src/FOLP/simp.ML
author wenzelm
Sun May 18 15:04:09 2008 +0200 (2008-05-18)
changeset 26939 1035c89b4c02
parent 26928 ca87aff1ad2d
child 29265 5b4247055bd7
permissions -rw-r--r--
moved global pretty/string_of functions from Sign to Syntax;
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(*  Title:      FOLP/simp
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    ID:         $Id$
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    Author:     Tobias Nipkow
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    Copyright   1993  University of Cambridge
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FOLP version of...
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Generic simplifier, suitable for most logics.  (from Provers)
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This version allows instantiation of Vars in the subgoal, since the proof
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term must change.
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*)
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signature SIMP_DATA =
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sig
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  val case_splits  : (thm * string) list
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  val dest_red     : term -> term * term * term
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  val mk_rew_rules : thm -> thm list
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  val norm_thms    : (thm*thm) list (* [(?x>>norm(?x), norm(?x)>>?x), ...] *)
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  val red1         : thm        (*  ?P>>?Q  ==>  ?P  ==>  ?Q  *)
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  val red2         : thm        (*  ?P>>?Q  ==>  ?Q  ==>  ?P  *)
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  val refl_thms    : thm list
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  val subst_thms   : thm list   (* [ ?a>>?b ==> ?P(?a) ==> ?P(?b), ...] *)
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  val trans_thms   : thm list
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end;
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infix 4 addrews addcongs delrews delcongs setauto;
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signature SIMP =
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sig
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  type simpset
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  val empty_ss  : simpset
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  val addcongs  : simpset * thm list -> simpset
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  val addrews   : simpset * thm list -> simpset
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  val delcongs  : simpset * thm list -> simpset
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  val delrews   : simpset * thm list -> simpset
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  val dest_ss   : simpset -> thm list * thm list
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  val print_ss  : simpset -> unit
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  val setauto   : simpset * (int -> tactic) -> simpset
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  val ASM_SIMP_CASE_TAC : simpset -> int -> tactic
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  val ASM_SIMP_TAC      : simpset -> int -> tactic
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  val CASE_TAC          : simpset -> int -> tactic
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  val SIMP_CASE2_TAC    : simpset -> int -> tactic
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  val SIMP_THM          : simpset -> thm -> thm
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  val SIMP_TAC          : simpset -> int -> tactic
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  val SIMP_CASE_TAC     : simpset -> int -> tactic
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  val mk_congs          : theory -> string list -> thm list
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  val mk_typed_congs    : theory -> (string * string) list -> thm list
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(* temporarily disabled:
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  val extract_free_congs        : unit -> thm list
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*)
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  val tracing   : bool ref
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end;
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functor SimpFun (Simp_data: SIMP_DATA) : SIMP = 
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struct
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local open Simp_data in
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(*For taking apart reductions into left, right hand sides*)
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val lhs_of = #2 o dest_red;
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val rhs_of = #3 o dest_red;
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(*** Indexing and filtering of theorems ***)
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fun eq_brl ((b1 : bool, th1), (b2, th2)) = b1 = b2 andalso Thm.eq_thm_prop (th1, th2);
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(*insert a thm in a discrimination net by its lhs*)
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fun lhs_insert_thm (th,net) =
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    Net.insert_term eq_brl (lhs_of (concl_of th), (false,th)) net
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    handle  Net.INSERT => net;
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(*match subgoal i against possible theorems in the net.
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  Similar to match_from_nat_tac, but the net does not contain numbers;
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  rewrite rules are not ordered.*)
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fun net_tac net =
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  SUBGOAL(fn (prem,i) => 
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          resolve_tac (Net.unify_term net (Logic.strip_assums_concl prem)) i);
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(*match subgoal i against possible theorems indexed by lhs in the net*)
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fun lhs_net_tac net =
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  SUBGOAL(fn (prem,i) => 
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          biresolve_tac (Net.unify_term net
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                       (lhs_of (Logic.strip_assums_concl prem))) i);
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fun nth_subgoal i thm = List.nth(prems_of thm,i-1);
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fun goal_concl i thm = Logic.strip_assums_concl (nth_subgoal i thm);
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fun lhs_of_eq i thm = lhs_of(goal_concl i thm)
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and rhs_of_eq i thm = rhs_of(goal_concl i thm);
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fun var_lhs(thm,i) =
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let fun var(Var _) = true
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      | var(Abs(_,_,t)) = var t
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      | var(f$_) = var f
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      | var _ = false;
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in var(lhs_of_eq i thm) end;
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fun contains_op opns =
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    let fun contains(Const(s,_)) = s mem opns |
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            contains(s$t) = contains s orelse contains t |
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            contains(Abs(_,_,t)) = contains t |
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            contains _ = false;
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    in contains end;
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fun may_match(match_ops,i) = contains_op match_ops o lhs_of_eq i;
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val (normI_thms,normE_thms) = split_list norm_thms;
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(*Get the norm constants from norm_thms*)
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val norms =
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  let fun norm thm = 
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      case lhs_of(concl_of thm) of
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          Const(n,_)$_ => n
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        | _ => (Display.prths normE_thms; error"No constant in lhs of a norm_thm")
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  in map norm normE_thms end;
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fun lhs_is_NORM(thm,i) = case lhs_of_eq i thm of
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        Const(s,_)$_ => s mem norms | _ => false;
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val refl_tac = resolve_tac refl_thms;
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fun find_res thms thm =
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    let fun find [] = (Display.prths thms; error"Check Simp_Data")
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          | find(th::thms) = thm RS th handle THM _ => find thms
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    in find thms end;
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val mk_trans = find_res trans_thms;
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fun mk_trans2 thm =
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let fun mk[] = error"Check transitivity"
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      | mk(t::ts) = (thm RSN (2,t))  handle THM _  => mk ts
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in mk trans_thms end;
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(*Applies tactic and returns the first resulting state, FAILS if none!*)
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fun one_result(tac,thm) = case Seq.pull(tac thm) of
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        SOME(thm',_) => thm'
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      | NONE => raise THM("Simplifier: could not continue", 0, [thm]);
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fun res1(thm,thms,i) = one_result(resolve_tac thms i,thm);
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(**** Adding "NORM" tags ****)
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(*get name of the constant from conclusion of a congruence rule*)
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fun cong_const cong = 
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    case head_of (lhs_of (concl_of cong)) of
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        Const(c,_) => c
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      | _ => ""                 (*a placeholder distinct from const names*);
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(*true if the term is an atomic proposition (no ==> signs) *)
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val atomic = null o Logic.strip_assums_hyp;
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(*ccs contains the names of the constants possessing congruence rules*)
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fun add_hidden_vars ccs =
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  let fun add_hvars tm hvars = case tm of
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              Abs(_,_,body) => add_term_vars(body,hvars)
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            | _$_ => let val (f,args) = strip_comb tm 
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                     in case f of
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                            Const(c,T) => 
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                                if member (op =) ccs c
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                                then fold_rev add_hvars args hvars
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                                else add_term_vars (tm, hvars)
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                          | _ => add_term_vars (tm, hvars)
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                     end
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            | _ => hvars;
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  in add_hvars end;
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fun add_new_asm_vars new_asms =
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    let fun itf (tm, at) vars =
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                if at then vars else add_term_vars(tm,vars)
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        fun add_list(tm,al,vars) = let val (_,tml) = strip_comb tm
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                in if length(tml)=length(al)
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                   then fold_rev itf (tml ~~ al) vars
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                   else vars
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                end
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        fun add_vars (tm,vars) = case tm of
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                  Abs (_,_,body) => add_vars(body,vars)
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                | r$s => (case head_of tm of
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                          Const(c,T) => (case AList.lookup (op =) new_asms c of
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                                  NONE => add_vars(r,add_vars(s,vars))
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                                | SOME(al) => add_list(tm,al,vars))
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                        | _ => add_vars(r,add_vars(s,vars)))
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                | _ => vars
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    in add_vars end;
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fun add_norms(congs,ccs,new_asms) thm =
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let val thm' = mk_trans2 thm;
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(* thm': [?z -> l; Prems; r -> ?t] ==> ?z -> ?t *)
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    val nops = nprems_of thm'
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    val lhs = rhs_of_eq 1 thm'
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    val rhs = lhs_of_eq nops thm'
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    val asms = tl(rev(tl(prems_of thm')))
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    val hvars = fold_rev (add_hidden_vars ccs) (lhs::rhs::asms) []
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    val hvars = add_new_asm_vars new_asms (rhs,hvars)
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    fun it_asms asm hvars =
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        if atomic asm then add_new_asm_vars new_asms (asm,hvars)
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        else add_term_frees(asm,hvars)
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    val hvars = fold_rev it_asms asms hvars
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    val hvs = map (#1 o dest_Var) hvars
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    val refl1_tac = refl_tac 1
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    fun norm_step_tac st = st |>
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	 (case head_of(rhs_of_eq 1 st) of
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	    Var(ixn,_) => if ixn mem hvs then refl1_tac
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			  else resolve_tac normI_thms 1 ORELSE refl1_tac
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	  | Const _ => resolve_tac normI_thms 1 ORELSE
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		       resolve_tac congs 1 ORELSE refl1_tac
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	  | Free _ => resolve_tac congs 1 ORELSE refl1_tac
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	  | _ => refl1_tac)
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    val add_norm_tac = DEPTH_FIRST (has_fewer_prems nops) norm_step_tac
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    val SOME(thm'',_) = Seq.pull(add_norm_tac thm')
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in thm'' end;
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fun add_norm_tags congs =
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    let val ccs = map cong_const congs
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        val new_asms = List.filter (exists not o #2)
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                (ccs ~~ (map (map atomic o prems_of) congs));
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    in add_norms(congs,ccs,new_asms) end;
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fun normed_rews congs =
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  let val add_norms = add_norm_tags congs in
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    fn thm => Variable.tradeT
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      (K (map (add_norms o mk_trans) o maps mk_rew_rules)) (Variable.thm_context thm) [thm]
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  end;
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fun NORM norm_lhs_tac = EVERY'[rtac red2 , norm_lhs_tac, refl_tac];
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val trans_norms = map mk_trans normE_thms;
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(* SIMPSET *)
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datatype simpset =
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        SS of {auto_tac: int -> tactic,
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               congs: thm list,
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               cong_net: thm Net.net,
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               mk_simps: thm -> thm list,
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               simps: (thm * thm list) list,
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               simp_net: thm Net.net}
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val empty_ss = SS{auto_tac= K no_tac, congs=[], cong_net=Net.empty,
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                  mk_simps=normed_rews[], simps=[], simp_net=Net.empty};
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(** Insertion of congruences and rewrites **)
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(*insert a thm in a thm net*)
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fun insert_thm_warn th net = 
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  Net.insert_term Thm.eq_thm_prop (concl_of th, th) net
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  handle Net.INSERT => 
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    (writeln"\nDuplicate rewrite or congruence rule:"; Display.print_thm th;
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     net);
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val insert_thms = fold_rev insert_thm_warn;
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fun addrew(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thm) =
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let val thms = mk_simps thm
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in SS{auto_tac=auto_tac,congs=congs, cong_net=cong_net, mk_simps=mk_simps,
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      simps = (thm,thms)::simps, simp_net = insert_thms thms simp_net}
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end;
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val op addrews = Library.foldl addrew;
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fun op addcongs(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thms) =
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let val congs' = thms @ congs;
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in SS{auto_tac=auto_tac, congs= congs',
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      cong_net= insert_thms (map mk_trans thms) cong_net,
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      mk_simps= normed_rews congs', simps=simps, simp_net=simp_net}
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end;
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(** Deletion of congruences and rewrites **)
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(*delete a thm from a thm net*)
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fun delete_thm_warn th net = 
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  Net.delete_term Thm.eq_thm_prop (concl_of th, th) net
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  handle Net.DELETE => 
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    (writeln"\nNo such rewrite or congruence rule:";  Display.print_thm th;
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     net);
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val delete_thms = fold_rev delete_thm_warn;
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fun op delcongs(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thms) =
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let val congs' = fold (remove Thm.eq_thm_prop) thms congs
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in SS{auto_tac=auto_tac, congs= congs',
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      cong_net= delete_thms (map mk_trans thms) cong_net,
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      mk_simps= normed_rews congs', simps=simps, simp_net=simp_net}
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end;
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fun delrew(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thm) =
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let fun find((p as (th,ths))::ps',ps) =
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          if Thm.eq_thm_prop(thm,th) then (ths,ps@ps') else find(ps',p::ps)
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      | find([],simps') = (writeln"\nNo such rewrite or congruence rule:";
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                           Display.print_thm thm;
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                           ([],simps'))
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    val (thms,simps') = find(simps,[])
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in SS{auto_tac=auto_tac, congs=congs, cong_net=cong_net, mk_simps=mk_simps,
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      simps = simps', simp_net = delete_thms thms simp_net }
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end;
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val op delrews = Library.foldl delrew;
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fun op setauto(SS{congs,cong_net,mk_simps,simps,simp_net,...}, auto_tac) =
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    SS{auto_tac=auto_tac, congs=congs, cong_net=cong_net, mk_simps=mk_simps,
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       simps=simps, simp_net=simp_net};
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(** Inspection of a simpset **)
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clasohm@0
   312
fun dest_ss(SS{congs,simps,...}) = (congs, map #1 simps);
clasohm@0
   313
clasohm@0
   314
fun print_ss(SS{congs,simps,...}) =
wenzelm@26928
   315
        (writeln"Congruences:"; Display.prths congs;
wenzelm@26928
   316
         writeln"Rewrite Rules:"; Display.prths (map #1 simps); ());
clasohm@0
   317
clasohm@0
   318
clasohm@0
   319
(* Rewriting with conditionals *)
clasohm@0
   320
clasohm@0
   321
val (case_thms,case_consts) = split_list case_splits;
clasohm@0
   322
val case_rews = map mk_trans case_thms;
clasohm@0
   323
clasohm@0
   324
fun if_rewritable ifc i thm =
clasohm@0
   325
    let val tm = goal_concl i thm
clasohm@1459
   326
        fun nobound(Abs(_,_,tm),j,k) = nobound(tm,j,k+1)
clasohm@1459
   327
          | nobound(s$t,j,k) = nobound(s,j,k) andalso nobound(t,j,k)
clasohm@1459
   328
          | nobound(Bound n,j,k) = n < k orelse k+j <= n
clasohm@1459
   329
          | nobound(_) = true;
clasohm@1459
   330
        fun check_args(al,j) = forall (fn t => nobound(t,j,0)) al
clasohm@1459
   331
        fun find_if(Abs(_,_,tm),j) = find_if(tm,j+1)
clasohm@1459
   332
          | find_if(tm as s$t,j) = let val (f,al) = strip_comb tm in
clasohm@1459
   333
                case f of Const(c,_) => if c=ifc then check_args(al,j)
clasohm@1459
   334
                        else find_if(s,j) orelse find_if(t,j)
clasohm@1459
   335
                | _ => find_if(s,j) orelse find_if(t,j) end
clasohm@1459
   336
          | find_if(_) = false;
clasohm@0
   337
    in find_if(tm,0) end;
clasohm@0
   338
clasohm@0
   339
fun IF1_TAC cong_tac i =
paulson@1512
   340
    let fun seq_try (ifth::ifths,ifc::ifcs) thm = 
paulson@1512
   341
                (COND (if_rewritable ifc i) (DETERM(rtac ifth i))
paulson@1512
   342
                        (seq_try(ifths,ifcs))) thm
paulson@1512
   343
              | seq_try([],_) thm = no_tac thm
paulson@1512
   344
        and try_rew thm = (seq_try(case_rews,case_consts) ORELSE one_subt) thm
clasohm@1459
   345
        and one_subt thm =
clasohm@1459
   346
                let val test = has_fewer_prems (nprems_of thm + 1)
paulson@1512
   347
                    fun loop thm = 
paulson@1512
   348
			COND test no_tac
paulson@1512
   349
                          ((try_rew THEN DEPTH_FIRST test (refl_tac i))
paulson@1512
   350
			   ORELSE (refl_tac i THEN loop)) thm
paulson@1512
   351
                in (cong_tac THEN loop) thm end
paulson@1512
   352
    in COND (may_match(case_consts,i)) try_rew no_tac end;
clasohm@0
   353
clasohm@0
   354
fun CASE_TAC (SS{cong_net,...}) i =
clasohm@0
   355
let val cong_tac = net_tac cong_net i
clasohm@0
   356
in NORM (IF1_TAC cong_tac) i end;
clasohm@0
   357
clasohm@0
   358
(* Rewriting Automaton *)
clasohm@0
   359
clasohm@0
   360
datatype cntrl = STOP | MK_EQ | ASMS of int | SIMP_LHS | REW | REFL | TRUE
clasohm@1459
   361
               | PROVE | POP_CS | POP_ARTR | IF;
wenzelm@22578
   362
clasohm@0
   363
fun simp_refl([],_,ss) = ss
clasohm@0
   364
  | simp_refl(a'::ns,a,ss) = if a'=a then simp_refl(ns,a,SIMP_LHS::REFL::ss)
clasohm@1459
   365
        else simp_refl(ns,a,ASMS(a)::SIMP_LHS::REFL::POP_ARTR::ss);
clasohm@0
   366
clasohm@0
   367
(** Tracing **)
clasohm@0
   368
clasohm@0
   369
val tracing = ref false;
clasohm@0
   370
clasohm@0
   371
(*Replace parameters by Free variables in P*)
clasohm@0
   372
fun variants_abs ([],P) = P
clasohm@0
   373
  | variants_abs ((a,T)::aTs, P) =
wenzelm@20194
   374
      variants_abs (aTs, #2 (Syntax.variant_abs(a,T,P)));
clasohm@0
   375
clasohm@0
   376
(*Select subgoal i from proof state; substitute parameters, for printing*)
clasohm@0
   377
fun prepare_goal i st =
clasohm@0
   378
    let val subgi = nth_subgoal i st
wenzelm@19805
   379
        val params = rev (Logic.strip_params subgi)
wenzelm@19805
   380
    in variants_abs (params, Logic.strip_assums_concl subgi) end;
clasohm@0
   381
clasohm@0
   382
(*print lhs of conclusion of subgoal i*)
clasohm@0
   383
fun pr_goal_lhs i st =
wenzelm@26939
   384
    writeln (Syntax.string_of_term_global (Thm.theory_of_thm st) 
clasohm@1459
   385
             (lhs_of (prepare_goal i st)));
clasohm@0
   386
clasohm@0
   387
(*print conclusion of subgoal i*)
clasohm@0
   388
fun pr_goal_concl i st =
wenzelm@26939
   389
    writeln (Syntax.string_of_term_global (Thm.theory_of_thm st) (prepare_goal i st)) 
clasohm@0
   390
clasohm@0
   391
(*print subgoals i to j (inclusive)*)
clasohm@0
   392
fun pr_goals (i,j) st =
clasohm@0
   393
    if i>j then ()
clasohm@0
   394
    else (pr_goal_concl i st;  pr_goals (i+1,j) st);
clasohm@0
   395
clasohm@0
   396
(*Print rewrite for tracing; i=subgoal#, n=number of new subgoals,
clasohm@0
   397
  thm=old state, thm'=new state *)
clasohm@0
   398
fun pr_rew (i,n,thm,thm',not_asms) =
clasohm@0
   399
    if !tracing
clasohm@0
   400
    then (if not_asms then () else writeln"Assumption used in";
clasohm@0
   401
          pr_goal_lhs i thm; writeln"->"; pr_goal_lhs (i+n) thm';
clasohm@1459
   402
          if n>0 then (writeln"Conditions:"; pr_goals (i, i+n-1) thm')
clasohm@0
   403
          else ();
clasohm@0
   404
          writeln"" )
clasohm@0
   405
    else ();
clasohm@0
   406
clasohm@0
   407
(* Skip the first n hyps of a goal, and return the rest in generalized form *)
clasohm@0
   408
fun strip_varify(Const("==>", _) $ H $ B, n, vs) =
clasohm@1459
   409
        if n=0 then subst_bounds(vs,H)::strip_varify(B,0,vs)
clasohm@1459
   410
        else strip_varify(B,n-1,vs)
clasohm@0
   411
  | strip_varify(Const("all",_)$Abs(_,T,t), n, vs) =
clasohm@1459
   412
        strip_varify(t,n,Var(("?",length vs),T)::vs)
clasohm@0
   413
  | strip_varify  _  = [];
clasohm@0
   414
clasohm@0
   415
fun execute(ss,if_fl,auto_tac,cong_tac,net,i,thm) = let
clasohm@0
   416
clasohm@0
   417
fun simp_lhs(thm,ss,anet,ats,cs) =
clasohm@0
   418
    if var_lhs(thm,i) then (ss,thm,anet,ats,cs) else
clasohm@0
   419
    if lhs_is_NORM(thm,i) then (ss, res1(thm,trans_norms,i), anet,ats,cs)
wenzelm@4271
   420
    else case Seq.pull(cong_tac i thm) of
skalberg@15531
   421
            SOME(thm',_) =>
clasohm@1459
   422
                    let val ps = prems_of thm and ps' = prems_of thm';
clasohm@1459
   423
                        val n = length(ps')-length(ps);
wenzelm@19805
   424
                        val a = length(Logic.strip_assums_hyp(List.nth(ps,i-1)))
wenzelm@19805
   425
                        val l = map (fn p => length(Logic.strip_assums_hyp(p)))
skalberg@15570
   426
                                    (Library.take(n,Library.drop(i-1,ps')));
clasohm@1459
   427
                    in (simp_refl(rev(l),a,REW::ss),thm',anet,ats,cs) end
skalberg@15531
   428
          | NONE => (REW::ss,thm,anet,ats,cs);
clasohm@0
   429
clasohm@0
   430
(*NB: the "Adding rewrites:" trace will look strange because assumptions
clasohm@0
   431
      are represented by rules, generalized over their parameters*)
clasohm@0
   432
fun add_asms(ss,thm,a,anet,ats,cs) =
clasohm@0
   433
    let val As = strip_varify(nth_subgoal i thm, a, []);
wenzelm@22596
   434
        val thms = map (trivial o cterm_of(Thm.theory_of_thm thm)) As;
skalberg@15570
   435
        val new_rws = List.concat(map mk_rew_rules thms);
skalberg@15570
   436
        val rwrls = map mk_trans (List.concat(map mk_rew_rules thms));
skalberg@15574
   437
        val anet' = foldr lhs_insert_thm anet rwrls
clasohm@0
   438
    in  if !tracing andalso not(null new_rws)
wenzelm@26928
   439
        then (writeln"Adding rewrites:";  Display.prths new_rws;  ())
clasohm@1459
   440
        else ();
clasohm@1459
   441
        (ss,thm,anet',anet::ats,cs) 
clasohm@0
   442
    end;
clasohm@0
   443
wenzelm@4271
   444
fun rew(seq,thm,ss,anet,ats,cs, more) = case Seq.pull seq of
skalberg@15531
   445
      SOME(thm',seq') =>
clasohm@1459
   446
            let val n = (nprems_of thm') - (nprems_of thm)
clasohm@1459
   447
            in pr_rew(i,n,thm,thm',more);
clasohm@1459
   448
               if n=0 then (SIMP_LHS::ss, thm', anet, ats, cs)
clasohm@1459
   449
               else ((replicate n PROVE) @ (POP_CS::SIMP_LHS::ss),
clasohm@1459
   450
                     thm', anet, ats, (ss,thm,anet,ats,seq',more)::cs)
clasohm@1459
   451
            end
skalberg@15531
   452
    | NONE => if more
paulson@1512
   453
            then rew((lhs_net_tac anet i THEN assume_tac i) thm,
clasohm@1459
   454
                     thm,ss,anet,ats,cs,false)
clasohm@1459
   455
            else (ss,thm,anet,ats,cs);
clasohm@0
   456
clasohm@0
   457
fun try_true(thm,ss,anet,ats,cs) =
wenzelm@4271
   458
    case Seq.pull(auto_tac i thm) of
skalberg@15531
   459
      SOME(thm',_) => (ss,thm',anet,ats,cs)
skalberg@15531
   460
    | NONE => let val (ss0,thm0,anet0,ats0,seq,more)::cs0 = cs
clasohm@1459
   461
              in if !tracing
clasohm@1459
   462
                 then (writeln"*** Failed to prove precondition. Normal form:";
clasohm@1459
   463
                       pr_goal_concl i thm;  writeln"")
clasohm@1459
   464
                 else ();
clasohm@1459
   465
                 rew(seq,thm0,ss0,anet0,ats0,cs0,more)
clasohm@1459
   466
              end;
clasohm@0
   467
clasohm@0
   468
fun if_exp(thm,ss,anet,ats,cs) =
wenzelm@4271
   469
        case Seq.pull (IF1_TAC (cong_tac i) i thm) of
skalberg@15531
   470
                SOME(thm',_) => (SIMP_LHS::IF::ss,thm',anet,ats,cs)
skalberg@15531
   471
              | NONE => (ss,thm,anet,ats,cs);
clasohm@0
   472
clasohm@0
   473
fun step(s::ss, thm, anet, ats, cs) = case s of
clasohm@1459
   474
          MK_EQ => (ss, res1(thm,[red2],i), anet, ats, cs)
clasohm@1459
   475
        | ASMS(a) => add_asms(ss,thm,a,anet,ats,cs)
clasohm@1459
   476
        | SIMP_LHS => simp_lhs(thm,ss,anet,ats,cs)
paulson@1512
   477
        | REW => rew(net_tac net i thm,thm,ss,anet,ats,cs,true)
clasohm@1459
   478
        | REFL => (ss, res1(thm,refl_thms,i), anet, ats, cs)
clasohm@1459
   479
        | TRUE => try_true(res1(thm,refl_thms,i),ss,anet,ats,cs)
clasohm@1459
   480
        | PROVE => (if if_fl then MK_EQ::SIMP_LHS::IF::TRUE::ss
clasohm@1459
   481
                    else MK_EQ::SIMP_LHS::TRUE::ss, thm, anet, ats, cs)
clasohm@1459
   482
        | POP_ARTR => (ss,thm,hd ats,tl ats,cs)
clasohm@1459
   483
        | POP_CS => (ss,thm,anet,ats,tl cs)
clasohm@1459
   484
        | IF => if_exp(thm,ss,anet,ats,cs);
clasohm@0
   485
clasohm@0
   486
fun exec(state as (s::ss, thm, _, _, _)) =
clasohm@1459
   487
        if s=STOP then thm else exec(step(state));
clasohm@0
   488
clasohm@0
   489
in exec(ss, thm, Net.empty, [], []) end;
clasohm@0
   490
clasohm@0
   491
clasohm@0
   492
fun EXEC_TAC(ss,fl) (SS{auto_tac,cong_net,simp_net,...}) =
clasohm@0
   493
let val cong_tac = net_tac cong_net
paulson@1512
   494
in fn i => 
paulson@1512
   495
    (fn thm =>
wenzelm@4271
   496
     if i <= 0 orelse nprems_of thm < i then Seq.empty
wenzelm@4271
   497
     else Seq.single(execute(ss,fl,auto_tac,cong_tac,simp_net,i,thm)))
paulson@1512
   498
    THEN TRY(auto_tac i)
clasohm@0
   499
end;
clasohm@0
   500
clasohm@0
   501
val SIMP_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,REFL,STOP],false);
clasohm@0
   502
val SIMP_CASE_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],false);
clasohm@0
   503
clasohm@0
   504
val ASM_SIMP_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,REFL,STOP],false);
clasohm@0
   505
val ASM_SIMP_CASE_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,IF,REFL,STOP],false);
clasohm@0
   506
clasohm@0
   507
val SIMP_CASE2_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],true);
clasohm@0
   508
clasohm@0
   509
fun REWRITE (ss,fl) (SS{auto_tac,cong_net,simp_net,...}) =
clasohm@0
   510
let val cong_tac = net_tac cong_net
clasohm@0
   511
in fn thm => let val state = thm RSN (2,red1)
clasohm@1459
   512
             in execute(ss,fl,auto_tac,cong_tac,simp_net,1,state) end
clasohm@0
   513
end;
clasohm@0
   514
clasohm@0
   515
val SIMP_THM = REWRITE ([ASMS(0),SIMP_LHS,IF,REFL,STOP],false);
clasohm@0
   516
clasohm@0
   517
clasohm@0
   518
(* Compute Congruence rules for individual constants using the substition
clasohm@0
   519
   rules *)
clasohm@0
   520
clasohm@0
   521
val subst_thms = map standard subst_thms;
clasohm@0
   522
clasohm@0
   523
clasohm@0
   524
fun exp_app(0,t) = t
clasohm@0
   525
  | exp_app(i,t) = exp_app(i-1,t $ Bound (i-1));
clasohm@0
   526
clasohm@0
   527
fun exp_abs(Type("fun",[T1,T2]),t,i) =
clasohm@1459
   528
        Abs("x"^string_of_int i,T1,exp_abs(T2,t,i+1))
clasohm@0
   529
  | exp_abs(T,t,i) = exp_app(i,t);
clasohm@0
   530
clasohm@0
   531
fun eta_Var(ixn,T) = exp_abs(T,Var(ixn,T),0);
clasohm@0
   532
clasohm@0
   533
clasohm@0
   534
fun Pinst(f,fT,(eq,eqT),k,i,T,yik,Ts) =
clasohm@0
   535
let fun xn_list(x,n) =
clasohm@1459
   536
        let val ixs = map (fn i => (x^(radixstring(26,"a",i)),0)) (0 upto n);
skalberg@15570
   537
        in ListPair.map eta_Var (ixs, Library.take(n+1,Ts)) end
clasohm@0
   538
    val lhs = list_comb(f,xn_list("X",k-1))
clasohm@0
   539
    val rhs = list_comb(f,xn_list("X",i-1) @ [Bound 0] @ yik)
clasohm@0
   540
in Abs("", T, Const(eq,[fT,fT]--->eqT) $ lhs $ rhs) end;
clasohm@0
   541
wenzelm@16931
   542
fun find_subst sg T =
clasohm@0
   543
let fun find (thm::thms) =
clasohm@1459
   544
        let val (Const(_,cT), va, vb) = dest_red(hd(prems_of thm));
clasohm@1459
   545
            val [P] = add_term_vars(concl_of thm,[]) \\ [va,vb]
clasohm@1459
   546
            val eqT::_ = binder_types cT
wenzelm@16931
   547
        in if Sign.typ_instance sg (T,eqT) then SOME(thm,va,vb,P)
clasohm@1459
   548
           else find thms
clasohm@1459
   549
        end
skalberg@15531
   550
      | find [] = NONE
clasohm@0
   551
in find subst_thms end;
clasohm@0
   552
clasohm@0
   553
fun mk_cong sg (f,aTs,rT) (refl,eq) =
wenzelm@16931
   554
let val k = length aTs;
clasohm@0
   555
    fun ri((subst,va as Var(_,Ta),vb as Var(_,Tb),P),i,si,T,yik) =
clasohm@1459
   556
        let val ca = cterm_of sg va
clasohm@1459
   557
            and cx = cterm_of sg (eta_Var(("X"^si,0),T))
clasohm@1459
   558
            val cb = cterm_of sg vb
clasohm@1459
   559
            and cy = cterm_of sg (eta_Var(("Y"^si,0),T))
clasohm@1459
   560
            val cP = cterm_of sg P
clasohm@1459
   561
            and cp = cterm_of sg (Pinst(f,rT,eq,k,i,T,yik,aTs))
clasohm@1459
   562
        in cterm_instantiate [(ca,cx),(cb,cy),(cP,cp)] subst end;
clasohm@0
   563
    fun mk(c,T::Ts,i,yik) =
clasohm@1459
   564
        let val si = radixstring(26,"a",i)
wenzelm@16931
   565
        in case find_subst sg T of
skalberg@15531
   566
             NONE => mk(c,Ts,i-1,eta_Var(("X"^si,0),T)::yik)
skalberg@15531
   567
           | SOME s => let val c' = c RSN (2,ri(s,i,si,T,yik))
clasohm@1459
   568
                       in mk(c',Ts,i-1,eta_Var(("Y"^si,0),T)::yik) end
clasohm@1459
   569
        end
clasohm@0
   570
      | mk(c,[],_,_) = c;
clasohm@0
   571
in mk(refl,rev aTs,k-1,[]) end;
clasohm@0
   572
clasohm@0
   573
fun mk_cong_type sg (f,T) =
clasohm@0
   574
let val (aTs,rT) = strip_type T;
clasohm@0
   575
    fun find_refl(r::rs) =
clasohm@1459
   576
        let val (Const(eq,eqT),_,_) = dest_red(concl_of r)
wenzelm@16931
   577
        in if Sign.typ_instance sg (rT, hd(binder_types eqT))
skalberg@15531
   578
           then SOME(r,(eq,body_type eqT)) else find_refl rs
clasohm@1459
   579
        end
skalberg@15531
   580
      | find_refl([]) = NONE;
clasohm@0
   581
in case find_refl refl_thms of
skalberg@15531
   582
     NONE => []  |  SOME(refl) => [mk_cong sg (f,aTs,rT) refl]
clasohm@0
   583
end;
clasohm@0
   584
clasohm@0
   585
fun mk_cong_thy thy f =
wenzelm@22578
   586
let val T = case Sign.const_type thy f of
skalberg@15531
   587
                NONE => error(f^" not declared") | SOME(T) => T;
wenzelm@16876
   588
    val T' = Logic.incr_tvar 9 T;
wenzelm@22578
   589
in mk_cong_type thy (Const(f,T'),T') end;
clasohm@0
   590
skalberg@15570
   591
fun mk_congs thy = List.concat o map (mk_cong_thy thy);
clasohm@0
   592
clasohm@0
   593
fun mk_typed_congs thy =
wenzelm@22675
   594
let
wenzelm@22675
   595
  fun readfT(f,s) =
wenzelm@22675
   596
    let
wenzelm@24707
   597
      val T = Logic.incr_tvar 9 (Syntax.read_typ_global thy s);
wenzelm@22675
   598
      val t = case Sign.const_type thy f of
wenzelm@22675
   599
                  SOME(_) => Const(f,T) | NONE => Free(f,T)
wenzelm@22675
   600
    in (t,T) end
wenzelm@22578
   601
in List.concat o map (mk_cong_type thy o readfT) end;
clasohm@0
   602
wenzelm@22675
   603
end;
wenzelm@22675
   604
end;