src/HOL/Tools/semiring_normalizer.ML
author haftmann
Fri Oct 10 19:55:32 2014 +0200 (2014-10-10)
changeset 58646 cd63a4b12a33
parent 54249 ce00f2fef556
child 58826 2ed2eaabe3df
permissions -rw-r--r--
specialized specification: avoid trivial instances
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(*  Title:      HOL/Tools/semiring_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 SEMIRING_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,
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    field: cterm list * thm list, idom: thm list, ideal: thm list} -> 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_funs: thm -> declaration
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  val field_funs: 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: cterm list -> cterm list * thm list
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    -> 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: Proof.context -> conv,
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         mul: Proof.context -> conv,
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         neg: Proof.context -> conv,
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         main: Proof.context -> conv,
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         pow: Proof.context -> conv,
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         sub: Proof.context -> conv}
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  val semiring_normalizers_ord_wrapper:  Proof.context -> entry ->
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    (cterm -> cterm -> bool) ->
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      {add: Proof.context -> conv,
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       mul: Proof.context -> conv,
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       neg: Proof.context -> conv,
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       main: Proof.context -> conv,
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       pow: Proof.context -> conv,
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       sub: Proof.context -> conv}
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  val setup: theory -> theory
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end
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structure Semiring_Normalizer: SEMIRING_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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structure Data = Generic_Data
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(
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  type T = (thm * entry) list;
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  val empty = [];
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  val extend = I;
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  fun merge data = AList.merge Thm.eq_thm (K true) data;
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);
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val get = Data.get o Context.Proof;
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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 (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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val del = Thm.declaration_attribute (Data.map o AList.delete Thm.eq_thm);
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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 (Thm.symmetric o mk_meta) ideal
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    in
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      AList.delete Thm.eq_thm key #>
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      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 (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 Thm.eq_thm 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 Thm.eq_thm key (apsnd (K fns)) data end);
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val semiring_norm_ss =
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  simpset_of (put_simpset HOL_basic_ss @{context} addsimps @{thms semiring_norm});
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fun semiring_funs key = funs key
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   {is_const = fn phi => can HOLogic.dest_number o Thm.term_of,
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    dest_const = fn phi => fn ct =>
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      Rat.rat_of_int (snd
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        (HOLogic.dest_number (Thm.term_of ct)
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          handle TERM _ => error "ring_dest_const")),
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    mk_const = fn phi => fn cT => fn x => Numeral.mk_cnumber cT
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      (case Rat.quotient_of_rat x of (i, 1) => i | _ => error "int_of_rat: bad int"),
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    conv = fn phi => fn ctxt =>
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      Simplifier.rewrite (put_simpset semiring_norm_ss ctxt)
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      then_conv Simplifier.rewrite (put_simpset HOL_basic_ss ctxt addsimps @{thms numeral_1_eq_1})};
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fun field_funs key =
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  let
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    fun numeral_is_const ct =
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      case term_of ct of
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       Const (@{const_name Fields.divide},_) $ a $ b =>
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         can HOLogic.dest_number a andalso can HOLogic.dest_number b
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     | Const (@{const_name Fields.inverse},_)$t => can HOLogic.dest_number t
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     | t => can HOLogic.dest_number t
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    fun dest_const ct = ((case term_of ct of
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       Const (@{const_name Fields.divide},_) $ a $ b=>
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        Rat.rat_of_quotient (snd (HOLogic.dest_number a), snd (HOLogic.dest_number b))
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     | Const (@{const_name Fields.inverse},_)$t => 
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                   Rat.inv (Rat.rat_of_int (snd (HOLogic.dest_number t)))
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     | t => Rat.rat_of_int (snd (HOLogic.dest_number t))) 
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       handle TERM _ => error "ring_dest_const")
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    fun mk_const phi cT x =
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      let val (a, b) = Rat.quotient_of_rat x
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      in if b = 1 then Numeral.mk_cnumber cT a
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        else Thm.apply
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             (Thm.apply (Drule.cterm_rule (instantiate' [SOME cT] []) @{cpat "op /"})
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                         (Numeral.mk_cnumber cT a))
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             (Numeral.mk_cnumber cT b)
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      end
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  in funs key
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     {is_const = K numeral_is_const,
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      dest_const = K dest_const,
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      mk_const = mk_const,
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      conv = K Numeral_Simprocs.field_comp_conv}
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  end;
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(** auxiliary **)
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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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fun numeral01_conv ctxt =
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  Simplifier.rewrite (put_simpset HOL_basic_ss ctxt addsimps [@{thm numeral_1_eq_1}]);
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fun zero1_numeral_conv ctxt =
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  Simplifier.rewrite (put_simpset HOL_basic_ss ctxt addsimps [@{thm numeral_1_eq_1} RS sym]);
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fun zerone_conv ctxt cv =
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  zero1_numeral_conv ctxt then_conv cv then_conv numeral01_conv ctxt;
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val natarith = [@{thm "numeral_plus_numeral"}, @{thm "diff_nat_numeral"},
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                @{thm "numeral_times_numeral"}, @{thm "numeral_eq_iff"}, 
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                @{thm "numeral_less_iff"}];
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val nat_add_ss =
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  simpset_of 
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    (put_simpset HOL_basic_ss @{context}
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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_numeral_left}, @{thm Suc_eq_plus1}]
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             @ map (fn th => th RS sym) @{thms numerals});
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fun nat_add_conv ctxt =
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  zerone_conv ctxt (Simplifier.rewrite (put_simpset nat_add_ss ctxt));
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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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(** normalizing conversions **)
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(* core conversion *)
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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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   307
wenzelm@23252
   308
val (neg_mul,sub_add,sub_tm,neg_tm,dest_sub,is_sub,cx',cy') =
wenzelm@23252
   309
  (case (r_ops, r_rules) of
chaieb@30866
   310
    ([sub_pat, neg_pat], [neg_mul, sub_add]) =>
wenzelm@23252
   311
      let
wenzelm@23252
   312
        val sub_tm = Thm.dest_fun (Thm.dest_fun sub_pat)
wenzelm@23252
   313
        val neg_tm = Thm.dest_fun neg_pat
wenzelm@23252
   314
        val dest_sub = dest_binop sub_tm
wenzelm@23252
   315
        val is_sub = is_binop sub_tm
wenzelm@23252
   316
      in (neg_mul,sub_add,sub_tm,neg_tm,dest_sub,is_sub, neg_mul |> concl |> Thm.dest_arg,
wenzelm@23252
   317
          sub_add |> concl |> Thm.dest_arg |> Thm.dest_arg)
chaieb@30866
   318
      end
chaieb@30866
   319
    | _ => (TrueI, TrueI, true_tm, true_tm, (fn t => (t,t)), K false, true_tm, true_tm));
chaieb@30866
   320
chaieb@30866
   321
val (divide_inverse, inverse_divide, divide_tm, inverse_tm, is_divide) = 
chaieb@30866
   322
  (case (f_ops, f_rules) of 
chaieb@30866
   323
   ([divide_pat, inverse_pat], [div_inv, inv_div]) => 
chaieb@30866
   324
     let val div_tm = funpow 2 Thm.dest_fun divide_pat
chaieb@30866
   325
         val inv_tm = Thm.dest_fun inverse_pat
chaieb@30866
   326
     in (div_inv, inv_div, div_tm, inv_tm, is_binop div_tm)
chaieb@30866
   327
     end
chaieb@30866
   328
   | _ => (TrueI, TrueI, true_tm, true_tm, K false));
chaieb@30866
   329
wenzelm@23252
   330
in fn variable_order =>
wenzelm@23252
   331
 let
wenzelm@23252
   332
wenzelm@23252
   333
(* Conversion for "x^n * x^m", with either x^n = x and/or x^m = x possible.  *)
wenzelm@23252
   334
(* Also deals with "const * const", but both terms must involve powers of    *)
wenzelm@23252
   335
(* the same variable, or both be constants, or behaviour may be incorrect.   *)
wenzelm@23252
   336
wenzelm@51717
   337
 fun powvar_mul_conv ctxt tm =
wenzelm@23252
   338
  let
wenzelm@23252
   339
  val (l,r) = dest_mul tm
wenzelm@23252
   340
  in if is_semiring_constant l andalso is_semiring_constant r
wenzelm@23252
   341
     then semiring_mul_conv tm
wenzelm@23252
   342
     else
wenzelm@23252
   343
      ((let
wenzelm@23252
   344
         val (lx,ln) = dest_pow l
wenzelm@23252
   345
        in
wenzelm@23252
   346
         ((let val (rx,rn) = dest_pow r
wenzelm@23252
   347
               val th1 = inst_thm [(cx,lx),(cp,ln),(cq,rn)] pthm_29
wenzelm@23252
   348
                val (tm1,tm2) = Thm.dest_comb(concl th1) in
wenzelm@51717
   349
               Thm.transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv ctxt tm2)) end)
wenzelm@23252
   350
           handle CTERM _ =>
wenzelm@23252
   351
            (let val th1 = inst_thm [(cx,lx),(cq,ln)] pthm_31
wenzelm@23252
   352
                 val (tm1,tm2) = Thm.dest_comb(concl th1) in
wenzelm@51717
   353
               Thm.transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv ctxt tm2)) end)) end)
wenzelm@23252
   354
       handle CTERM _ =>
wenzelm@23252
   355
           ((let val (rx,rn) = dest_pow r
wenzelm@23252
   356
                val th1 = inst_thm [(cx,rx),(cq,rn)] pthm_30
wenzelm@23252
   357
                val (tm1,tm2) = Thm.dest_comb(concl th1) in
wenzelm@51717
   358
               Thm.transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv ctxt tm2)) end)
wenzelm@23252
   359
           handle CTERM _ => inst_thm [(cx,l)] pthm_32
wenzelm@23252
   360
wenzelm@23252
   361
))
wenzelm@23252
   362
 end;
wenzelm@23252
   363
wenzelm@23252
   364
(* Remove "1 * m" from a monomial, and just leave m.                         *)
wenzelm@23252
   365
wenzelm@23252
   366
 fun monomial_deone th =
wenzelm@23252
   367
       (let val (l,r) = dest_mul(concl th) in
wenzelm@23252
   368
           if l aconvc one_tm
wenzelm@36945
   369
          then Thm.transitive th (inst_thm [(ca,r)] pthm_13)  else th end)
wenzelm@23252
   370
       handle CTERM _ => th;
wenzelm@23252
   371
wenzelm@23252
   372
(* Conversion for "(monomial)^n", where n is a numeral.                      *)
wenzelm@23252
   373
wenzelm@51717
   374
 fun monomial_pow_conv ctxt =
wenzelm@23252
   375
  let
wenzelm@23252
   376
   fun monomial_pow tm bod ntm =
wenzelm@23252
   377
    if not(is_comb bod)
wenzelm@36945
   378
    then Thm.reflexive tm
wenzelm@23252
   379
    else
wenzelm@23252
   380
     if is_semiring_constant bod
wenzelm@23252
   381
     then semiring_pow_conv tm
wenzelm@23252
   382
     else
wenzelm@23252
   383
      let
wenzelm@23252
   384
      val (lopr,r) = Thm.dest_comb bod
wenzelm@23252
   385
      in if not(is_comb lopr)
wenzelm@36945
   386
         then Thm.reflexive tm
wenzelm@23252
   387
        else
wenzelm@23252
   388
          let
wenzelm@23252
   389
          val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   390
         in
wenzelm@23252
   391
           if opr aconvc pow_tm andalso is_numeral r
wenzelm@23252
   392
          then
wenzelm@23252
   393
            let val th1 = inst_thm [(cx,l),(cp,r),(cq,ntm)] pthm_34
wenzelm@23252
   394
                val (l,r) = Thm.dest_comb(concl th1)
wenzelm@51717
   395
           in Thm.transitive th1 (Drule.arg_cong_rule l (nat_add_conv ctxt r))
wenzelm@23252
   396
           end
wenzelm@23252
   397
           else
wenzelm@23252
   398
            if opr aconvc mul_tm
wenzelm@23252
   399
            then
wenzelm@23252
   400
             let
wenzelm@23252
   401
              val th1 = inst_thm [(cx,l),(cy,r),(cq,ntm)] pthm_33
wenzelm@23252
   402
             val (xy,z) = Thm.dest_comb(concl th1)
wenzelm@23252
   403
              val (x,y) = Thm.dest_comb xy
wenzelm@23252
   404
              val thl = monomial_pow y l ntm
wenzelm@23252
   405
              val thr = monomial_pow z r ntm
wenzelm@36945
   406
             in Thm.transitive th1 (Thm.combination (Drule.arg_cong_rule x thl) thr)
wenzelm@23252
   407
             end
wenzelm@36945
   408
             else Thm.reflexive tm
wenzelm@23252
   409
          end
wenzelm@23252
   410
      end
wenzelm@23252
   411
  in fn tm =>
wenzelm@23252
   412
   let
wenzelm@23252
   413
    val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   414
    val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   415
   in if not (opr aconvc pow_tm) orelse not(is_numeral r)
wenzelm@23252
   416
      then raise CTERM ("monomial_pow_conv", [tm])
wenzelm@23252
   417
      else if r aconvc zeron_tm
wenzelm@23252
   418
      then inst_thm [(cx,l)] pthm_35
wenzelm@23252
   419
      else if r aconvc onen_tm
wenzelm@23252
   420
      then inst_thm [(cx,l)] pthm_36
wenzelm@23252
   421
      else monomial_deone(monomial_pow tm l r)
wenzelm@23252
   422
   end
wenzelm@23252
   423
  end;
wenzelm@23252
   424
wenzelm@23252
   425
(* Multiplication of canonical monomials.                                    *)
wenzelm@51717
   426
 fun monomial_mul_conv ctxt =
wenzelm@23252
   427
  let
wenzelm@23252
   428
   fun powvar tm =
wenzelm@23252
   429
    if is_semiring_constant tm then one_tm
wenzelm@23252
   430
    else
wenzelm@23252
   431
     ((let val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   432
           val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   433
       in if opr aconvc pow_tm andalso is_numeral r then l 
wenzelm@23252
   434
          else raise CTERM ("monomial_mul_conv",[tm]) end)
wenzelm@23252
   435
     handle CTERM _ => tm)   (* FIXME !? *)
wenzelm@23252
   436
   fun  vorder x y =
wenzelm@23252
   437
    if x aconvc y then 0
wenzelm@23252
   438
    else
wenzelm@23252
   439
     if x aconvc one_tm then ~1
wenzelm@23252
   440
     else if y aconvc one_tm then 1
wenzelm@23252
   441
      else if variable_order x y then ~1 else 1
wenzelm@23252
   442
   fun monomial_mul tm l r =
wenzelm@23252
   443
    ((let val (lx,ly) = dest_mul l val vl = powvar lx
wenzelm@23252
   444
      in
wenzelm@23252
   445
      ((let
wenzelm@23252
   446
        val (rx,ry) = dest_mul r
wenzelm@23252
   447
         val vr = powvar rx
wenzelm@23252
   448
         val ord = vorder vl vr
wenzelm@23252
   449
        in
wenzelm@23252
   450
         if ord = 0
wenzelm@23252
   451
        then
wenzelm@23252
   452
          let
wenzelm@23252
   453
             val th1 = inst_thm [(clx,lx),(cly,ly),(crx,rx),(cry,ry)] pthm_15
wenzelm@23252
   454
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   455
             val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@51717
   456
             val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv ctxt tm4)) tm2
wenzelm@36945
   457
             val th3 = Thm.transitive th1 th2
wenzelm@23252
   458
              val  (tm5,tm6) = Thm.dest_comb(concl th3)
wenzelm@23252
   459
              val  (tm7,tm8) = Thm.dest_comb tm6
wenzelm@23252
   460
             val  th4 = monomial_mul tm6 (Thm.dest_arg tm7) tm8
wenzelm@36945
   461
         in Thm.transitive th3 (Drule.arg_cong_rule tm5 th4)
wenzelm@23252
   462
         end
wenzelm@23252
   463
         else
wenzelm@23252
   464
          let val th0 = if ord < 0 then pthm_16 else pthm_17
wenzelm@23252
   465
             val th1 = inst_thm [(clx,lx),(cly,ly),(crx,rx),(cry,ry)] th0
wenzelm@23252
   466
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   467
             val (tm3,tm4) = Thm.dest_comb tm2
wenzelm@36945
   468
         in Thm.transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4))
wenzelm@23252
   469
         end
wenzelm@23252
   470
        end)
wenzelm@23252
   471
       handle CTERM _ =>
wenzelm@23252
   472
        (let val vr = powvar r val ord = vorder vl vr
wenzelm@23252
   473
        in
wenzelm@23252
   474
          if ord = 0 then
wenzelm@23252
   475
           let
wenzelm@23252
   476
           val th1 = inst_thm [(clx,lx),(cly,ly),(crx,r)] pthm_18
wenzelm@23252
   477
                 val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   478
           val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@51717
   479
           val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv ctxt tm4)) tm2
wenzelm@36945
   480
          in Thm.transitive th1 th2
wenzelm@23252
   481
          end
wenzelm@23252
   482
          else
wenzelm@23252
   483
          if ord < 0 then
wenzelm@23252
   484
            let val th1 = inst_thm [(clx,lx),(cly,ly),(crx,r)] pthm_19
wenzelm@23252
   485
                val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   486
                val (tm3,tm4) = Thm.dest_comb tm2
wenzelm@36945
   487
           in Thm.transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4))
wenzelm@23252
   488
           end
wenzelm@23252
   489
           else inst_thm [(ca,l),(cb,r)] pthm_09
wenzelm@23252
   490
        end)) end)
wenzelm@23252
   491
     handle CTERM _ =>
wenzelm@23252
   492
      (let val vl = powvar l in
wenzelm@23252
   493
        ((let
wenzelm@23252
   494
          val (rx,ry) = dest_mul r
wenzelm@23252
   495
          val vr = powvar rx
wenzelm@23252
   496
           val ord = vorder vl vr
wenzelm@23252
   497
         in if ord = 0 then
wenzelm@23252
   498
              let val th1 = inst_thm [(clx,l),(crx,rx),(cry,ry)] pthm_21
wenzelm@23252
   499
                 val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   500
                 val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@51717
   501
             in Thm.transitive th1 (Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv ctxt tm4)) tm2)
wenzelm@23252
   502
             end
wenzelm@23252
   503
             else if ord > 0 then
wenzelm@23252
   504
                 let val th1 = inst_thm [(clx,l),(crx,rx),(cry,ry)] pthm_22
wenzelm@23252
   505
                     val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   506
                    val (tm3,tm4) = Thm.dest_comb tm2
wenzelm@36945
   507
                in Thm.transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4))
wenzelm@23252
   508
                end
wenzelm@36945
   509
             else Thm.reflexive tm
wenzelm@23252
   510
         end)
wenzelm@23252
   511
        handle CTERM _ =>
wenzelm@23252
   512
          (let val vr = powvar r
wenzelm@23252
   513
               val  ord = vorder vl vr
wenzelm@51717
   514
          in if ord = 0 then powvar_mul_conv ctxt tm
wenzelm@23252
   515
              else if ord > 0 then inst_thm [(ca,l),(cb,r)] pthm_09
wenzelm@36945
   516
              else Thm.reflexive tm
wenzelm@23252
   517
          end)) end))
wenzelm@23252
   518
  in fn tm => let val (l,r) = dest_mul tm in monomial_deone(monomial_mul tm l r)
wenzelm@23252
   519
             end
wenzelm@23252
   520
  end;
wenzelm@23252
   521
(* Multiplication by monomial of a polynomial.                               *)
wenzelm@23252
   522
wenzelm@51717
   523
 fun polynomial_monomial_mul_conv ctxt =
wenzelm@23252
   524
  let
wenzelm@23252
   525
   fun pmm_conv tm =
wenzelm@23252
   526
    let val (l,r) = dest_mul tm
wenzelm@23252
   527
    in
wenzelm@23252
   528
    ((let val (y,z) = dest_add r
wenzelm@23252
   529
          val th1 = inst_thm [(cx,l),(cy,y),(cz,z)] pthm_37
wenzelm@23252
   530
          val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   531
          val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@51717
   532
          val th2 =
wenzelm@51717
   533
            Thm.combination (Drule.arg_cong_rule tm3 (monomial_mul_conv ctxt tm4)) (pmm_conv tm2)
wenzelm@36945
   534
      in Thm.transitive th1 th2
wenzelm@23252
   535
      end)
wenzelm@51717
   536
     handle CTERM _ => monomial_mul_conv ctxt tm)
wenzelm@23252
   537
   end
wenzelm@23252
   538
 in pmm_conv
wenzelm@23252
   539
 end;
wenzelm@23252
   540
wenzelm@23252
   541
(* Addition of two monomials identical except for constant multiples.        *)
wenzelm@23252
   542
wenzelm@23252
   543
fun monomial_add_conv tm =
wenzelm@23252
   544
 let val (l,r) = dest_add tm
wenzelm@23252
   545
 in if is_semiring_constant l andalso is_semiring_constant r
wenzelm@23252
   546
    then semiring_add_conv tm
wenzelm@23252
   547
    else
wenzelm@23252
   548
     let val th1 =
wenzelm@23252
   549
           if is_mul l andalso is_semiring_constant(Thm.dest_arg1 l)
wenzelm@23252
   550
           then if is_mul r andalso is_semiring_constant(Thm.dest_arg1 r) then
wenzelm@23252
   551
                    inst_thm [(ca,Thm.dest_arg1 l),(cm,Thm.dest_arg r), (cb,Thm.dest_arg1 r)] pthm_02
wenzelm@23252
   552
                else inst_thm [(ca,Thm.dest_arg1 l),(cm,r)] pthm_03
wenzelm@23252
   553
           else if is_mul r andalso is_semiring_constant(Thm.dest_arg1 r)
wenzelm@23252
   554
           then inst_thm [(cm,l),(ca,Thm.dest_arg1 r)] pthm_04
wenzelm@23252
   555
           else inst_thm [(cm,r)] pthm_05
wenzelm@23252
   556
         val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   557
         val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   558
         val th2 = Drule.arg_cong_rule tm3 (semiring_add_conv tm4)
wenzelm@36945
   559
         val th3 = Thm.transitive th1 (Drule.fun_cong_rule th2 tm2)
wenzelm@23252
   560
         val tm5 = concl th3
wenzelm@23252
   561
      in
wenzelm@23252
   562
      if (Thm.dest_arg1 tm5) aconvc zero_tm
wenzelm@36945
   563
      then Thm.transitive th3 (inst_thm [(ca,Thm.dest_arg tm5)] pthm_11)
wenzelm@23252
   564
      else monomial_deone th3
wenzelm@23252
   565
     end
wenzelm@23252
   566
 end;
wenzelm@23252
   567
wenzelm@23252
   568
(* Ordering on monomials.                                                    *)
wenzelm@23252
   569
wenzelm@23252
   570
fun striplist dest =
wenzelm@23252
   571
 let fun strip x acc =
wenzelm@23252
   572
   ((let val (l,r) = dest x in
wenzelm@23252
   573
        strip l (strip r acc) end)
wenzelm@23252
   574
    handle CTERM _ => x::acc)    (* FIXME !? *)
wenzelm@23252
   575
 in fn x => strip x []
wenzelm@23252
   576
 end;
wenzelm@23252
   577
wenzelm@23252
   578
wenzelm@23252
   579
fun powervars tm =
wenzelm@23252
   580
 let val ptms = striplist dest_mul tm
wenzelm@23252
   581
 in if is_semiring_constant (hd ptms) then tl ptms else ptms
wenzelm@23252
   582
 end;
wenzelm@23252
   583
val num_0 = 0;
wenzelm@23252
   584
val num_1 = 1;
wenzelm@23252
   585
fun dest_varpow tm =
wenzelm@23252
   586
 ((let val (x,n) = dest_pow tm in (x,dest_numeral n) end)
wenzelm@23252
   587
   handle CTERM _ =>
wenzelm@23252
   588
   (tm,(if is_semiring_constant tm then num_0 else num_1)));
wenzelm@23252
   589
wenzelm@23252
   590
val morder =
wenzelm@23252
   591
 let fun lexorder l1 l2 =
wenzelm@23252
   592
  case (l1,l2) of
wenzelm@23252
   593
    ([],[]) => 0
wenzelm@23252
   594
  | (vps,[]) => ~1
wenzelm@23252
   595
  | ([],vps) => 1
wenzelm@23252
   596
  | (((x1,n1)::vs1),((x2,n2)::vs2)) =>
wenzelm@23252
   597
     if variable_order x1 x2 then 1
wenzelm@23252
   598
     else if variable_order x2 x1 then ~1
wenzelm@23252
   599
     else if n1 < n2 then ~1
wenzelm@23252
   600
     else if n2 < n1 then 1
wenzelm@23252
   601
     else lexorder vs1 vs2
wenzelm@23252
   602
 in fn tm1 => fn tm2 =>
wenzelm@23252
   603
  let val vdegs1 = map dest_varpow (powervars tm1)
wenzelm@23252
   604
      val vdegs2 = map dest_varpow (powervars tm2)
wenzelm@33002
   605
      val deg1 = fold (Integer.add o snd) vdegs1 num_0
wenzelm@33002
   606
      val deg2 = fold (Integer.add o snd) vdegs2 num_0
wenzelm@23252
   607
  in if deg1 < deg2 then ~1 else if deg1 > deg2 then 1
wenzelm@23252
   608
                            else lexorder vdegs1 vdegs2
wenzelm@23252
   609
  end
wenzelm@23252
   610
 end;
wenzelm@23252
   611
wenzelm@23252
   612
(* Addition of two polynomials.                                              *)
wenzelm@23252
   613
wenzelm@51717
   614
fun polynomial_add_conv ctxt =
wenzelm@23252
   615
 let
wenzelm@23252
   616
 fun dezero_rule th =
wenzelm@23252
   617
  let
wenzelm@23252
   618
   val tm = concl th
wenzelm@23252
   619
  in
wenzelm@23252
   620
   if not(is_add tm) then th else
wenzelm@23252
   621
   let val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   622
       val l = Thm.dest_arg lopr
wenzelm@23252
   623
   in
wenzelm@23252
   624
    if l aconvc zero_tm
wenzelm@36945
   625
    then Thm.transitive th (inst_thm [(ca,r)] pthm_07)   else
wenzelm@23252
   626
        if r aconvc zero_tm
wenzelm@36945
   627
        then Thm.transitive th (inst_thm [(ca,l)] pthm_08)  else th
wenzelm@23252
   628
   end
wenzelm@23252
   629
  end
wenzelm@23252
   630
 fun padd tm =
wenzelm@23252
   631
  let
wenzelm@23252
   632
   val (l,r) = dest_add tm
wenzelm@23252
   633
  in
wenzelm@23252
   634
   if l aconvc zero_tm then inst_thm [(ca,r)] pthm_07
wenzelm@23252
   635
   else if r aconvc zero_tm then inst_thm [(ca,l)] pthm_08
wenzelm@23252
   636
   else
wenzelm@23252
   637
    if is_add l
wenzelm@23252
   638
    then
wenzelm@23252
   639
     let val (a,b) = dest_add l
wenzelm@23252
   640
     in
wenzelm@23252
   641
     if is_add r then
wenzelm@23252
   642
      let val (c,d) = dest_add r
wenzelm@23252
   643
          val ord = morder a c
wenzelm@23252
   644
      in
wenzelm@23252
   645
       if ord = 0 then
wenzelm@23252
   646
        let val th1 = inst_thm [(ca,a),(cb,b),(cc,c),(cd,d)] pthm_23
wenzelm@23252
   647
            val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   648
            val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   649
            val th2 = Drule.arg_cong_rule tm3 (monomial_add_conv tm4)
wenzelm@36945
   650
        in dezero_rule (Thm.transitive th1 (Thm.combination th2 (padd tm2)))
wenzelm@23252
   651
        end
wenzelm@23252
   652
       else (* ord <> 0*)
wenzelm@23252
   653
        let val th1 =
wenzelm@23252
   654
                if ord > 0 then inst_thm [(ca,a),(cb,b),(cc,r)] pthm_24
wenzelm@23252
   655
                else inst_thm [(ca,l),(cc,c),(cd,d)] pthm_25
wenzelm@23252
   656
            val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@36945
   657
        in dezero_rule (Thm.transitive th1 (Drule.arg_cong_rule tm1 (padd tm2)))
wenzelm@23252
   658
        end
wenzelm@23252
   659
      end
wenzelm@23252
   660
     else (* not (is_add r)*)
wenzelm@23252
   661
      let val ord = morder a r
wenzelm@23252
   662
      in
wenzelm@23252
   663
       if ord = 0 then
wenzelm@23252
   664
        let val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_26
wenzelm@23252
   665
            val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   666
            val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   667
            val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (monomial_add_conv tm4)) tm2
wenzelm@36945
   668
        in dezero_rule (Thm.transitive th1 th2)
wenzelm@23252
   669
        end
wenzelm@23252
   670
       else (* ord <> 0*)
wenzelm@23252
   671
        if ord > 0 then
wenzelm@23252
   672
          let val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_24
wenzelm@23252
   673
              val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@36945
   674
          in dezero_rule (Thm.transitive th1 (Drule.arg_cong_rule tm1 (padd tm2)))
wenzelm@23252
   675
          end
wenzelm@23252
   676
        else dezero_rule (inst_thm [(ca,l),(cc,r)] pthm_27)
wenzelm@23252
   677
      end
wenzelm@23252
   678
    end
wenzelm@23252
   679
   else (* not (is_add l)*)
wenzelm@23252
   680
    if is_add r then
wenzelm@23252
   681
      let val (c,d) = dest_add r
wenzelm@23252
   682
          val  ord = morder l c
wenzelm@23252
   683
      in
wenzelm@23252
   684
       if ord = 0 then
wenzelm@23252
   685
         let val th1 = inst_thm [(ca,l),(cc,c),(cd,d)] pthm_28
wenzelm@23252
   686
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   687
             val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   688
             val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (monomial_add_conv tm4)) tm2
wenzelm@36945
   689
         in dezero_rule (Thm.transitive th1 th2)
wenzelm@23252
   690
         end
wenzelm@23252
   691
       else
wenzelm@36945
   692
        if ord > 0 then Thm.reflexive tm
wenzelm@23252
   693
        else
wenzelm@23252
   694
         let val th1 = inst_thm [(ca,l),(cc,c),(cd,d)] pthm_25
wenzelm@23252
   695
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@36945
   696
         in dezero_rule (Thm.transitive th1 (Drule.arg_cong_rule tm1 (padd tm2)))
wenzelm@23252
   697
         end
wenzelm@23252
   698
      end
wenzelm@23252
   699
    else
wenzelm@23252
   700
     let val ord = morder l r
wenzelm@23252
   701
     in
wenzelm@23252
   702
      if ord = 0 then monomial_add_conv tm
wenzelm@36945
   703
      else if ord > 0 then dezero_rule(Thm.reflexive tm)
wenzelm@23252
   704
      else dezero_rule (inst_thm [(ca,l),(cc,r)] pthm_27)
wenzelm@23252
   705
     end
wenzelm@23252
   706
  end
wenzelm@23252
   707
 in padd
wenzelm@23252
   708
 end;
wenzelm@23252
   709
wenzelm@23252
   710
(* Multiplication of two polynomials.                                        *)
wenzelm@23252
   711
wenzelm@51717
   712
fun polynomial_mul_conv ctxt =
wenzelm@23252
   713
 let
wenzelm@23252
   714
  fun pmul tm =
wenzelm@23252
   715
   let val (l,r) = dest_mul tm
wenzelm@23252
   716
   in
wenzelm@51717
   717
    if not(is_add l) then polynomial_monomial_mul_conv ctxt tm
wenzelm@23252
   718
    else
wenzelm@23252
   719
     if not(is_add r) then
wenzelm@23252
   720
      let val th1 = inst_thm [(ca,l),(cb,r)] pthm_09
wenzelm@51717
   721
      in Thm.transitive th1 (polynomial_monomial_mul_conv ctxt (concl th1))
wenzelm@23252
   722
      end
wenzelm@23252
   723
     else
wenzelm@23252
   724
       let val (a,b) = dest_add l
wenzelm@23252
   725
           val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_10
wenzelm@23252
   726
           val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   727
           val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@51717
   728
           val th2 = Drule.arg_cong_rule tm3 (polynomial_monomial_mul_conv ctxt tm4)
wenzelm@36945
   729
           val th3 = Thm.transitive th1 (Thm.combination th2 (pmul tm2))
wenzelm@51717
   730
       in Thm.transitive th3 (polynomial_add_conv ctxt (concl th3))
wenzelm@23252
   731
       end
wenzelm@23252
   732
   end
wenzelm@23252
   733
 in fn tm =>
wenzelm@23252
   734
   let val (l,r) = dest_mul tm
wenzelm@23252
   735
   in
wenzelm@23252
   736
    if l aconvc zero_tm then inst_thm [(ca,r)] pthm_11
wenzelm@23252
   737
    else if r aconvc zero_tm then inst_thm [(ca,l)] pthm_12
wenzelm@23252
   738
    else if l aconvc one_tm then inst_thm [(ca,r)] pthm_13
wenzelm@23252
   739
    else if r aconvc one_tm then inst_thm [(ca,l)] pthm_14
wenzelm@23252
   740
    else pmul tm
wenzelm@23252
   741
   end
wenzelm@23252
   742
 end;
wenzelm@23252
   743
wenzelm@23252
   744
(* Power of polynomial (optimized for the monomial and trivial cases).       *)
wenzelm@23252
   745
wenzelm@51717
   746
fun num_conv ctxt n =
wenzelm@51717
   747
  nat_add_conv ctxt (Thm.apply @{cterm Suc} (Numeral.mk_cnumber @{ctyp nat} (dest_numeral n - 1)))
wenzelm@23580
   748
  |> Thm.symmetric;
wenzelm@23252
   749
wenzelm@23252
   750
wenzelm@51717
   751
fun polynomial_pow_conv ctxt =
wenzelm@23252
   752
 let
wenzelm@23252
   753
  fun ppow tm =
wenzelm@23252
   754
    let val (l,n) = dest_pow tm
wenzelm@23252
   755
    in
wenzelm@23252
   756
     if n aconvc zeron_tm then inst_thm [(cx,l)] pthm_35
wenzelm@23252
   757
     else if n aconvc onen_tm then inst_thm [(cx,l)] pthm_36
wenzelm@23252
   758
     else
wenzelm@51717
   759
         let val th1 = num_conv ctxt n
wenzelm@23252
   760
             val th2 = inst_thm [(cx,l),(cq,Thm.dest_arg (concl th1))] pthm_38
wenzelm@23252
   761
             val (tm1,tm2) = Thm.dest_comb(concl th2)
wenzelm@36945
   762
             val th3 = Thm.transitive th2 (Drule.arg_cong_rule tm1 (ppow tm2))
wenzelm@36945
   763
             val th4 = Thm.transitive (Drule.arg_cong_rule (Thm.dest_fun tm) th1) th3
wenzelm@51717
   764
         in Thm.transitive th4 (polynomial_mul_conv ctxt (concl th4))
wenzelm@23252
   765
         end
wenzelm@23252
   766
    end
wenzelm@23252
   767
 in fn tm =>
wenzelm@51717
   768
       if is_add(Thm.dest_arg1 tm) then ppow tm else monomial_pow_conv ctxt tm
wenzelm@23252
   769
 end;
wenzelm@23252
   770
wenzelm@23252
   771
(* Negation.                                                                 *)
wenzelm@23252
   772
wenzelm@51717
   773
fun polynomial_neg_conv ctxt tm =
wenzelm@23252
   774
   let val (l,r) = Thm.dest_comb tm in
wenzelm@23252
   775
        if not (l aconvc neg_tm) then raise CTERM ("polynomial_neg_conv",[tm]) else
wenzelm@23252
   776
        let val th1 = inst_thm [(cx',r)] neg_mul
wenzelm@36945
   777
            val th2 = Thm.transitive th1 (Conv.arg1_conv semiring_mul_conv (concl th1))
wenzelm@51717
   778
        in Thm.transitive th2 (polynomial_monomial_mul_conv ctxt (concl th2))
wenzelm@23252
   779
        end
wenzelm@23252
   780
   end;
wenzelm@23252
   781
wenzelm@23252
   782
wenzelm@23252
   783
(* Subtraction.                                                              *)
wenzelm@51717
   784
fun polynomial_sub_conv ctxt tm =
wenzelm@23252
   785
  let val (l,r) = dest_sub tm
wenzelm@23252
   786
      val th1 = inst_thm [(cx',l),(cy',r)] sub_add
wenzelm@23252
   787
      val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@51717
   788
      val th2 = Drule.arg_cong_rule tm1 (polynomial_neg_conv ctxt tm2)
wenzelm@51717
   789
  in Thm.transitive th1 (Thm.transitive th2 (polynomial_add_conv ctxt (concl th2)))
wenzelm@23252
   790
  end;
wenzelm@23252
   791
wenzelm@23252
   792
(* Conversion from HOL term.                                                 *)
wenzelm@23252
   793
wenzelm@51717
   794
fun polynomial_conv ctxt tm =
chaieb@23407
   795
 if is_semiring_constant tm then semiring_add_conv tm
wenzelm@36945
   796
 else if not(is_comb tm) then Thm.reflexive tm
wenzelm@23252
   797
 else
wenzelm@23252
   798
  let val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   799
  in if lopr aconvc neg_tm then
wenzelm@51717
   800
       let val th1 = Drule.arg_cong_rule lopr (polynomial_conv ctxt r)
wenzelm@51717
   801
       in Thm.transitive th1 (polynomial_neg_conv ctxt (concl th1))
wenzelm@23252
   802
       end
chaieb@30866
   803
     else if lopr aconvc inverse_tm then
wenzelm@51717
   804
       let val th1 = Drule.arg_cong_rule lopr (polynomial_conv ctxt r)
wenzelm@36945
   805
       in Thm.transitive th1 (semiring_mul_conv (concl th1))
chaieb@30866
   806
       end
wenzelm@23252
   807
     else
wenzelm@36945
   808
       if not(is_comb lopr) then Thm.reflexive tm
wenzelm@23252
   809
       else
wenzelm@23252
   810
         let val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   811
         in if opr aconvc pow_tm andalso is_numeral r
wenzelm@23252
   812
            then
wenzelm@51717
   813
              let val th1 = Drule.fun_cong_rule (Drule.arg_cong_rule opr (polynomial_conv ctxt l)) r
wenzelm@51717
   814
              in Thm.transitive th1 (polynomial_pow_conv ctxt (concl th1))
wenzelm@23252
   815
              end
chaieb@30866
   816
         else if opr aconvc divide_tm 
chaieb@30866
   817
            then
wenzelm@51717
   818
              let val th1 = Thm.combination (Drule.arg_cong_rule opr (polynomial_conv ctxt l)) 
wenzelm@51717
   819
                                        (polynomial_conv ctxt r)
wenzelm@51717
   820
                  val th2 = (Conv.rewr_conv divide_inverse then_conv polynomial_mul_conv ctxt)
chaieb@30866
   821
                              (Thm.rhs_of th1)
wenzelm@36945
   822
              in Thm.transitive th1 th2
chaieb@30866
   823
              end
wenzelm@23252
   824
            else
wenzelm@23252
   825
              if opr aconvc add_tm orelse opr aconvc mul_tm orelse opr aconvc sub_tm
wenzelm@23252
   826
              then
wenzelm@36945
   827
               let val th1 =
wenzelm@51717
   828
                    Thm.combination
wenzelm@51717
   829
                      (Drule.arg_cong_rule opr (polynomial_conv ctxt l)) (polynomial_conv ctxt r)
wenzelm@51717
   830
                   val f = if opr aconvc add_tm then polynomial_add_conv ctxt
wenzelm@51717
   831
                      else if opr aconvc mul_tm then polynomial_mul_conv ctxt
wenzelm@51717
   832
                      else polynomial_sub_conv ctxt
wenzelm@36945
   833
               in Thm.transitive th1 (f (concl th1))
wenzelm@23252
   834
               end
wenzelm@36945
   835
              else Thm.reflexive tm
wenzelm@23252
   836
         end
wenzelm@23252
   837
  end;
wenzelm@23252
   838
 in
wenzelm@23252
   839
   {main = polynomial_conv,
wenzelm@23252
   840
    add = polynomial_add_conv,
wenzelm@23252
   841
    mul = polynomial_mul_conv,
wenzelm@23252
   842
    pow = polynomial_pow_conv,
wenzelm@23252
   843
    neg = polynomial_neg_conv,
wenzelm@23252
   844
    sub = polynomial_sub_conv}
wenzelm@23252
   845
 end
wenzelm@23252
   846
end;
wenzelm@23252
   847
wenzelm@35410
   848
val nat_exp_ss =
wenzelm@51717
   849
  simpset_of
wenzelm@51717
   850
   (put_simpset HOL_basic_ss @{context}
haftmann@54249
   851
    addsimps (@{thms eval_nat_numeral} @ @{thms diff_nat_numeral} @ @{thms arith_simps} @ @{thms rel_simps})
wenzelm@51717
   852
    addsimps [@{thm Let_def}, @{thm if_False}, @{thm if_True}, @{thm Nat.add_0}, @{thm add_Suc}]);
wenzelm@23252
   853
wenzelm@35408
   854
fun simple_cterm_ord t u = Term_Ord.term_ord (term_of t, term_of u) = LESS;
chaieb@27222
   855
haftmann@36710
   856
haftmann@36710
   857
(* various normalizing conversions *)
haftmann@36710
   858
chaieb@30866
   859
fun semiring_normalizers_ord_wrapper ctxt ({vars, semiring, ring, field, idom, ideal}, 
chaieb@23407
   860
                                     {conv, dest_const, mk_const, is_const}) ord =
wenzelm@23252
   861
  let
wenzelm@23252
   862
    val pow_conv =
wenzelm@51717
   863
      Conv.arg_conv (Simplifier.rewrite (put_simpset nat_exp_ss ctxt))
wenzelm@23252
   864
      then_conv Simplifier.rewrite
wenzelm@51717
   865
        (put_simpset HOL_basic_ss ctxt addsimps [nth (snd semiring) 31, nth (snd semiring) 34])
chaieb@23330
   866
      then_conv conv ctxt
chaieb@23330
   867
    val dat = (is_const, conv ctxt, conv ctxt, pow_conv)
chaieb@30866
   868
  in semiring_normalizers_conv vars semiring ring field dat ord end;
chaieb@27222
   869
chaieb@30866
   870
fun semiring_normalize_ord_wrapper ctxt ({vars, semiring, ring, field, idom, ideal}, {conv, dest_const, mk_const, is_const}) ord =
wenzelm@51717
   871
 #main (semiring_normalizers_ord_wrapper ctxt
wenzelm@51717
   872
  ({vars = vars, semiring = semiring, ring = ring, field = field, idom = idom, ideal = ideal},
wenzelm@51717
   873
   {conv = conv, dest_const = dest_const, mk_const = mk_const, is_const = is_const}) ord) ctxt;
wenzelm@23252
   874
chaieb@23407
   875
fun semiring_normalize_wrapper ctxt data = 
chaieb@23407
   876
  semiring_normalize_ord_wrapper ctxt data simple_cterm_ord;
chaieb@23407
   877
chaieb@23407
   878
fun semiring_normalize_ord_conv ctxt ord tm =
haftmann@36700
   879
  (case match ctxt tm of
wenzelm@36945
   880
    NONE => Thm.reflexive tm
chaieb@23407
   881
  | SOME res => semiring_normalize_ord_wrapper ctxt res ord tm);
chaieb@23407
   882
 
chaieb@23407
   883
fun semiring_normalize_conv ctxt = semiring_normalize_ord_conv ctxt simple_cterm_ord;
wenzelm@23252
   884
haftmann@36708
   885
haftmann@36708
   886
(** Isar setup **)
haftmann@36708
   887
haftmann@36708
   888
local
haftmann@36708
   889
haftmann@36708
   890
fun keyword k = Scan.lift (Args.$$$ k -- Args.colon) >> K ();
haftmann@36708
   891
fun keyword2 k1 k2 = Scan.lift (Args.$$$ k1 -- Args.$$$ k2 -- Args.colon) >> K ();
haftmann@36708
   892
fun keyword3 k1 k2 k3 =
haftmann@36708
   893
  Scan.lift (Args.$$$ k1 -- Args.$$$ k2 -- Args.$$$ k3 -- Args.colon) >> K ();
haftmann@36708
   894
haftmann@36708
   895
val opsN = "ops";
haftmann@36708
   896
val rulesN = "rules";
haftmann@36708
   897
haftmann@36708
   898
val normN = "norm";
haftmann@36708
   899
val constN = "const";
haftmann@36708
   900
val delN = "del";
haftmann@36700
   901
haftmann@36708
   902
val any_keyword =
haftmann@36708
   903
  keyword2 semiringN opsN || keyword2 semiringN rulesN ||
haftmann@36708
   904
  keyword2 ringN opsN || keyword2 ringN rulesN ||
haftmann@36708
   905
  keyword2 fieldN opsN || keyword2 fieldN rulesN ||
haftmann@36708
   906
  keyword2 idomN rulesN || keyword2 idealN rulesN;
haftmann@36708
   907
haftmann@36708
   908
val thms = Scan.repeat (Scan.unless any_keyword Attrib.multi_thm) >> flat;
haftmann@36708
   909
val terms = thms >> map Drule.dest_term;
haftmann@36708
   910
haftmann@36708
   911
fun optional scan = Scan.optional scan [];
haftmann@36708
   912
haftmann@36708
   913
in
haftmann@36708
   914
haftmann@36708
   915
val setup =
haftmann@36708
   916
  Attrib.setup @{binding normalizer}
haftmann@36708
   917
    (Scan.lift (Args.$$$ delN >> K del) ||
haftmann@36708
   918
      ((keyword2 semiringN opsN |-- terms) --
haftmann@36708
   919
       (keyword2 semiringN rulesN |-- thms)) --
haftmann@36708
   920
      (optional (keyword2 ringN opsN |-- terms) --
haftmann@36708
   921
       optional (keyword2 ringN rulesN |-- thms)) --
haftmann@36708
   922
      (optional (keyword2 fieldN opsN |-- terms) --
haftmann@36708
   923
       optional (keyword2 fieldN rulesN |-- thms)) --
haftmann@36708
   924
      optional (keyword2 idomN rulesN |-- thms) --
haftmann@36708
   925
      optional (keyword2 idealN rulesN |-- thms)
haftmann@36708
   926
      >> (fn ((((sr, r), f), id), idl) => 
haftmann@36708
   927
             add {semiring = sr, ring = r, field = f, idom = id, ideal = idl}))
haftmann@36708
   928
    "semiring normalizer data";
haftmann@36700
   929
wenzelm@23252
   930
end;
haftmann@36708
   931
haftmann@36708
   932
end;