vl vr
wenzelm@23252
   466
        in
wenzelm@23252
   467
          if ord = 0 then
wenzelm@23252
   468
           let
wenzelm@23252
   469
           val th1 = inst_thm [(clx,lx),(cly,ly),(crx,r)] pthm_18
wenzelm@23252
   470
                 val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   471
           val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   472
           val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv tm4)) tm2
wenzelm@23252
   473
          in transitive th1 th2
wenzelm@23252
   474
          end
wenzelm@23252
   475
          else
wenzelm@23252
   476
          if ord < 0 then
wenzelm@23252
   477
            let val th1 = inst_thm [(clx,lx),(cly,ly),(crx,r)] pthm_19
wenzelm@23252
   478
                val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   479
                val (tm3,tm4) = Thm.dest_comb tm2
wenzelm@23252
   480
           in transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4))
wenzelm@23252
   481
           end
wenzelm@23252
   482
           else inst_thm [(ca,l),(cb,r)] pthm_09
wenzelm@23252
   483
        end)) end)
wenzelm@23252
   484
     handle CTERM _ =>
wenzelm@23252
   485
      (let val vl = powvar l in
wenzelm@23252
   486
        ((let
wenzelm@23252
   487
          val (rx,ry) = dest_mul r
wenzelm@23252
   488
          val vr = powvar rx
wenzelm@23252
   489
           val ord = vorder vl vr
wenzelm@23252
   490
         in if ord = 0 then
wenzelm@23252
   491
              let val th1 = inst_thm [(clx,l),(crx,rx),(cry,ry)] pthm_21
wenzelm@23252
   492
                 val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   493
                 val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   494
             in transitive th1 (Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv tm4)) tm2)
wenzelm@23252
   495
             end
wenzelm@23252
   496
             else if ord > 0 then
wenzelm@23252
   497
                 let val th1 = inst_thm [(clx,l),(crx,rx),(cry,ry)] pthm_22
wenzelm@23252
   498
                     val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   499
                    val (tm3,tm4) = Thm.dest_comb tm2
wenzelm@23252
   500
                in transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4))
wenzelm@23252
   501
                end
wenzelm@23252
   502
             else reflexive tm
wenzelm@23252
   503
         end)
wenzelm@23252
   504
        handle CTERM _ =>
wenzelm@23252
   505
          (let val vr = powvar r
wenzelm@23252
   506
               val  ord = vorder vl vr
wenzelm@23252
   507
          in if ord = 0 then powvar_mul_conv tm
wenzelm@23252
   508
              else if ord > 0 then inst_thm [(ca,l),(cb,r)] pthm_09
wenzelm@23252
   509
              else reflexive tm
wenzelm@23252
   510
          end)) end))
wenzelm@23252
   511
  in fn tm => let val (l,r) = dest_mul tm in monomial_deone(monomial_mul tm l r)
wenzelm@23252
   512
             end
wenzelm@23252
   513
  end;
wenzelm@23252
   514
(* Multiplication by monomial of a polynomial.                               *)
wenzelm@23252
   515
wenzelm@23252
   516
 val polynomial_monomial_mul_conv =
wenzelm@23252
   517
  let
wenzelm@23252
   518
   fun pmm_conv tm =
wenzelm@23252
   519
    let val (l,r) = dest_mul tm
wenzelm@23252
   520
    in
wenzelm@23252
   521
    ((let val (y,z) = dest_add r
wenzelm@23252
   522
          val th1 = inst_thm [(cx,l),(cy,y),(cz,z)] pthm_37
wenzelm@23252
   523
          val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   524
          val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   525
          val th2 = combination (Drule.arg_cong_rule tm3 (monomial_mul_conv tm4)) (pmm_conv tm2)
wenzelm@23252
   526
      in transitive th1 th2
wenzelm@23252
   527
      end)
wenzelm@23252
   528
     handle CTERM _ => monomial_mul_conv tm)
wenzelm@23252
   529
   end
wenzelm@23252
   530
 in pmm_conv
wenzelm@23252
   531
 end;
wenzelm@23252
   532
wenzelm@23252
   533
(* Addition of two monomials identical except for constant multiples.        *)
wenzelm@23252
   534
wenzelm@23252
   535
fun monomial_add_conv tm =
wenzelm@23252
   536
 let val (l,r) = dest_add tm
wenzelm@23252
   537
 in if is_semiring_constant l andalso is_semiring_constant r
wenzelm@23252
   538
    then semiring_add_conv tm
wenzelm@23252
   539
    else
wenzelm@23252
   540
     let val th1 =
wenzelm@23252
   541
           if is_mul l andalso is_semiring_constant(Thm.dest_arg1 l)
wenzelm@23252
   542
           then if is_mul r andalso is_semiring_constant(Thm.dest_arg1 r) then
wenzelm@23252
   543
                    inst_thm [(ca,Thm.dest_arg1 l),(cm,Thm.dest_arg r), (cb,Thm.dest_arg1 r)] pthm_02
wenzelm@23252
   544
                else inst_thm [(ca,Thm.dest_arg1 l),(cm,r)] pthm_03
wenzelm@23252
   545
           else if is_mul r andalso is_semiring_constant(Thm.dest_arg1 r)
wenzelm@23252
   546
           then inst_thm [(cm,l),(ca,Thm.dest_arg1 r)] pthm_04
wenzelm@23252
   547
           else inst_thm [(cm,r)] pthm_05
wenzelm@23252
   548
         val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   549
         val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   550
         val th2 = Drule.arg_cong_rule tm3 (semiring_add_conv tm4)
wenzelm@23252
   551
         val th3 = transitive th1 (Drule.fun_cong_rule th2 tm2)
wenzelm@23252
   552
         val tm5 = concl th3
wenzelm@23252
   553
      in
wenzelm@23252
   554
      if (Thm.dest_arg1 tm5) aconvc zero_tm
wenzelm@23252
   555
      then transitive th3 (inst_thm [(ca,Thm.dest_arg tm5)] pthm_11)
wenzelm@23252
   556
      else monomial_deone th3
wenzelm@23252
   557
     end
wenzelm@23252
   558
 end;
wenzelm@23252
   559
wenzelm@23252
   560
(* Ordering on monomials.                                                    *)
wenzelm@23252
   561
wenzelm@23252
   562
fun striplist dest =
wenzelm@23252
   563
 let fun strip x acc =
wenzelm@23252
   564
   ((let val (l,r) = dest x in
wenzelm@23252
   565
        strip l (strip r acc) end)
wenzelm@23252
   566
    handle CTERM _ => x::acc)    (* FIXME !? *)
wenzelm@23252
   567
 in fn x => strip x []
wenzelm@23252
   568
 end;
wenzelm@23252
   569
wenzelm@23252
   570
wenzelm@23252
   571
fun powervars tm =
wenzelm@23252
   572
 let val ptms = striplist dest_mul tm
wenzelm@23252
   573
 in if is_semiring_constant (hd ptms) then tl ptms else ptms
wenzelm@23252
   574
 end;
wenzelm@23252
   575
val num_0 = 0;
wenzelm@23252
   576
val num_1 = 1;
wenzelm@23252
   577
fun dest_varpow tm =
wenzelm@23252
   578
 ((let val (x,n) = dest_pow tm in (x,dest_numeral n) end)
wenzelm@23252
   579
   handle CTERM _ =>
wenzelm@23252
   580
   (tm,(if is_semiring_constant tm then num_0 else num_1)));
wenzelm@23252
   581
wenzelm@23252
   582
val morder =
wenzelm@23252
   583
 let fun lexorder l1 l2 =
wenzelm@23252
   584
  case (l1,l2) of
wenzelm@23252
   585
    ([],[]) => 0
wenzelm@23252
   586
  | (vps,[]) => ~1
wenzelm@23252
   587
  | ([],vps) => 1
wenzelm@23252
   588
  | (((x1,n1)::vs1),((x2,n2)::vs2)) =>
wenzelm@23252
   589
     if variable_order x1 x2 then 1
wenzelm@23252
   590
     else if variable_order x2 x1 then ~1
wenzelm@23252
   591
     else if n1 < n2 then ~1
wenzelm@23252
   592
     else if n2 < n1 then 1
wenzelm@23252
   593
     else lexorder vs1 vs2
wenzelm@23252
   594
 in fn tm1 => fn tm2 =>
wenzelm@23252
   595
  let val vdegs1 = map dest_varpow (powervars tm1)
wenzelm@23252
   596
      val vdegs2 = map dest_varpow (powervars tm2)
wenzelm@33002
   597
      val deg1 = fold (Integer.add o snd) vdegs1 num_0
wenzelm@33002
   598
      val deg2 = fold (Integer.add o snd) vdegs2 num_0
wenzelm@23252
   599
  in if deg1 < deg2 then ~1 else if deg1 > deg2 then 1
wenzelm@23252
   600
                            else lexorder vdegs1 vdegs2
wenzelm@23252
   601
  end
wenzelm@23252
   602
 end;
wenzelm@23252
   603
wenzelm@23252
   604
(* Addition of two polynomials.                                              *)
wenzelm@23252
   605
wenzelm@23252
   606
val polynomial_add_conv =
wenzelm@23252
   607
 let
wenzelm@23252
   608
 fun dezero_rule th =
wenzelm@23252
   609
  let
wenzelm@23252
   610
   val tm = concl th
wenzelm@23252
   611
  in
wenzelm@23252
   612
   if not(is_add tm) then th else
wenzelm@23252
   613
   let val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   614
       val l = Thm.dest_arg lopr
wenzelm@23252
   615
   in
wenzelm@23252
   616
    if l aconvc zero_tm
wenzelm@23252
   617
    then transitive th (inst_thm [(ca,r)] pthm_07)   else
wenzelm@23252
   618
        if r aconvc zero_tm
wenzelm@23252
   619
        then transitive th (inst_thm [(ca,l)] pthm_08)  else th
wenzelm@23252
   620
   end
wenzelm@23252
   621
  end
wenzelm@23252
   622
 fun padd tm =
wenzelm@23252
   623
  let
wenzelm@23252
   624
   val (l,r) = dest_add tm
wenzelm@23252
   625
  in
wenzelm@23252
   626
   if l aconvc zero_tm then inst_thm [(ca,r)] pthm_07
wenzelm@23252
   627
   else if r aconvc zero_tm then inst_thm [(ca,l)] pthm_08
wenzelm@23252
   628
   else
wenzelm@23252
   629
    if is_add l
wenzelm@23252
   630
    then
wenzelm@23252
   631
     let val (a,b) = dest_add l
wenzelm@23252
   632
     in
wenzelm@23252
   633
     if is_add r then
wenzelm@23252
   634
      let val (c,d) = dest_add r
wenzelm@23252
   635
          val ord = morder a c
wenzelm@23252
   636
      in
wenzelm@23252
   637
       if ord = 0 then
wenzelm@23252
   638
        let val th1 = inst_thm [(ca,a),(cb,b),(cc,c),(cd,d)] pthm_23
wenzelm@23252
   639
            val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   640
            val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   641
            val th2 = Drule.arg_cong_rule tm3 (monomial_add_conv tm4)
wenzelm@23252
   642
        in dezero_rule (transitive th1 (combination th2 (padd tm2)))
wenzelm@23252
   643
        end
wenzelm@23252
   644
       else (* ord <> 0*)
wenzelm@23252
   645
        let val th1 =
wenzelm@23252
   646
                if ord > 0 then inst_thm [(ca,a),(cb,b),(cc,r)] pthm_24
wenzelm@23252
   647
                else inst_thm [(ca,l),(cc,c),(cd,d)] pthm_25
wenzelm@23252
   648
            val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   649
        in dezero_rule (transitive th1 (Drule.arg_cong_rule tm1 (padd tm2)))
wenzelm@23252
   650
        end
wenzelm@23252
   651
      end
wenzelm@23252
   652
     else (* not (is_add r)*)
wenzelm@23252
   653
      let val ord = morder a r
wenzelm@23252
   654
      in
wenzelm@23252
   655
       if ord = 0 then
wenzelm@23252
   656
        let val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_26
wenzelm@23252
   657
            val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   658
            val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   659
            val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (monomial_add_conv tm4)) tm2
wenzelm@23252
   660
        in dezero_rule (transitive th1 th2)
wenzelm@23252
   661
        end
wenzelm@23252
   662
       else (* ord <> 0*)
wenzelm@23252
   663
        if ord > 0 then
wenzelm@23252
   664
          let val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_24
wenzelm@23252
   665
              val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   666
          in dezero_rule (transitive th1 (Drule.arg_cong_rule tm1 (padd tm2)))
wenzelm@23252
   667
          end
wenzelm@23252
   668
        else dezero_rule (inst_thm [(ca,l),(cc,r)] pthm_27)
wenzelm@23252
   669
      end
wenzelm@23252
   670
    end
wenzelm@23252
   671
   else (* not (is_add l)*)
wenzelm@23252
   672
    if is_add r then
wenzelm@23252
   673
      let val (c,d) = dest_add r
wenzelm@23252
   674
          val  ord = morder l c
wenzelm@23252
   675
      in
wenzelm@23252
   676
       if ord = 0 then
wenzelm@23252
   677
         let val th1 = inst_thm [(ca,l),(cc,c),(cd,d)] pthm_28
wenzelm@23252
   678
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   679
             val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   680
             val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (monomial_add_conv tm4)) tm2
wenzelm@23252
   681
         in dezero_rule (transitive th1 th2)
wenzelm@23252
   682
         end
wenzelm@23252
   683
       else
wenzelm@23252
   684
        if ord > 0 then reflexive tm
wenzelm@23252
   685
        else
wenzelm@23252
   686
         let val th1 = inst_thm [(ca,l),(cc,c),(cd,d)] pthm_25
wenzelm@23252
   687
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   688
         in dezero_rule (transitive th1 (Drule.arg_cong_rule tm1 (padd tm2)))
wenzelm@23252
   689
         end
wenzelm@23252
   690
      end
wenzelm@23252
   691
    else
wenzelm@23252
   692
     let val ord = morder l r
wenzelm@23252
   693
     in
wenzelm@23252
   694
      if ord = 0 then monomial_add_conv tm
wenzelm@23252
   695
      else if ord > 0 then dezero_rule(reflexive tm)
wenzelm@23252
   696
      else dezero_rule (inst_thm [(ca,l),(cc,r)] pthm_27)
wenzelm@23252
   697
     end
wenzelm@23252
   698
  end
wenzelm@23252
   699
 in padd
wenzelm@23252
   700
 end;
wenzelm@23252
   701
wenzelm@23252
   702
(* Multiplication of two polynomials.                                        *)
wenzelm@23252
   703
wenzelm@23252
   704
val polynomial_mul_conv =
wenzelm@23252
   705
 let
wenzelm@23252
   706
  fun pmul tm =
wenzelm@23252
   707
   let val (l,r) = dest_mul tm
wenzelm@23252
   708
   in
wenzelm@23252
   709
    if not(is_add l) then polynomial_monomial_mul_conv tm
wenzelm@23252
   710
    else
wenzelm@23252
   711
     if not(is_add r) then
wenzelm@23252
   712
      let val th1 = inst_thm [(ca,l),(cb,r)] pthm_09
wenzelm@23252
   713
      in transitive th1 (polynomial_monomial_mul_conv(concl th1))
wenzelm@23252
   714
      end
wenzelm@23252
   715
     else
wenzelm@23252
   716
       let val (a,b) = dest_add l
wenzelm@23252
   717
           val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_10
wenzelm@23252
   718
           val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   719
           val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   720
           val th2 = Drule.arg_cong_rule tm3 (polynomial_monomial_mul_conv tm4)
wenzelm@23252
   721
           val th3 = transitive th1 (combination th2 (pmul tm2))
wenzelm@23252
   722
       in transitive th3 (polynomial_add_conv (concl th3))
wenzelm@23252
   723
       end
wenzelm@23252
   724
   end
wenzelm@23252
   725
 in fn tm =>
wenzelm@23252
   726
   let val (l,r) = dest_mul tm
wenzelm@23252
   727
   in
wenzelm@23252
   728
    if l aconvc zero_tm then inst_thm [(ca,r)] pthm_11
wenzelm@23252
   729
    else if r aconvc zero_tm then inst_thm [(ca,l)] pthm_12
wenzelm@23252
   730
    else if l aconvc one_tm then inst_thm [(ca,r)] pthm_13
wenzelm@23252
   731
    else if r aconvc one_tm then inst_thm [(ca,l)] pthm_14
wenzelm@23252
   732
    else pmul tm
wenzelm@23252
   733
   end
wenzelm@23252
   734
 end;
wenzelm@23252
   735
wenzelm@23252
   736
(* Power of polynomial (optimized for the monomial and trivial cases).       *)
wenzelm@23252
   737
wenzelm@23580
   738
fun num_conv n =
wenzelm@23580
   739
  nat_add_conv (Thm.capply @{cterm Suc} (Numeral.mk_cnumber @{ctyp nat} (dest_numeral n - 1)))
wenzelm@23580
   740
  |> Thm.symmetric;
wenzelm@23252
   741
wenzelm@23252
   742
wenzelm@23252
   743
val polynomial_pow_conv =
wenzelm@23252
   744
 let
wenzelm@23252
   745
  fun ppow tm =
wenzelm@23252
   746
    let val (l,n) = dest_pow tm
wenzelm@23252
   747
    in
wenzelm@23252
   748
     if n aconvc zeron_tm then inst_thm [(cx,l)] pthm_35
wenzelm@23252
   749
     else if n aconvc onen_tm then inst_thm [(cx,l)] pthm_36
wenzelm@23252
   750
     else
wenzelm@23252
   751
         let val th1 = num_conv n
wenzelm@23252
   752
             val th2 = inst_thm [(cx,l),(cq,Thm.dest_arg (concl th1))] pthm_38
wenzelm@23252
   753
             val (tm1,tm2) = Thm.dest_comb(concl th2)
wenzelm@23252
   754
             val th3 = transitive th2 (Drule.arg_cong_rule tm1 (ppow tm2))
wenzelm@23252
   755
             val th4 = transitive (Drule.arg_cong_rule (Thm.dest_fun tm) th1) th3
wenzelm@23252
   756
         in transitive th4 (polynomial_mul_conv (concl th4))
wenzelm@23252
   757
         end
wenzelm@23252
   758
    end
wenzelm@23252
   759
 in fn tm =>
wenzelm@23252
   760
       if is_add(Thm.dest_arg1 tm) then ppow tm else monomial_pow_conv tm
wenzelm@23252
   761
 end;
wenzelm@23252
   762
wenzelm@23252
   763
(* Negation.                                                                 *)
wenzelm@23252
   764
wenzelm@23580
   765
fun polynomial_neg_conv tm =
wenzelm@23252
   766
   let val (l,r) = Thm.dest_comb tm in
wenzelm@23252
   767
        if not (l aconvc neg_tm) then raise CTERM ("polynomial_neg_conv",[tm]) else
wenzelm@23252
   768
        let val th1 = inst_thm [(cx',r)] neg_mul
wenzelm@23252
   769
            val th2 = transitive th1 (arg1_conv semiring_mul_conv (concl th1))
wenzelm@23252
   770
        in transitive th2 (polynomial_monomial_mul_conv (concl th2))
wenzelm@23252
   771
        end
wenzelm@23252
   772
   end;
wenzelm@23252
   773
wenzelm@23252
   774
wenzelm@23252
   775
(* Subtraction.                                                              *)
wenzelm@23580
   776
fun polynomial_sub_conv tm =
wenzelm@23252
   777
  let val (l,r) = dest_sub tm
wenzelm@23252
   778
      val th1 = inst_thm [(cx',l),(cy',r)] sub_add
wenzelm@23252
   779
      val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   780
      val th2 = Drule.arg_cong_rule tm1 (polynomial_neg_conv tm2)
wenzelm@23252
   781
  in transitive th1 (transitive th2 (polynomial_add_conv (concl th2)))
wenzelm@23252
   782
  end;
wenzelm@23252
   783
wenzelm@23252
   784
(* Conversion from HOL term.                                                 *)
wenzelm@23252
   785
wenzelm@23252
   786
fun polynomial_conv tm =
chaieb@23407
   787
 if is_semiring_constant tm then semiring_add_conv tm
chaieb@23407
   788
 else if not(is_comb tm) then reflexive tm
wenzelm@23252
   789
 else
wenzelm@23252
   790
  let val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   791
  in if lopr aconvc neg_tm then
wenzelm@23252
   792
       let val th1 = Drule.arg_cong_rule lopr (polynomial_conv r)
wenzelm@23252
   793
       in transitive th1 (polynomial_neg_conv (concl th1))
wenzelm@23252
   794
       end
chaieb@30866
   795
     else if lopr aconvc inverse_tm then
chaieb@30866
   796
       let val th1 = Drule.arg_cong_rule lopr (polynomial_conv r)
chaieb@30866
   797
       in transitive th1 (semiring_mul_conv (concl th1))
chaieb@30866
   798
       end
wenzelm@23252
   799
     else
wenzelm@23252
   800
       if not(is_comb lopr) then reflexive tm
wenzelm@23252
   801
       else
wenzelm@23252
   802
         let val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   803
         in if opr aconvc pow_tm andalso is_numeral r
wenzelm@23252
   804
            then
wenzelm@23252
   805
              let val th1 = Drule.fun_cong_rule (Drule.arg_cong_rule opr (polynomial_conv l)) r
wenzelm@23252
   806
              in transitive th1 (polynomial_pow_conv (concl th1))
wenzelm@23252
   807
              end
chaieb@30866
   808
         else if opr aconvc divide_tm 
chaieb@30866
   809
            then
chaieb@30866
   810
              let val th1 = combination (Drule.arg_cong_rule opr (polynomial_conv l)) 
chaieb@30866
   811
                                        (polynomial_conv r)
chaieb@30866
   812
                  val th2 = (rewr_conv divide_inverse then_conv polynomial_mul_conv) 
chaieb@30866
   813
                              (Thm.rhs_of th1)
chaieb@30866
   814
              in transitive th1 th2
chaieb@30866
   815
              end
wenzelm@23252
   816
            else
wenzelm@23252
   817
              if opr aconvc add_tm orelse opr aconvc mul_tm orelse opr aconvc sub_tm
wenzelm@23252
   818
              then
wenzelm@23252
   819
               let val th1 = combination (Drule.arg_cong_rule opr (polynomial_conv l)) (polynomial_conv r)
wenzelm@23252
   820
                   val f = if opr aconvc add_tm then polynomial_add_conv
wenzelm@23252
   821
                      else if opr aconvc mul_tm then polynomial_mul_conv
wenzelm@23252
   822
                      else polynomial_sub_conv
wenzelm@23252
   823
               in transitive th1 (f (concl th1))
wenzelm@23252
   824
               end
wenzelm@23252
   825
              else reflexive tm
wenzelm@23252
   826
         end
wenzelm@23252
   827
  end;
wenzelm@23252
   828
 in
wenzelm@23252
   829
   {main = polynomial_conv,
wenzelm@23252
   830
    add = polynomial_add_conv,
wenzelm@23252
   831
    mul = polynomial_mul_conv,
wenzelm@23252
   832
    pow = polynomial_pow_conv,
wenzelm@23252
   833
    neg = polynomial_neg_conv,
wenzelm@23252
   834
    sub = polynomial_sub_conv}
wenzelm@23252
   835
 end
wenzelm@23252
   836
end;
wenzelm@23252
   837
wenzelm@35410
   838
val nat_exp_ss =
wenzelm@35410
   839
  HOL_basic_ss addsimps (@{thms nat_number} @ @{thms nat_arith} @ @{thms arith_simps} @ @{thms rel_simps})
wenzelm@35410
   840
    addsimps [@{thm Let_def}, @{thm if_False}, @{thm if_True}, @{thm Nat.add_0}, @{thm add_Suc}];
wenzelm@23252
   841
wenzelm@35408
   842
fun simple_cterm_ord t u = Term_Ord.term_ord (term_of t, term_of u) = LESS;
chaieb@27222
   843
chaieb@30866
   844
fun semiring_normalizers_ord_wrapper ctxt ({vars, semiring, ring, field, idom, ideal}, 
chaieb@23407
   845
                                     {conv, dest_const, mk_const, is_const}) ord =
wenzelm@23252
   846
  let
wenzelm@23252
   847
    val pow_conv =
wenzelm@23252
   848
      arg_conv (Simplifier.rewrite nat_exp_ss)
wenzelm@23252
   849
      then_conv Simplifier.rewrite
wenzelm@23252
   850
        (HOL_basic_ss addsimps [nth (snd semiring) 31, nth (snd semiring) 34])
chaieb@23330
   851
      then_conv conv ctxt
chaieb@23330
   852
    val dat = (is_const, conv ctxt, conv ctxt, pow_conv)
chaieb@30866
   853
  in semiring_normalizers_conv vars semiring ring field dat ord end;
chaieb@27222
   854
chaieb@30866
   855
fun semiring_normalize_ord_wrapper ctxt ({vars, semiring, ring, field, idom, ideal}, {conv, dest_const, mk_const, is_const}) ord =
chaieb@30866
   856
 #main (semiring_normalizers_ord_wrapper ctxt ({vars = vars, semiring = semiring, ring = ring, field = field, idom = idom, ideal = ideal},{conv = conv, dest_const = dest_const, mk_const = mk_const, is_const = is_const}) ord);
wenzelm@23252
   857
chaieb@23407
   858
fun semiring_normalize_wrapper ctxt data = 
chaieb@23407
   859
  semiring_normalize_ord_wrapper ctxt data simple_cterm_ord;
chaieb@23407
   860
chaieb@23407
   861
fun semiring_normalize_ord_conv ctxt ord tm =
haftmann@36700
   862
  (case match ctxt tm of
wenzelm@23252
   863
    NONE => reflexive tm
chaieb@23407
   864
  | SOME res => semiring_normalize_ord_wrapper ctxt res ord tm);
chaieb@23407
   865
 
chaieb@23407
   866
fun semiring_normalize_conv ctxt = semiring_normalize_ord_conv ctxt simple_cterm_ord;
wenzelm@23252
   867
haftmann@36700
   868
(* theory setup *)
haftmann@36700
   869
haftmann@36702
   870
val setup = normalizer_setup
haftmann@36700
   871
wenzelm@23252
   872
end;