src/FOLP/simp.ML
author wenzelm
Sun Dec 21 22:49:17 2014 +0100 (2014-12-21)
changeset 59170 de18f8b1a5a2
parent 58963 26bf09b95dda
child 59498 50b60f501b05
permissions -rw-r--r--
tuned signature;
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(*  Title:      FOLP/simp.ML
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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 Unsynchronized.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 = 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$_) = var f
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      | var _ = false;
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in var(lhs_of_eq i thm) end;
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fun contains_op opns =
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    let fun contains(Const(s,_)) = member (op =) opns s |
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            contains(s$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,_)$_ => n
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        | _ => error "No constant in lhs of a norm_thm"
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  in map norm normE_thms end;
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fun lhs_is_NORM(thm,i) = case lhs_of_eq i thm of
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        Const(s,_)$_ => member (op =) norms s | _ => 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 [] = 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) => Misc_Legacy.add_term_vars(body,hvars)
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            | _$_ => let val (f,args) = strip_comb tm
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                     in case f of
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                            Const(c,T) =>
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                                if member (op =) ccs c
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                                then fold_rev add_hvars args hvars
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                                else Misc_Legacy.add_term_vars (tm, hvars)
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                          | _ => Misc_Legacy.add_term_vars (tm, hvars)
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                     end
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            | _ => hvars;
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  in add_hvars end;
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fun add_new_asm_vars new_asms =
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    let fun itf (tm, at) vars =
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                if at then vars else Misc_Legacy.add_term_vars(tm,vars)
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        fun add_list(tm,al,vars) = let val (_,tml) = strip_comb tm
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                in if length(tml)=length(al)
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                   then fold_rev itf (tml ~~ al) vars
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                   else vars
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                end
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        fun add_vars (tm,vars) = case tm of
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                  Abs (_,_,body) => add_vars(body,vars)
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                | r$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 Misc_Legacy.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 member (op =) hvs ixn 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 = 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 =>
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      let
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        val ctxt =
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          Thm.theory_of_thm thm
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          |> Proof_Context.init_global
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          |> Variable.declare_thm thm;
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      in Variable.tradeT (K (map (add_norms o mk_trans) o maps mk_rew_rules)) ctxt [thm] end
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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 ("Duplicate rewrite or congruence rule:\n" ^
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        Display.string_of_thm_without_context th); net);
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val insert_thms = fold_rev insert_thm_warn;
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fun addrew thm (SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}) =
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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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fun ss addrews thms = fold addrew thms ss;
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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 ("No such rewrite or congruence rule:\n" ^
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        Display.string_of_thm_without_context th); 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 thm (SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}) =
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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') =
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          (writeln ("No such rewrite or congruence rule:\n" ^
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              Display.string_of_thm_without_context thm); ([], 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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fun ss delrews thms = fold delrew thms ss;
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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,
clasohm@0
   311
       simps=simps, simp_net=simp_net};
clasohm@0
   312
clasohm@0
   313
clasohm@0
   314
(** Inspection of a simpset **)
clasohm@0
   315
clasohm@0
   316
fun dest_ss(SS{congs,simps,...}) = (congs, map #1 simps);
clasohm@0
   317
clasohm@0
   318
fun print_ss(SS{congs,simps,...}) =
wenzelm@32091
   319
  writeln (cat_lines
wenzelm@32091
   320
   (["Congruences:"] @ map Display.string_of_thm_without_context congs @
wenzelm@32091
   321
    ["Rewrite Rules:"] @ map (Display.string_of_thm_without_context o #1) simps));
clasohm@0
   322
clasohm@0
   323
clasohm@0
   324
(* Rewriting with conditionals *)
clasohm@0
   325
clasohm@0
   326
val (case_thms,case_consts) = split_list case_splits;
clasohm@0
   327
val case_rews = map mk_trans case_thms;
clasohm@0
   328
clasohm@0
   329
fun if_rewritable ifc i thm =
clasohm@0
   330
    let val tm = goal_concl i thm
clasohm@1459
   331
        fun nobound(Abs(_,_,tm),j,k) = nobound(tm,j,k+1)
clasohm@1459
   332
          | nobound(s$t,j,k) = nobound(s,j,k) andalso nobound(t,j,k)
clasohm@1459
   333
          | nobound(Bound n,j,k) = n < k orelse k+j <= n
clasohm@1459
   334
          | nobound(_) = true;
clasohm@1459
   335
        fun check_args(al,j) = forall (fn t => nobound(t,j,0)) al
clasohm@1459
   336
        fun find_if(Abs(_,_,tm),j) = find_if(tm,j+1)
clasohm@1459
   337
          | find_if(tm as s$t,j) = let val (f,al) = strip_comb tm in
clasohm@1459
   338
                case f of Const(c,_) => if c=ifc then check_args(al,j)
clasohm@1459
   339
                        else find_if(s,j) orelse find_if(t,j)
clasohm@1459
   340
                | _ => find_if(s,j) orelse find_if(t,j) end
clasohm@1459
   341
          | find_if(_) = false;
clasohm@0
   342
    in find_if(tm,0) end;
clasohm@0
   343
clasohm@0
   344
fun IF1_TAC cong_tac i =
wenzelm@32449
   345
    let fun seq_try (ifth::ifths,ifc::ifcs) thm =
paulson@1512
   346
                (COND (if_rewritable ifc i) (DETERM(rtac ifth i))
paulson@1512
   347
                        (seq_try(ifths,ifcs))) thm
paulson@1512
   348
              | seq_try([],_) thm = no_tac thm
paulson@1512
   349
        and try_rew thm = (seq_try(case_rews,case_consts) ORELSE one_subt) thm
clasohm@1459
   350
        and one_subt thm =
clasohm@1459
   351
                let val test = has_fewer_prems (nprems_of thm + 1)
wenzelm@32449
   352
                    fun loop thm =
wenzelm@32449
   353
                        COND test no_tac
paulson@1512
   354
                          ((try_rew THEN DEPTH_FIRST test (refl_tac i))
wenzelm@32449
   355
                           ORELSE (refl_tac i THEN loop)) thm
paulson@1512
   356
                in (cong_tac THEN loop) thm end
paulson@1512
   357
    in COND (may_match(case_consts,i)) try_rew no_tac end;
clasohm@0
   358
clasohm@0
   359
fun CASE_TAC (SS{cong_net,...}) i =
clasohm@0
   360
let val cong_tac = net_tac cong_net i
clasohm@0
   361
in NORM (IF1_TAC cong_tac) i end;
clasohm@0
   362
clasohm@0
   363
(* Rewriting Automaton *)
clasohm@0
   364
clasohm@0
   365
datatype cntrl = STOP | MK_EQ | ASMS of int | SIMP_LHS | REW | REFL | TRUE
clasohm@1459
   366
               | PROVE | POP_CS | POP_ARTR | IF;
wenzelm@22578
   367
clasohm@0
   368
fun simp_refl([],_,ss) = ss
clasohm@0
   369
  | simp_refl(a'::ns,a,ss) = if a'=a then simp_refl(ns,a,SIMP_LHS::REFL::ss)
clasohm@1459
   370
        else simp_refl(ns,a,ASMS(a)::SIMP_LHS::REFL::POP_ARTR::ss);
clasohm@0
   371
clasohm@0
   372
(** Tracing **)
clasohm@0
   373
wenzelm@32740
   374
val tracing = Unsynchronized.ref false;
clasohm@0
   375
clasohm@0
   376
(*Replace parameters by Free variables in P*)
clasohm@0
   377
fun variants_abs ([],P) = P
clasohm@0
   378
  | variants_abs ((a,T)::aTs, P) =
wenzelm@42284
   379
      variants_abs (aTs, #2 (Syntax_Trans.variant_abs(a,T,P)));
clasohm@0
   380
clasohm@0
   381
(*Select subgoal i from proof state; substitute parameters, for printing*)
clasohm@0
   382
fun prepare_goal i st =
clasohm@0
   383
    let val subgi = nth_subgoal i st
wenzelm@19805
   384
        val params = rev (Logic.strip_params subgi)
wenzelm@19805
   385
    in variants_abs (params, Logic.strip_assums_concl subgi) end;
clasohm@0
   386
clasohm@0
   387
(*print lhs of conclusion of subgoal i*)
clasohm@0
   388
fun pr_goal_lhs i st =
wenzelm@32449
   389
    writeln (Syntax.string_of_term_global (Thm.theory_of_thm st)
clasohm@1459
   390
             (lhs_of (prepare_goal i st)));
clasohm@0
   391
clasohm@0
   392
(*print conclusion of subgoal i*)
clasohm@0
   393
fun pr_goal_concl i st =
wenzelm@32449
   394
    writeln (Syntax.string_of_term_global (Thm.theory_of_thm st) (prepare_goal i st))
clasohm@0
   395
clasohm@0
   396
(*print subgoals i to j (inclusive)*)
clasohm@0
   397
fun pr_goals (i,j) st =
clasohm@0
   398
    if i>j then ()
clasohm@0
   399
    else (pr_goal_concl i st;  pr_goals (i+1,j) st);
clasohm@0
   400
clasohm@0
   401
(*Print rewrite for tracing; i=subgoal#, n=number of new subgoals,
clasohm@0
   402
  thm=old state, thm'=new state *)
clasohm@0
   403
fun pr_rew (i,n,thm,thm',not_asms) =
clasohm@0
   404
    if !tracing
clasohm@0
   405
    then (if not_asms then () else writeln"Assumption used in";
clasohm@0
   406
          pr_goal_lhs i thm; writeln"->"; pr_goal_lhs (i+n) thm';
clasohm@1459
   407
          if n>0 then (writeln"Conditions:"; pr_goals (i, i+n-1) thm')
clasohm@0
   408
          else ();
clasohm@0
   409
          writeln"" )
clasohm@0
   410
    else ();
clasohm@0
   411
clasohm@0
   412
(* Skip the first n hyps of a goal, and return the rest in generalized form *)
wenzelm@56245
   413
fun strip_varify(Const(@{const_name Pure.imp}, _) $ H $ B, n, vs) =
clasohm@1459
   414
        if n=0 then subst_bounds(vs,H)::strip_varify(B,0,vs)
clasohm@1459
   415
        else strip_varify(B,n-1,vs)
wenzelm@56245
   416
  | strip_varify(Const(@{const_name Pure.all},_)$Abs(_,T,t), n, vs) =
clasohm@1459
   417
        strip_varify(t,n,Var(("?",length vs),T)::vs)
clasohm@0
   418
  | strip_varify  _  = [];
clasohm@0
   419
clasohm@0
   420
fun execute(ss,if_fl,auto_tac,cong_tac,net,i,thm) = let
clasohm@0
   421
clasohm@0
   422
fun simp_lhs(thm,ss,anet,ats,cs) =
clasohm@0
   423
    if var_lhs(thm,i) then (ss,thm,anet,ats,cs) else
clasohm@0
   424
    if lhs_is_NORM(thm,i) then (ss, res1(thm,trans_norms,i), anet,ats,cs)
wenzelm@4271
   425
    else case Seq.pull(cong_tac i thm) of
skalberg@15531
   426
            SOME(thm',_) =>
haftmann@33955
   427
                    let val ps = prems_of thm
haftmann@33955
   428
                        and ps' = prems_of thm';
clasohm@1459
   429
                        val n = length(ps')-length(ps);
wenzelm@42364
   430
                        val a = length(Logic.strip_assums_hyp(nth ps (i - 1)))
haftmann@33955
   431
                        val l = map (length o Logic.strip_assums_hyp) (take n (drop (i-1) ps'));
clasohm@1459
   432
                    in (simp_refl(rev(l),a,REW::ss),thm',anet,ats,cs) end
skalberg@15531
   433
          | NONE => (REW::ss,thm,anet,ats,cs);
clasohm@0
   434
clasohm@0
   435
(*NB: the "Adding rewrites:" trace will look strange because assumptions
clasohm@0
   436
      are represented by rules, generalized over their parameters*)
clasohm@0
   437
fun add_asms(ss,thm,a,anet,ats,cs) =
clasohm@0
   438
    let val As = strip_varify(nth_subgoal i thm, a, []);
wenzelm@36945
   439
        val thms = map (Thm.trivial o cterm_of(Thm.theory_of_thm thm)) As;
wenzelm@32952
   440
        val new_rws = maps mk_rew_rules thms;
wenzelm@32952
   441
        val rwrls = map mk_trans (maps mk_rew_rules thms);
wenzelm@33339
   442
        val anet' = fold_rev lhs_insert_thm rwrls anet;
clasohm@0
   443
    in  if !tracing andalso not(null new_rws)
wenzelm@32091
   444
        then writeln (cat_lines
wenzelm@32091
   445
          ("Adding rewrites:" :: map Display.string_of_thm_without_context new_rws))
clasohm@1459
   446
        else ();
wenzelm@32449
   447
        (ss,thm,anet',anet::ats,cs)
clasohm@0
   448
    end;
clasohm@0
   449
wenzelm@4271
   450
fun rew(seq,thm,ss,anet,ats,cs, more) = case Seq.pull seq of
skalberg@15531
   451
      SOME(thm',seq') =>
clasohm@1459
   452
            let val n = (nprems_of thm') - (nprems_of thm)
clasohm@1459
   453
            in pr_rew(i,n,thm,thm',more);
clasohm@1459
   454
               if n=0 then (SIMP_LHS::ss, thm', anet, ats, cs)
clasohm@1459
   455
               else ((replicate n PROVE) @ (POP_CS::SIMP_LHS::ss),
clasohm@1459
   456
                     thm', anet, ats, (ss,thm,anet,ats,seq',more)::cs)
clasohm@1459
   457
            end
skalberg@15531
   458
    | NONE => if more
wenzelm@58963
   459
            then rew((lhs_net_tac anet i THEN atac i) thm,
clasohm@1459
   460
                     thm,ss,anet,ats,cs,false)
clasohm@1459
   461
            else (ss,thm,anet,ats,cs);
clasohm@0
   462
clasohm@0
   463
fun try_true(thm,ss,anet,ats,cs) =
wenzelm@4271
   464
    case Seq.pull(auto_tac i thm) of
skalberg@15531
   465
      SOME(thm',_) => (ss,thm',anet,ats,cs)
skalberg@15531
   466
    | NONE => let val (ss0,thm0,anet0,ats0,seq,more)::cs0 = cs
clasohm@1459
   467
              in if !tracing
clasohm@1459
   468
                 then (writeln"*** Failed to prove precondition. Normal form:";
clasohm@1459
   469
                       pr_goal_concl i thm;  writeln"")
clasohm@1459
   470
                 else ();
clasohm@1459
   471
                 rew(seq,thm0,ss0,anet0,ats0,cs0,more)
clasohm@1459
   472
              end;
clasohm@0
   473
clasohm@0
   474
fun if_exp(thm,ss,anet,ats,cs) =
wenzelm@4271
   475
        case Seq.pull (IF1_TAC (cong_tac i) i thm) of
skalberg@15531
   476
                SOME(thm',_) => (SIMP_LHS::IF::ss,thm',anet,ats,cs)
skalberg@15531
   477
              | NONE => (ss,thm,anet,ats,cs);
clasohm@0
   478
clasohm@0
   479
fun step(s::ss, thm, anet, ats, cs) = case s of
clasohm@1459
   480
          MK_EQ => (ss, res1(thm,[red2],i), anet, ats, cs)
clasohm@1459
   481
        | ASMS(a) => add_asms(ss,thm,a,anet,ats,cs)
clasohm@1459
   482
        | SIMP_LHS => simp_lhs(thm,ss,anet,ats,cs)
paulson@1512
   483
        | REW => rew(net_tac net i thm,thm,ss,anet,ats,cs,true)
clasohm@1459
   484
        | REFL => (ss, res1(thm,refl_thms,i), anet, ats, cs)
clasohm@1459
   485
        | TRUE => try_true(res1(thm,refl_thms,i),ss,anet,ats,cs)
clasohm@1459
   486
        | PROVE => (if if_fl then MK_EQ::SIMP_LHS::IF::TRUE::ss
clasohm@1459
   487
                    else MK_EQ::SIMP_LHS::TRUE::ss, thm, anet, ats, cs)
clasohm@1459
   488
        | POP_ARTR => (ss,thm,hd ats,tl ats,cs)
clasohm@1459
   489
        | POP_CS => (ss,thm,anet,ats,tl cs)
clasohm@1459
   490
        | IF => if_exp(thm,ss,anet,ats,cs);
clasohm@0
   491
clasohm@0
   492
fun exec(state as (s::ss, thm, _, _, _)) =
clasohm@1459
   493
        if s=STOP then thm else exec(step(state));
clasohm@0
   494
clasohm@0
   495
in exec(ss, thm, Net.empty, [], []) end;
clasohm@0
   496
clasohm@0
   497
clasohm@0
   498
fun EXEC_TAC(ss,fl) (SS{auto_tac,cong_net,simp_net,...}) =
clasohm@0
   499
let val cong_tac = net_tac cong_net
wenzelm@32449
   500
in fn i =>
paulson@1512
   501
    (fn thm =>
wenzelm@4271
   502
     if i <= 0 orelse nprems_of thm < i then Seq.empty
wenzelm@4271
   503
     else Seq.single(execute(ss,fl,auto_tac,cong_tac,simp_net,i,thm)))
paulson@1512
   504
    THEN TRY(auto_tac i)
clasohm@0
   505
end;
clasohm@0
   506
clasohm@0
   507
val SIMP_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,REFL,STOP],false);
clasohm@0
   508
val SIMP_CASE_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],false);
clasohm@0
   509
clasohm@0
   510
val ASM_SIMP_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,REFL,STOP],false);
clasohm@0
   511
val ASM_SIMP_CASE_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,IF,REFL,STOP],false);
clasohm@0
   512
clasohm@0
   513
val SIMP_CASE2_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],true);
clasohm@0
   514
clasohm@0
   515
fun REWRITE (ss,fl) (SS{auto_tac,cong_net,simp_net,...}) =
clasohm@0
   516
let val cong_tac = net_tac cong_net
clasohm@0
   517
in fn thm => let val state = thm RSN (2,red1)
clasohm@1459
   518
             in execute(ss,fl,auto_tac,cong_tac,simp_net,1,state) end
clasohm@0
   519
end;
clasohm@0
   520
clasohm@0
   521
val SIMP_THM = REWRITE ([ASMS(0),SIMP_LHS,IF,REFL,STOP],false);
clasohm@0
   522
clasohm@0
   523
clasohm@0
   524
(* Compute Congruence rules for individual constants using the substition
clasohm@0
   525
   rules *)
clasohm@0
   526
wenzelm@35021
   527
val subst_thms = map Drule.export_without_context subst_thms;
clasohm@0
   528
clasohm@0
   529
clasohm@0
   530
fun exp_app(0,t) = t
clasohm@0
   531
  | exp_app(i,t) = exp_app(i-1,t $ Bound (i-1));
clasohm@0
   532
clasohm@0
   533
fun exp_abs(Type("fun",[T1,T2]),t,i) =
clasohm@1459
   534
        Abs("x"^string_of_int i,T1,exp_abs(T2,t,i+1))
clasohm@0
   535
  | exp_abs(T,t,i) = exp_app(i,t);
clasohm@0
   536
clasohm@0
   537
fun eta_Var(ixn,T) = exp_abs(T,Var(ixn,T),0);
clasohm@0
   538
clasohm@0
   539
clasohm@0
   540
fun Pinst(f,fT,(eq,eqT),k,i,T,yik,Ts) =
clasohm@0
   541
let fun xn_list(x,n) =
haftmann@33063
   542
        let val ixs = map_range (fn i => (x^(radixstring(26,"a",i)),0)) (n - 1);
haftmann@33955
   543
        in ListPair.map eta_Var (ixs, take (n+1) Ts) end
clasohm@0
   544
    val lhs = list_comb(f,xn_list("X",k-1))
clasohm@0
   545
    val rhs = list_comb(f,xn_list("X",i-1) @ [Bound 0] @ yik)
clasohm@0
   546
in Abs("", T, Const(eq,[fT,fT]--->eqT) $ lhs $ rhs) end;
clasohm@0
   547
wenzelm@16931
   548
fun find_subst sg T =
clasohm@0
   549
let fun find (thm::thms) =
clasohm@1459
   550
        let val (Const(_,cT), va, vb) = dest_red(hd(prems_of thm));
wenzelm@44121
   551
            val [P] = subtract (op =) [va, vb] (Misc_Legacy.add_term_vars (concl_of thm, []));
clasohm@1459
   552
            val eqT::_ = binder_types cT
wenzelm@16931
   553
        in if Sign.typ_instance sg (T,eqT) then SOME(thm,va,vb,P)
clasohm@1459
   554
           else find thms
clasohm@1459
   555
        end
skalberg@15531
   556
      | find [] = NONE
clasohm@0
   557
in find subst_thms end;
clasohm@0
   558
clasohm@0
   559
fun mk_cong sg (f,aTs,rT) (refl,eq) =
wenzelm@16931
   560
let val k = length aTs;
clasohm@0
   561
    fun ri((subst,va as Var(_,Ta),vb as Var(_,Tb),P),i,si,T,yik) =
clasohm@1459
   562
        let val ca = cterm_of sg va
clasohm@1459
   563
            and cx = cterm_of sg (eta_Var(("X"^si,0),T))
clasohm@1459
   564
            val cb = cterm_of sg vb
clasohm@1459
   565
            and cy = cterm_of sg (eta_Var(("Y"^si,0),T))
clasohm@1459
   566
            val cP = cterm_of sg P
clasohm@1459
   567
            and cp = cterm_of sg (Pinst(f,rT,eq,k,i,T,yik,aTs))
clasohm@1459
   568
        in cterm_instantiate [(ca,cx),(cb,cy),(cP,cp)] subst end;
clasohm@0
   569
    fun mk(c,T::Ts,i,yik) =
clasohm@1459
   570
        let val si = radixstring(26,"a",i)
wenzelm@16931
   571
        in case find_subst sg T of
skalberg@15531
   572
             NONE => mk(c,Ts,i-1,eta_Var(("X"^si,0),T)::yik)
skalberg@15531
   573
           | SOME s => let val c' = c RSN (2,ri(s,i,si,T,yik))
clasohm@1459
   574
                       in mk(c',Ts,i-1,eta_Var(("Y"^si,0),T)::yik) end
clasohm@1459
   575
        end
clasohm@0
   576
      | mk(c,[],_,_) = c;
clasohm@0
   577
in mk(refl,rev aTs,k-1,[]) end;
clasohm@0
   578
clasohm@0
   579
fun mk_cong_type sg (f,T) =
clasohm@0
   580
let val (aTs,rT) = strip_type T;
clasohm@0
   581
    fun find_refl(r::rs) =
clasohm@1459
   582
        let val (Const(eq,eqT),_,_) = dest_red(concl_of r)
wenzelm@16931
   583
        in if Sign.typ_instance sg (rT, hd(binder_types eqT))
skalberg@15531
   584
           then SOME(r,(eq,body_type eqT)) else find_refl rs
clasohm@1459
   585
        end
skalberg@15531
   586
      | find_refl([]) = NONE;
clasohm@0
   587
in case find_refl refl_thms of
skalberg@15531
   588
     NONE => []  |  SOME(refl) => [mk_cong sg (f,aTs,rT) refl]
clasohm@0
   589
end;
clasohm@0
   590
clasohm@0
   591
fun mk_cong_thy thy f =
wenzelm@22578
   592
let val T = case Sign.const_type thy f of
skalberg@15531
   593
                NONE => error(f^" not declared") | SOME(T) => T;
wenzelm@16876
   594
    val T' = Logic.incr_tvar 9 T;
wenzelm@22578
   595
in mk_cong_type thy (Const(f,T'),T') end;
clasohm@0
   596
wenzelm@32952
   597
fun mk_congs thy = maps (mk_cong_thy thy);
clasohm@0
   598
clasohm@0
   599
fun mk_typed_congs thy =
wenzelm@22675
   600
let
wenzelm@22675
   601
  fun readfT(f,s) =
wenzelm@22675
   602
    let
wenzelm@24707
   603
      val T = Logic.incr_tvar 9 (Syntax.read_typ_global thy s);
wenzelm@22675
   604
      val t = case Sign.const_type thy f of
wenzelm@22675
   605
                  SOME(_) => Const(f,T) | NONE => Free(f,T)
wenzelm@22675
   606
    in (t,T) end
wenzelm@32952
   607
in maps (mk_cong_type thy o readfT) end;
clasohm@0
   608
wenzelm@22675
   609
end;
wenzelm@22675
   610
end;