src/Pure/meta_simplifier.ML
author wenzelm
Wed Jan 16 20:58:27 2002 +0100 (2002-01-16)
changeset 12779 c5739c1431ab
parent 12603 7d2bca103101
child 12783 36ca5ea8092c
permissions -rw-r--r--
export beta_eta_conversion;
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(*  Title:      Pure/meta_simplifier.ML
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    ID:         $Id$
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    Author:     Tobias Nipkow and Stefan Berghofer
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    Copyright   1994  University of Cambridge
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Meta-level Simplification.
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*)
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signature BASIC_META_SIMPLIFIER =
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sig
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  val trace_simp: bool ref
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  val debug_simp: bool ref
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end;
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signature META_SIMPLIFIER =
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sig
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  include BASIC_META_SIMPLIFIER
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  exception SIMPLIFIER of string * thm
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  type meta_simpset
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  val dest_mss          : meta_simpset ->
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    {simps: thm list, congs: thm list, procs: (string * cterm list) list}
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  val empty_mss         : meta_simpset
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  val clear_mss         : meta_simpset -> meta_simpset
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  val merge_mss         : meta_simpset * meta_simpset -> meta_simpset
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  val add_simps         : meta_simpset * thm list -> meta_simpset
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  val del_simps         : meta_simpset * thm list -> meta_simpset
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  val mss_of            : thm list -> meta_simpset
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  val add_congs         : meta_simpset * thm list -> meta_simpset
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  val del_congs         : meta_simpset * thm list -> meta_simpset
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  val add_simprocs      : meta_simpset *
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    (string * cterm list * (Sign.sg -> thm list -> term -> thm option) * stamp) list
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      -> meta_simpset
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  val del_simprocs      : meta_simpset *
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    (string * cterm list * (Sign.sg -> thm list -> term -> thm option) * stamp) list
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      -> meta_simpset
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  val add_prems         : meta_simpset * thm list -> meta_simpset
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  val prems_of_mss      : meta_simpset -> thm list
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  val set_mk_rews       : meta_simpset * (thm -> thm list) -> meta_simpset
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  val set_mk_sym        : meta_simpset * (thm -> thm option) -> meta_simpset
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  val set_mk_eq_True    : meta_simpset * (thm -> thm option) -> meta_simpset
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  val set_termless      : meta_simpset * (term * term -> bool) -> meta_simpset
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  val beta_eta_conversion: cterm -> thm
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  val rewrite_cterm: bool * bool * bool ->
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    (meta_simpset -> thm -> thm option) -> meta_simpset -> cterm -> thm
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  val goals_conv        : (int -> bool) -> (cterm -> thm) -> cterm -> thm
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  val forall_conv       : (cterm -> thm) -> cterm -> thm
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  val fconv_rule        : (cterm -> thm) -> thm -> thm
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  val rewrite_aux       : (meta_simpset -> thm -> thm option) -> bool -> thm list -> cterm -> thm
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  val simplify_aux      : (meta_simpset -> thm -> thm option) -> bool -> thm list -> thm -> thm
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  val rewrite_thm       : bool * bool * bool
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                          -> (meta_simpset -> thm -> thm option)
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                          -> meta_simpset -> thm -> thm
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  val rewrite_goals_rule_aux: (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm
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  val rewrite_goal_rule : bool* bool * bool
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                          -> (meta_simpset -> thm -> thm option)
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                          -> meta_simpset -> int -> thm -> thm
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end;
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structure MetaSimplifier : META_SIMPLIFIER =
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struct
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(** diagnostics **)
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exception SIMPLIFIER of string * thm;
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val simp_depth = ref 0;
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local
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fun println a =
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  tracing ((case ! simp_depth of 0 => "" | n => "[" ^ string_of_int n ^ "]") ^ a);
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fun prnt warn a = if warn then warning a else println a;
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fun prtm warn a sign t = prnt warn (a ^ "\n" ^ Sign.string_of_term sign t);
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fun prctm warn a t = prnt warn (a ^ "\n" ^ Display.string_of_cterm t);
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in
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fun prthm warn a = prctm warn a o Thm.cprop_of;
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val trace_simp = ref false;
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val debug_simp = ref false;
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fun trace warn a = if !trace_simp then prnt warn a else ();
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fun debug warn a = if !debug_simp then prnt warn a else ();
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fun trace_term warn a sign t = if !trace_simp then prtm warn a sign t else ();
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fun trace_cterm warn a t = if !trace_simp then prctm warn a t else ();
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fun debug_term warn a sign t = if !debug_simp then prtm warn a sign t else ();
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fun trace_thm warn a thm =
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  let val {sign, prop, ...} = rep_thm thm
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  in trace_term warn a sign prop end;
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end;
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(** meta simp sets **)
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(* basic components *)
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type rrule = {thm: thm, lhs: term, elhs: cterm, fo: bool, perm: bool};
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(* thm: the rewrite rule
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   lhs: the left-hand side
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   elhs: the etac-contracted lhs.
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   fo:  use first-order matching
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   perm: the rewrite rule is permutative
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Remarks:
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  - elhs is used for matching,
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    lhs only for preservation of bound variable names.
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  - fo is set iff
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    either elhs is first-order (no Var is applied),
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           in which case fo-matching is complete,
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    or elhs is not a pattern,
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       in which case there is nothing better to do.
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*)
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type cong = {thm: thm, lhs: cterm};
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type simproc =
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 {name: string, proc: Sign.sg -> thm list -> term -> thm option, lhs: cterm, id: stamp};
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fun eq_rrule ({thm = thm1, ...}: rrule, {thm = thm2, ...}: rrule) =
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  #prop (rep_thm thm1) aconv #prop (rep_thm thm2);
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fun eq_cong ({thm = thm1, ...}: cong, {thm = thm2, ...}: cong) =
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  #prop (rep_thm thm1) aconv #prop (rep_thm thm2);
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fun eq_prem (thm1, thm2) =
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  #prop (rep_thm thm1) aconv #prop (rep_thm thm2);
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fun eq_simproc ({id = s1, ...}:simproc, {id = s2, ...}:simproc) = (s1 = s2);
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fun mk_simproc (name, proc, lhs, id) =
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  {name = name, proc = proc, lhs = lhs, id = id};
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(* datatype mss *)
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(*
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  A "mss" contains data needed during conversion:
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    rules: discrimination net of rewrite rules;
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    congs: association list of congruence rules and
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           a list of `weak' congruence constants.
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           A congruence is `weak' if it avoids normalization of some argument.
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    procs: discrimination net of simplification procedures
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      (functions that prove rewrite rules on the fly);
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    bounds: names of bound variables already used
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      (for generating new names when rewriting under lambda abstractions);
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    prems: current premises;
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    mk_rews: mk: turns simplification thms into rewrite rules;
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             mk_sym: turns == around; (needs Drule!)
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             mk_eq_True: turns P into P == True - logic specific;
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    termless: relation for ordered rewriting;
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    depth: depth of conditional rewriting;
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*)
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datatype meta_simpset =
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  Mss of {
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    rules: rrule Net.net,
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    congs: (string * cong) list * string list,
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    procs: simproc Net.net,
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    bounds: string list,
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    prems: thm list,
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    mk_rews: {mk: thm -> thm list,
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              mk_sym: thm -> thm option,
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              mk_eq_True: thm -> thm option},
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    termless: term * term -> bool,
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    depth: int};
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fun mk_mss (rules, congs, procs, bounds, prems, mk_rews, termless, depth) =
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  Mss {rules = rules, congs = congs, procs = procs, bounds = bounds,
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       prems=prems, mk_rews=mk_rews, termless=termless, depth=depth};
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fun upd_rules(Mss{rules,congs,procs,bounds,prems,mk_rews,termless,depth}, rules') =
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  mk_mss(rules',congs,procs,bounds,prems,mk_rews,termless,depth);
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val empty_mss =
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  let val mk_rews = {mk = K [], mk_sym = K None, mk_eq_True = K None}
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  in mk_mss (Net.empty, ([], []), Net.empty, [], [], mk_rews, Term.termless, 0) end;
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fun clear_mss (Mss {mk_rews, termless, ...}) =
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  mk_mss (Net.empty, ([], []), Net.empty, [], [], mk_rews, termless,0);
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fun incr_depth(Mss{rules,congs,procs,bounds,prems,mk_rews,termless,depth}) =
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  mk_mss (rules, congs, procs, bounds, prems, mk_rews, termless, depth+1)
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(** simpset operations **)
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(* term variables *)
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val add_term_varnames = foldl_aterms (fn (xs, Var (x, _)) => ins_ix (x, xs) | (xs, _) => xs);
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fun term_varnames t = add_term_varnames ([], t);
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(* dest_mss *)
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fun dest_mss (Mss {rules, congs, procs, ...}) =
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  {simps = map (fn (_, {thm, ...}) => thm) (Net.dest rules),
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   congs = map (fn (_, {thm, ...}) => thm) (fst congs),
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   procs =
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     map (fn (_, {name, lhs, id, ...}) => ((name, lhs), id)) (Net.dest procs)
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     |> partition_eq eq_snd
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     |> map (fn ps => (#1 (#1 (hd ps)), map (#2 o #1) ps))
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     |> Library.sort_wrt #1};
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(* merge_mss *)       (*NOTE: ignores mk_rews, termless and depth of 2nd mss*)
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fun merge_mss
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 (Mss {rules = rules1, congs = (congs1,weak1), procs = procs1,
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       bounds = bounds1, prems = prems1, mk_rews, termless, depth},
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  Mss {rules = rules2, congs = (congs2,weak2), procs = procs2,
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       bounds = bounds2, prems = prems2, ...}) =
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      mk_mss
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       (Net.merge (rules1, rules2, eq_rrule),
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        (gen_merge_lists (eq_cong o pairself snd) congs1 congs2,
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        merge_lists weak1 weak2),
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        Net.merge (procs1, procs2, eq_simproc),
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        merge_lists bounds1 bounds2,
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        gen_merge_lists eq_prem prems1 prems2,
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        mk_rews, termless, depth);
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(* add_simps *)
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fun mk_rrule2{thm,lhs,elhs,perm} =
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  let val fo = Pattern.first_order (term_of elhs) orelse not(Pattern.pattern (term_of elhs))
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  in {thm=thm,lhs=lhs,elhs=elhs,fo=fo,perm=perm} end
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fun insert_rrule(mss as Mss {rules,...},
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                 rrule as {thm,lhs,elhs,perm}) =
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  (trace_thm false "Adding rewrite rule:" thm;
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   let val rrule2 as {elhs,...} = mk_rrule2 rrule
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       val rules' = Net.insert_term ((term_of elhs, rrule2), rules, eq_rrule)
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   in upd_rules(mss,rules') end
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   handle Net.INSERT =>
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     (prthm true "Ignoring duplicate rewrite rule:" thm; mss));
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fun vperm (Var _, Var _) = true
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  | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)
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  | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)
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  | vperm (t, u) = (t = u);
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fun var_perm (t, u) =
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  vperm (t, u) andalso eq_set (term_varnames t, term_varnames u);
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(* FIXME: it seems that the conditions on extra variables are too liberal if
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prems are nonempty: does solving the prems really guarantee instantiation of
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all its Vars? Better: a dynamic check each time a rule is applied.
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*)
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fun rewrite_rule_extra_vars prems elhs erhs =
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  not (term_varnames erhs subset foldl add_term_varnames (term_varnames elhs, prems))
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  orelse
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  not ((term_tvars erhs) subset
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       (term_tvars elhs  union  List.concat(map term_tvars prems)));
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(*Simple test for looping rewrite rules and stupid orientations*)
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fun reorient sign prems lhs rhs =
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   rewrite_rule_extra_vars prems lhs rhs
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  orelse
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   is_Var (head_of lhs)
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  orelse
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   (exists (apl (lhs, Logic.occs)) (rhs :: prems))
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  orelse
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   (null prems andalso
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    Pattern.matches (#tsig (Sign.rep_sg sign)) (lhs, rhs))
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    (*the condition "null prems" is necessary because conditional rewrites
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      with extra variables in the conditions may terminate although
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      the rhs is an instance of the lhs. Example: ?m < ?n ==> f(?n) == f(?m)*)
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  orelse
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   (is_Const lhs andalso not(is_Const rhs))
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fun decomp_simp thm =
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  let val {sign, prop, ...} = rep_thm thm;
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      val prems = Logic.strip_imp_prems prop;
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      val concl = Drule.strip_imp_concl (cprop_of thm);
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      val (lhs, rhs) = Drule.dest_equals concl handle TERM _ =>
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        raise SIMPLIFIER ("Rewrite rule not a meta-equality", thm)
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      val elhs = snd (Drule.dest_equals (cprop_of (Thm.eta_conversion lhs)));
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      val elhs = if elhs=lhs then lhs else elhs (* try to share *)
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      val erhs = Pattern.eta_contract (term_of rhs);
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      val perm = var_perm (term_of elhs, erhs) andalso not (term_of elhs aconv erhs)
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                 andalso not (is_Var (term_of elhs))
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  in (sign, prems, term_of lhs, elhs, term_of rhs, perm) end;
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fun mk_eq_True (Mss{mk_rews={mk_eq_True,...},...}) thm =
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  case mk_eq_True thm of
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    None => []
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  | Some eq_True => let val (_,_,lhs,elhs,_,_) = decomp_simp eq_True
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                    in [{thm=eq_True, lhs=lhs, elhs=elhs, perm=false}] end;
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(* create the rewrite rule and possibly also the ==True variant,
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   in case there are extra vars on the rhs *)
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fun rrule_eq_True(thm,lhs,elhs,rhs,mss,thm2) =
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  let val rrule = {thm=thm, lhs=lhs, elhs=elhs, perm=false}
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  in if (term_varnames rhs)  subset (term_varnames lhs) andalso
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        (term_tvars rhs) subset (term_tvars lhs)
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     then [rrule]
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     else mk_eq_True mss thm2 @ [rrule]
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  end;
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fun mk_rrule mss thm =
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  let val (_,prems,lhs,elhs,rhs,perm) = decomp_simp thm
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  in if perm then [{thm=thm, lhs=lhs, elhs=elhs, perm=true}] else
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     (* weak test for loops: *)
berghofe@10413
   307
     if rewrite_rule_extra_vars prems lhs rhs orelse
berghofe@10413
   308
        is_Var (term_of elhs)
berghofe@10413
   309
     then mk_eq_True mss thm
berghofe@10413
   310
     else rrule_eq_True(thm,lhs,elhs,rhs,mss,thm)
berghofe@10413
   311
  end;
berghofe@10413
   312
berghofe@10413
   313
fun orient_rrule mss thm =
berghofe@10413
   314
  let val (sign,prems,lhs,elhs,rhs,perm) = decomp_simp thm
berghofe@10413
   315
  in if perm then [{thm=thm,lhs=lhs,elhs=elhs,perm=true}]
berghofe@10413
   316
     else if reorient sign prems lhs rhs
berghofe@10413
   317
          then if reorient sign prems rhs lhs
berghofe@10413
   318
               then mk_eq_True mss thm
berghofe@10413
   319
               else let val Mss{mk_rews={mk_sym,...},...} = mss
berghofe@10413
   320
                    in case mk_sym thm of
berghofe@10413
   321
                         None => []
berghofe@10413
   322
                       | Some thm' =>
berghofe@10413
   323
                           let val (_,_,lhs',elhs',rhs',_) = decomp_simp thm'
berghofe@10413
   324
                           in rrule_eq_True(thm',lhs',elhs',rhs',mss,thm) end
berghofe@10413
   325
                    end
berghofe@10413
   326
          else rrule_eq_True(thm,lhs,elhs,rhs,mss,thm)
berghofe@10413
   327
  end;
berghofe@10413
   328
berghofe@10413
   329
fun extract_rews(Mss{mk_rews = {mk,...},...},thms) = flat(map mk thms);
berghofe@10413
   330
berghofe@10413
   331
fun orient_comb_simps comb mk_rrule (mss,thms) =
berghofe@10413
   332
  let val rews = extract_rews(mss,thms)
berghofe@10413
   333
      val rrules = flat (map mk_rrule rews)
berghofe@10413
   334
  in foldl comb (mss,rrules) end
berghofe@10413
   335
berghofe@10413
   336
(* Add rewrite rules explicitly; do not reorient! *)
berghofe@10413
   337
fun add_simps(mss,thms) =
berghofe@10413
   338
  orient_comb_simps insert_rrule (mk_rrule mss) (mss,thms);
berghofe@10413
   339
berghofe@10413
   340
fun mss_of thms =
berghofe@10413
   341
  foldl insert_rrule (empty_mss, flat(map (mk_rrule empty_mss) thms));
berghofe@10413
   342
berghofe@10413
   343
fun extract_safe_rrules(mss,thm) =
berghofe@10413
   344
  flat (map (orient_rrule mss) (extract_rews(mss,[thm])));
berghofe@10413
   345
berghofe@10413
   346
fun add_safe_simp(mss,thm) =
berghofe@10413
   347
  foldl insert_rrule (mss, extract_safe_rrules(mss,thm))
berghofe@10413
   348
berghofe@10413
   349
(* del_simps *)
berghofe@10413
   350
berghofe@10413
   351
fun del_rrule(mss as Mss {rules,...},
berghofe@10413
   352
              rrule as {thm, elhs, ...}) =
berghofe@10413
   353
  (upd_rules(mss, Net.delete_term ((term_of elhs, rrule), rules, eq_rrule))
berghofe@10413
   354
   handle Net.DELETE =>
berghofe@10413
   355
     (prthm true "Rewrite rule not in simpset:" thm; mss));
berghofe@10413
   356
berghofe@10413
   357
fun del_simps(mss,thms) =
berghofe@10413
   358
  orient_comb_simps del_rrule (map mk_rrule2 o mk_rrule mss) (mss,thms);
berghofe@10413
   359
berghofe@10413
   360
berghofe@10413
   361
(* add_congs *)
berghofe@10413
   362
berghofe@10413
   363
fun is_full_cong_prems [] varpairs = null varpairs
berghofe@10413
   364
  | is_full_cong_prems (p::prems) varpairs =
berghofe@10413
   365
    (case Logic.strip_assums_concl p of
berghofe@10413
   366
       Const("==",_) $ lhs $ rhs =>
berghofe@10413
   367
         let val (x,xs) = strip_comb lhs and (y,ys) = strip_comb rhs
berghofe@10413
   368
         in is_Var x  andalso  forall is_Bound xs  andalso
berghofe@10413
   369
            null(findrep(xs))  andalso xs=ys andalso
berghofe@10413
   370
            (x,y) mem varpairs andalso
berghofe@10413
   371
            is_full_cong_prems prems (varpairs\(x,y))
berghofe@10413
   372
         end
berghofe@10413
   373
     | _ => false);
berghofe@10413
   374
berghofe@10413
   375
fun is_full_cong thm =
berghofe@10413
   376
let val prems = prems_of thm
berghofe@10413
   377
    and concl = concl_of thm
berghofe@10413
   378
    val (lhs,rhs) = Logic.dest_equals concl
berghofe@10413
   379
    val (f,xs) = strip_comb lhs
berghofe@10413
   380
    and (g,ys) = strip_comb rhs
berghofe@10413
   381
in
berghofe@10413
   382
  f=g andalso null(findrep(xs@ys)) andalso length xs = length ys andalso
berghofe@10413
   383
  is_full_cong_prems prems (xs ~~ ys)
berghofe@10413
   384
end
berghofe@10413
   385
nipkow@11504
   386
fun add_cong (Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, thm) =
berghofe@10413
   387
  let
berghofe@10413
   388
    val (lhs, _) = Drule.dest_equals (Drule.strip_imp_concl (cprop_of thm)) handle TERM _ =>
berghofe@10413
   389
      raise SIMPLIFIER ("Congruence not a meta-equality", thm);
berghofe@10413
   390
(*   val lhs = Pattern.eta_contract lhs; *)
berghofe@10413
   391
    val (a, _) = dest_Const (head_of (term_of lhs)) handle TERM _ =>
berghofe@10413
   392
      raise SIMPLIFIER ("Congruence must start with a constant", thm);
berghofe@10413
   393
    val (alist,weak) = congs
berghofe@10413
   394
    val alist2 = overwrite_warn (alist, (a,{lhs=lhs, thm=thm}))
berghofe@10413
   395
           ("Overwriting congruence rule for " ^ quote a);
berghofe@10413
   396
    val weak2 = if is_full_cong thm then weak else a::weak
berghofe@10413
   397
  in
nipkow@11504
   398
    mk_mss (rules,(alist2,weak2),procs,bounds,prems,mk_rews,termless,depth)
berghofe@10413
   399
  end;
berghofe@10413
   400
berghofe@10413
   401
val (op add_congs) = foldl add_cong;
berghofe@10413
   402
berghofe@10413
   403
berghofe@10413
   404
(* del_congs *)
berghofe@10413
   405
nipkow@11504
   406
fun del_cong (Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, thm) =
berghofe@10413
   407
  let
berghofe@10413
   408
    val (lhs, _) = Logic.dest_equals (concl_of thm) handle TERM _ =>
berghofe@10413
   409
      raise SIMPLIFIER ("Congruence not a meta-equality", thm);
berghofe@10413
   410
(*   val lhs = Pattern.eta_contract lhs; *)
berghofe@10413
   411
    val (a, _) = dest_Const (head_of lhs) handle TERM _ =>
berghofe@10413
   412
      raise SIMPLIFIER ("Congruence must start with a constant", thm);
berghofe@10413
   413
    val (alist,_) = congs
berghofe@10413
   414
    val alist2 = filter (fn (x,_)=> x<>a) alist
berghofe@10413
   415
    val weak2 = mapfilter (fn(a,{thm,...}) => if is_full_cong thm then None
berghofe@10413
   416
                                              else Some a)
berghofe@10413
   417
                   alist2
berghofe@10413
   418
  in
nipkow@11504
   419
    mk_mss (rules,(alist2,weak2),procs,bounds,prems,mk_rews,termless,depth)
berghofe@10413
   420
  end;
berghofe@10413
   421
berghofe@10413
   422
val (op del_congs) = foldl del_cong;
berghofe@10413
   423
berghofe@10413
   424
berghofe@10413
   425
(* add_simprocs *)
berghofe@10413
   426
nipkow@11504
   427
fun add_proc (mss as Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth},
berghofe@10413
   428
    (name, lhs, proc, id)) =
berghofe@10413
   429
  let val {sign, t, ...} = rep_cterm lhs
berghofe@10413
   430
  in (trace_term false ("Adding simplification procedure " ^ quote name ^ " for")
berghofe@10413
   431
      sign t;
berghofe@10413
   432
    mk_mss (rules, congs,
berghofe@10413
   433
      Net.insert_term ((t, mk_simproc (name, proc, lhs, id)), procs, eq_simproc)
wenzelm@12603
   434
        handle Net.INSERT =>
wenzelm@12603
   435
            (warning ("Ignoring duplicate simplification procedure \""
wenzelm@12603
   436
                      ^ name ^ "\"");
wenzelm@12603
   437
             procs),
nipkow@11504
   438
        bounds, prems, mk_rews, termless,depth))
berghofe@10413
   439
  end;
berghofe@10413
   440
berghofe@10413
   441
fun add_simproc (mss, (name, lhss, proc, id)) =
berghofe@10413
   442
  foldl add_proc (mss, map (fn lhs => (name, lhs, proc, id)) lhss);
berghofe@10413
   443
berghofe@10413
   444
val add_simprocs = foldl add_simproc;
berghofe@10413
   445
berghofe@10413
   446
berghofe@10413
   447
(* del_simprocs *)
berghofe@10413
   448
nipkow@11504
   449
fun del_proc (mss as Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth},
berghofe@10413
   450
    (name, lhs, proc, id)) =
berghofe@10413
   451
  mk_mss (rules, congs,
berghofe@10413
   452
    Net.delete_term ((term_of lhs, mk_simproc (name, proc, lhs, id)), procs, eq_simproc)
wenzelm@12603
   453
      handle Net.DELETE =>
wenzelm@12603
   454
          (warning ("Simplification procedure \"" ^ name ^
wenzelm@12603
   455
                       "\" not in simpset"); procs),
nipkow@11504
   456
      bounds, prems, mk_rews, termless, depth);
berghofe@10413
   457
berghofe@10413
   458
fun del_simproc (mss, (name, lhss, proc, id)) =
berghofe@10413
   459
  foldl del_proc (mss, map (fn lhs => (name, lhs, proc, id)) lhss);
berghofe@10413
   460
berghofe@10413
   461
val del_simprocs = foldl del_simproc;
berghofe@10413
   462
berghofe@10413
   463
berghofe@10413
   464
(* prems *)
berghofe@10413
   465
nipkow@11504
   466
fun add_prems (Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, thms) =
nipkow@11504
   467
  mk_mss (rules, congs, procs, bounds, thms @ prems, mk_rews, termless, depth);
berghofe@10413
   468
berghofe@10413
   469
fun prems_of_mss (Mss {prems, ...}) = prems;
berghofe@10413
   470
berghofe@10413
   471
berghofe@10413
   472
(* mk_rews *)
berghofe@10413
   473
berghofe@10413
   474
fun set_mk_rews
nipkow@11504
   475
  (Mss {rules, congs, procs, bounds, prems, mk_rews, termless, depth}, mk) =
berghofe@10413
   476
    mk_mss (rules, congs, procs, bounds, prems,
berghofe@10413
   477
            {mk=mk, mk_sym= #mk_sym mk_rews, mk_eq_True= #mk_eq_True mk_rews},
nipkow@11504
   478
            termless, depth);
berghofe@10413
   479
berghofe@10413
   480
fun set_mk_sym
nipkow@11504
   481
  (Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, mk_sym) =
berghofe@10413
   482
    mk_mss (rules, congs, procs, bounds, prems,
berghofe@10413
   483
            {mk= #mk mk_rews, mk_sym= mk_sym, mk_eq_True= #mk_eq_True mk_rews},
nipkow@11504
   484
            termless,depth);
berghofe@10413
   485
berghofe@10413
   486
fun set_mk_eq_True
nipkow@11504
   487
  (Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, mk_eq_True) =
berghofe@10413
   488
    mk_mss (rules, congs, procs, bounds, prems,
berghofe@10413
   489
            {mk= #mk mk_rews, mk_sym= #mk_sym mk_rews, mk_eq_True= mk_eq_True},
nipkow@11504
   490
            termless,depth);
berghofe@10413
   491
berghofe@10413
   492
(* termless *)
berghofe@10413
   493
berghofe@10413
   494
fun set_termless
nipkow@11504
   495
  (Mss {rules, congs, procs, bounds, prems, mk_rews, depth, ...}, termless) =
nipkow@11504
   496
    mk_mss (rules, congs, procs, bounds, prems, mk_rews, termless, depth);
berghofe@10413
   497
berghofe@10413
   498
berghofe@10413
   499
berghofe@10413
   500
(** rewriting **)
berghofe@10413
   501
berghofe@10413
   502
(*
berghofe@10413
   503
  Uses conversions, see:
berghofe@10413
   504
    L C Paulson, A higher-order implementation of rewriting,
berghofe@10413
   505
    Science of Computer Programming 3 (1983), pages 119-149.
berghofe@10413
   506
*)
berghofe@10413
   507
berghofe@10413
   508
type prover = meta_simpset -> thm -> thm option;
berghofe@10413
   509
type termrec = (Sign.sg_ref * term list) * term;
berghofe@10413
   510
type conv = meta_simpset -> termrec -> termrec;
berghofe@10413
   511
berghofe@10413
   512
val dest_eq = Drule.dest_equals o cprop_of;
berghofe@10413
   513
val lhs_of = fst o dest_eq;
berghofe@10413
   514
val rhs_of = snd o dest_eq;
berghofe@10413
   515
berghofe@10413
   516
fun beta_eta_conversion t =
berghofe@10413
   517
  let val thm = beta_conversion true t;
berghofe@10413
   518
  in transitive thm (eta_conversion (rhs_of thm)) end;
berghofe@10413
   519
berghofe@10413
   520
fun check_conv msg thm thm' =
berghofe@10413
   521
  let
berghofe@10413
   522
    val thm'' = transitive thm (transitive
berghofe@10413
   523
      (symmetric (beta_eta_conversion (lhs_of thm'))) thm')
berghofe@10413
   524
  in (if msg then trace_thm false "SUCCEEDED" thm' else (); Some thm'') end
berghofe@10413
   525
  handle THM _ =>
berghofe@10413
   526
    let val {sign, prop = _ $ _ $ prop0, ...} = rep_thm thm;
berghofe@10413
   527
    in
berghofe@10413
   528
      (trace_thm false "Proved wrong thm (Check subgoaler?)" thm';
berghofe@10413
   529
       trace_term false "Should have proved:" sign prop0;
berghofe@10413
   530
       None)
berghofe@10413
   531
    end;
berghofe@10413
   532
berghofe@10413
   533
berghofe@10413
   534
(* mk_procrule *)
berghofe@10413
   535
berghofe@10413
   536
fun mk_procrule thm =
berghofe@10413
   537
  let val (_,prems,lhs,elhs,rhs,_) = decomp_simp thm
berghofe@10413
   538
  in if rewrite_rule_extra_vars prems lhs rhs
berghofe@10413
   539
     then (prthm true "Extra vars on rhs:" thm; [])
berghofe@10413
   540
     else [mk_rrule2{thm=thm, lhs=lhs, elhs=elhs, perm=false}]
berghofe@10413
   541
  end;
berghofe@10413
   542
berghofe@10413
   543
berghofe@10413
   544
(* conversion to apply the meta simpset to a term *)
berghofe@10413
   545
berghofe@10413
   546
(* Since the rewriting strategy is bottom-up, we avoid re-normalizing already
berghofe@10413
   547
   normalized terms by carrying around the rhs of the rewrite rule just
berghofe@10413
   548
   applied. This is called the `skeleton'. It is decomposed in parallel
berghofe@10413
   549
   with the term. Once a Var is encountered, the corresponding term is
berghofe@10413
   550
   already in normal form.
berghofe@10413
   551
   skel0 is a dummy skeleton that is to enforce complete normalization.
berghofe@10413
   552
*)
berghofe@10413
   553
val skel0 = Bound 0;
berghofe@10413
   554
berghofe@10413
   555
(* Use rhs as skeleton only if the lhs does not contain unnormalized bits.
berghofe@10413
   556
   The latter may happen iff there are weak congruence rules for constants
berghofe@10413
   557
   in the lhs.
berghofe@10413
   558
*)
berghofe@10413
   559
fun uncond_skel((_,weak),(lhs,rhs)) =
berghofe@10413
   560
  if null weak then rhs (* optimization *)
berghofe@10413
   561
  else if exists_Const (fn (c,_) => c mem weak) lhs then skel0
berghofe@10413
   562
       else rhs;
berghofe@10413
   563
berghofe@10413
   564
(* Behaves like unconditional rule if rhs does not contain vars not in the lhs.
berghofe@10413
   565
   Otherwise those vars may become instantiated with unnormalized terms
berghofe@10413
   566
   while the premises are solved.
berghofe@10413
   567
*)
berghofe@10413
   568
fun cond_skel(args as (congs,(lhs,rhs))) =
berghofe@10413
   569
  if term_varnames rhs subset term_varnames lhs then uncond_skel(args)
berghofe@10413
   570
  else skel0;
berghofe@10413
   571
berghofe@10413
   572
(*
berghofe@10413
   573
  we try in order:
berghofe@10413
   574
    (1) beta reduction
berghofe@10413
   575
    (2) unconditional rewrite rules
berghofe@10413
   576
    (3) conditional rewrite rules
berghofe@10413
   577
    (4) simplification procedures
berghofe@10413
   578
berghofe@10413
   579
  IMPORTANT: rewrite rules must not introduce new Vars or TVars!
berghofe@10413
   580
berghofe@10413
   581
*)
berghofe@10413
   582
berghofe@10413
   583
fun rewritec (prover, signt, maxt)
nipkow@11504
   584
             (mss as Mss{rules, procs, termless, prems, congs, depth,...}) t =
berghofe@10413
   585
  let
berghofe@10413
   586
    val eta_thm = Thm.eta_conversion t;
berghofe@10413
   587
    val eta_t' = rhs_of eta_thm;
berghofe@10413
   588
    val eta_t = term_of eta_t';
berghofe@10413
   589
    val tsigt = Sign.tsig_of signt;
berghofe@10413
   590
    fun rew {thm, lhs, elhs, fo, perm} =
berghofe@10413
   591
      let
berghofe@10413
   592
        val {sign, prop, maxidx, ...} = rep_thm thm;
berghofe@10413
   593
        val _ = if Sign.subsig (sign, signt) then ()
berghofe@10413
   594
                else (prthm true "Ignoring rewrite rule from different theory:" thm;
berghofe@10413
   595
                      raise Pattern.MATCH);
berghofe@10413
   596
        val (rthm, elhs') = if maxt = ~1 then (thm, elhs)
berghofe@10413
   597
          else (Thm.incr_indexes (maxt+1) thm, Thm.cterm_incr_indexes (maxt+1) elhs);
berghofe@10413
   598
        val insts = if fo then Thm.cterm_first_order_match (elhs', eta_t')
berghofe@10413
   599
                          else Thm.cterm_match (elhs', eta_t');
berghofe@10413
   600
        val thm' = Thm.instantiate insts (Thm.rename_boundvars lhs eta_t rthm);
berghofe@10413
   601
        val prop' = #prop (rep_thm thm');
berghofe@10413
   602
        val unconditional = (Logic.count_prems (prop',0) = 0);
berghofe@10413
   603
        val (lhs', rhs') = Logic.dest_equals (Logic.strip_imp_concl prop')
berghofe@10413
   604
      in
nipkow@11295
   605
        if perm andalso not (termless (rhs', lhs'))
nipkow@11295
   606
        then (trace_thm false "Cannot apply permutative rewrite rule:" thm;
nipkow@11295
   607
              trace_thm false "Term does not become smaller:" thm'; None)
nipkow@11505
   608
        else (trace_thm false "Applying instance of rewrite rule:" thm;
berghofe@10413
   609
           if unconditional
berghofe@10413
   610
           then
nipkow@11505
   611
             (trace_thm false "Rewriting:" thm';
berghofe@10413
   612
              let val lr = Logic.dest_equals prop;
berghofe@10413
   613
                  val Some thm'' = check_conv false eta_thm thm'
berghofe@10413
   614
              in Some (thm'', uncond_skel (congs, lr)) end)
berghofe@10413
   615
           else
nipkow@11505
   616
             (trace_thm false "Trying to rewrite:" thm';
nipkow@11504
   617
              case prover (incr_depth mss) thm' of
nipkow@11505
   618
                None       => (trace_thm false "FAILED" thm'; None)
berghofe@10413
   619
              | Some thm2 =>
berghofe@10413
   620
                  (case check_conv true eta_thm thm2 of
berghofe@10413
   621
                     None => None |
berghofe@10413
   622
                     Some thm2' =>
berghofe@10413
   623
                       let val concl = Logic.strip_imp_concl prop
berghofe@10413
   624
                           val lr = Logic.dest_equals concl
nipkow@11505
   625
                       in Some (thm2', cond_skel (congs, lr)) end)))
berghofe@10413
   626
      end
berghofe@10413
   627
berghofe@10413
   628
    fun rews [] = None
berghofe@10413
   629
      | rews (rrule :: rrules) =
berghofe@10413
   630
          let val opt = rew rrule handle Pattern.MATCH => None
berghofe@10413
   631
          in case opt of None => rews rrules | some => some end;
berghofe@10413
   632
berghofe@10413
   633
    fun sort_rrules rrs = let
wenzelm@12603
   634
      fun is_simple({thm, ...}:rrule) = case #prop (rep_thm thm) of
berghofe@10413
   635
                                      Const("==",_) $ _ $ _ => true
wenzelm@12603
   636
                                      | _                   => false
berghofe@10413
   637
      fun sort []        (re1,re2) = re1 @ re2
wenzelm@12603
   638
        | sort (rr::rrs) (re1,re2) = if is_simple rr
berghofe@10413
   639
                                     then sort rrs (rr::re1,re2)
berghofe@10413
   640
                                     else sort rrs (re1,rr::re2)
berghofe@10413
   641
    in sort rrs ([],[]) end
berghofe@10413
   642
berghofe@10413
   643
    fun proc_rews ([]:simproc list) = None
berghofe@10413
   644
      | proc_rews ({name, proc, lhs, ...} :: ps) =
berghofe@10413
   645
          if Pattern.matches tsigt (term_of lhs, term_of t) then
berghofe@10413
   646
            (debug_term false ("Trying procedure " ^ quote name ^ " on:") signt eta_t;
berghofe@10413
   647
             case proc signt prems eta_t of
berghofe@10413
   648
               None => (debug false "FAILED"; proc_rews ps)
berghofe@10413
   649
             | Some raw_thm =>
berghofe@10413
   650
                 (trace_thm false ("Procedure " ^ quote name ^ " produced rewrite rule:") raw_thm;
berghofe@10413
   651
                  (case rews (mk_procrule raw_thm) of
nipkow@11291
   652
                    None => (trace_cterm false "IGNORED - does not match" t; proc_rews ps)
berghofe@10413
   653
                  | some => some)))
berghofe@10413
   654
          else proc_rews ps;
berghofe@10413
   655
  in case eta_t of
berghofe@10413
   656
       Abs _ $ _ => Some (transitive eta_thm
berghofe@12155
   657
         (beta_conversion false eta_t'), skel0)
berghofe@10413
   658
     | _ => (case rews (sort_rrules (Net.match_term rules eta_t)) of
berghofe@10413
   659
               None => proc_rews (Net.match_term procs eta_t)
berghofe@10413
   660
             | some => some)
berghofe@10413
   661
  end;
berghofe@10413
   662
berghofe@10413
   663
berghofe@10413
   664
(* conversion to apply a congruence rule to a term *)
berghofe@10413
   665
berghofe@10413
   666
fun congc (prover,signt,maxt) {thm=cong,lhs=lhs} t =
berghofe@10413
   667
  let val {sign, ...} = rep_thm cong
berghofe@10413
   668
      val _ = if Sign.subsig (sign, signt) then ()
berghofe@10413
   669
                 else error("Congruence rule from different theory")
berghofe@10413
   670
      val rthm = if maxt = ~1 then cong else Thm.incr_indexes (maxt+1) cong;
berghofe@10413
   671
      val rlhs = fst (Drule.dest_equals (Drule.strip_imp_concl (cprop_of rthm)));
berghofe@10413
   672
      val insts = Thm.cterm_match (rlhs, t)
berghofe@10413
   673
      (* Pattern.match can raise Pattern.MATCH;
berghofe@10413
   674
         is handled when congc is called *)
berghofe@10413
   675
      val thm' = Thm.instantiate insts (Thm.rename_boundvars (term_of rlhs) (term_of t) rthm);
berghofe@10413
   676
      val unit = trace_thm false "Applying congruence rule:" thm';
berghofe@10413
   677
      fun err (msg, thm) = (prthm false msg thm; error "Failed congruence proof!")
berghofe@10413
   678
  in case prover thm' of
berghofe@10413
   679
       None => err ("Could not prove", thm')
berghofe@10413
   680
     | Some thm2 => (case check_conv true (beta_eta_conversion t) thm2 of
berghofe@10413
   681
          None => err ("Should not have proved", thm2)
berghofe@12155
   682
        | Some thm2' =>
berghofe@12155
   683
            if op aconv (pairself term_of (dest_equals (cprop_of thm2')))
berghofe@12155
   684
            then None else Some thm2')
berghofe@10413
   685
  end;
berghofe@10413
   686
berghofe@10413
   687
val (cA, (cB, cC)) =
berghofe@10413
   688
  apsnd dest_equals (dest_implies (hd (cprems_of Drule.imp_cong)));
berghofe@10413
   689
berghofe@10413
   690
fun transitive' thm1 None = Some thm1
berghofe@10413
   691
  | transitive' thm1 (Some thm2) = Some (transitive thm1 thm2);
berghofe@10413
   692
berghofe@12155
   693
fun transitive'' None thm2 = Some thm2
berghofe@12155
   694
  | transitive'' (Some thm1) thm2 = Some (transitive thm1 thm2);
berghofe@12155
   695
berghofe@10413
   696
fun bottomc ((simprem,useprem,mutsimp), prover, sign, maxidx) =
berghofe@10413
   697
  let
berghofe@10413
   698
    fun botc skel mss t =
berghofe@10413
   699
          if is_Var skel then None
berghofe@10413
   700
          else
berghofe@10413
   701
          (case subc skel mss t of
berghofe@10413
   702
             some as Some thm1 =>
berghofe@10413
   703
               (case rewritec (prover, sign, maxidx) mss (rhs_of thm1) of
berghofe@10413
   704
                  Some (thm2, skel2) =>
berghofe@10413
   705
                    transitive' (transitive thm1 thm2)
berghofe@10413
   706
                      (botc skel2 mss (rhs_of thm2))
berghofe@10413
   707
                | None => some)
berghofe@10413
   708
           | None =>
berghofe@10413
   709
               (case rewritec (prover, sign, maxidx) mss t of
berghofe@10413
   710
                  Some (thm2, skel2) => transitive' thm2
berghofe@10413
   711
                    (botc skel2 mss (rhs_of thm2))
berghofe@10413
   712
                | None => None))
berghofe@10413
   713
berghofe@10413
   714
    and try_botc mss t =
berghofe@10413
   715
          (case botc skel0 mss t of
berghofe@10413
   716
             Some trec1 => trec1 | None => (reflexive t))
berghofe@10413
   717
berghofe@10413
   718
    and subc skel
nipkow@11504
   719
          (mss as Mss{rules,congs,procs,bounds,prems,mk_rews,termless,depth}) t0 =
berghofe@10413
   720
       (case term_of t0 of
berghofe@10413
   721
           Abs (a, T, t) =>
berghofe@10413
   722
             let val b = variant bounds a
wenzelm@10767
   723
                 val (v, t') = Thm.dest_abs (Some ("." ^ b)) t0
nipkow@11504
   724
                 val mss' = mk_mss (rules, congs, procs, b :: bounds, prems, mk_rews, termless,depth)
berghofe@10413
   725
                 val skel' = case skel of Abs (_, _, sk) => sk | _ => skel0
berghofe@10413
   726
             in case botc skel' mss' t' of
berghofe@10413
   727
                  Some thm => Some (abstract_rule a v thm)
berghofe@10413
   728
                | None => None
berghofe@10413
   729
             end
berghofe@10413
   730
         | t $ _ => (case t of
berghofe@10413
   731
             Const ("==>", _) $ _  =>
berghofe@10413
   732
               let val (s, u) = Drule.dest_implies t0
berghofe@10413
   733
               in impc (s, u, mss) end
berghofe@10413
   734
           | Abs _ =>
berghofe@10413
   735
               let val thm = beta_conversion false t0
berghofe@10413
   736
               in case subc skel0 mss (rhs_of thm) of
berghofe@10413
   737
                    None => Some thm
berghofe@10413
   738
                  | Some thm' => Some (transitive thm thm')
berghofe@10413
   739
               end
berghofe@10413
   740
           | _  =>
berghofe@10413
   741
               let fun appc () =
berghofe@10413
   742
                     let
berghofe@10413
   743
                       val (tskel, uskel) = case skel of
berghofe@10413
   744
                           tskel $ uskel => (tskel, uskel)
berghofe@10413
   745
                         | _ => (skel0, skel0);
wenzelm@10767
   746
                       val (ct, cu) = Thm.dest_comb t0
berghofe@10413
   747
                     in
berghofe@10413
   748
                     (case botc tskel mss ct of
berghofe@10413
   749
                        Some thm1 =>
berghofe@10413
   750
                          (case botc uskel mss cu of
berghofe@10413
   751
                             Some thm2 => Some (combination thm1 thm2)
berghofe@10413
   752
                           | None => Some (combination thm1 (reflexive cu)))
berghofe@10413
   753
                      | None =>
berghofe@10413
   754
                          (case botc uskel mss cu of
berghofe@10413
   755
                             Some thm1 => Some (combination (reflexive ct) thm1)
berghofe@10413
   756
                           | None => None))
berghofe@10413
   757
                     end
berghofe@10413
   758
                   val (h, ts) = strip_comb t
berghofe@10413
   759
               in case h of
berghofe@10413
   760
                    Const(a, _) =>
berghofe@10413
   761
                      (case assoc_string (fst congs, a) of
berghofe@10413
   762
                         None => appc ()
berghofe@10413
   763
                       | Some cong =>
berghofe@10413
   764
(* post processing: some partial applications h t1 ... tj, j <= length ts,
berghofe@10413
   765
   may be a redex. Example: map (%x.x) = (%xs.xs) wrt map_cong *)
berghofe@10413
   766
                          (let
berghofe@10413
   767
                             val thm = congc (prover mss, sign, maxidx) cong t0;
berghofe@12155
   768
                             val t = if_none (apsome rhs_of thm) t0;
wenzelm@10767
   769
                             val (cl, cr) = Thm.dest_comb t
berghofe@10413
   770
                             val dVar = Var(("", 0), dummyT)
berghofe@10413
   771
                             val skel =
berghofe@10413
   772
                               list_comb (h, replicate (length ts) dVar)
berghofe@10413
   773
                           in case botc skel mss cl of
berghofe@12155
   774
                                None => thm
berghofe@12155
   775
                              | Some thm' => transitive'' thm
berghofe@12155
   776
                                  (combination thm' (reflexive cr))
berghofe@10413
   777
                           end handle TERM _ => error "congc result"
berghofe@10413
   778
                                    | Pattern.MATCH => appc ()))
berghofe@10413
   779
                  | _ => appc ()
berghofe@10413
   780
               end)
berghofe@10413
   781
         | _ => None)
berghofe@10413
   782
berghofe@10413
   783
    and impc args =
berghofe@10413
   784
      if mutsimp
berghofe@10413
   785
      then let val (prem, conc, mss) = args
berghofe@10413
   786
           in apsome snd (mut_impc ([], prem, conc, mss)) end
berghofe@10413
   787
      else nonmut_impc args
berghofe@10413
   788
berghofe@10413
   789
    and mut_impc (prems, prem, conc, mss) = (case botc skel0 mss prem of
berghofe@10413
   790
        None => mut_impc1 (prems, prem, conc, mss)
berghofe@10413
   791
      | Some thm1 =>
berghofe@10413
   792
          let val prem1 = rhs_of thm1
berghofe@10413
   793
          in (case mut_impc1 (prems, prem1, conc, mss) of
berghofe@10413
   794
              None => Some (None,
berghofe@10413
   795
                combination (combination refl_implies thm1) (reflexive conc))
berghofe@10413
   796
            | Some (x, thm2) => Some (x, transitive (combination (combination
berghofe@10413
   797
                refl_implies thm1) (reflexive conc)) thm2))
berghofe@10413
   798
          end)
berghofe@10413
   799
berghofe@10413
   800
    and mut_impc1 (prems, prem1, conc, mss) =
berghofe@10413
   801
      let
berghofe@10413
   802
        fun uncond ({thm, lhs, elhs, perm}) =
berghofe@10413
   803
          if Thm.no_prems thm then Some lhs else None
berghofe@10413
   804
berghofe@10413
   805
        val (lhss1, mss1) =
berghofe@10413
   806
          if maxidx_of_term (term_of prem1) <> ~1
berghofe@10413
   807
          then (trace_cterm true
berghofe@10413
   808
            "Cannot add premise as rewrite rule because it contains (type) unknowns:" prem1;
berghofe@10413
   809
                ([],mss))
berghofe@10413
   810
          else let val thm = assume prem1
berghofe@10413
   811
                   val rrules1 = extract_safe_rrules (mss, thm)
berghofe@10413
   812
                   val lhss1 = mapfilter uncond rrules1
berghofe@10413
   813
                   val mss1 = foldl insert_rrule (add_prems (mss, [thm]), rrules1)
berghofe@10413
   814
               in (lhss1, mss1) end
berghofe@10413
   815
berghofe@10413
   816
        fun disch1 thm =
berghofe@10413
   817
          let val (cB', cC') = dest_eq thm
berghofe@10413
   818
          in
berghofe@10413
   819
            implies_elim (Thm.instantiate
berghofe@10413
   820
              ([], [(cA, prem1), (cB, cB'), (cC, cC')]) Drule.imp_cong)
berghofe@10413
   821
              (implies_intr prem1 thm)
berghofe@10413
   822
          end
berghofe@10413
   823
berghofe@10413
   824
        fun rebuild None = (case rewritec (prover, sign, maxidx) mss
berghofe@10413
   825
            (mk_implies (prem1, conc)) of
berghofe@10413
   826
              None => None
wenzelm@12603
   827
            | Some (thm, _) =>
berghofe@11371
   828
                let val (prem, conc) = Drule.dest_implies (rhs_of thm)
berghofe@11371
   829
                in (case mut_impc (prems, prem, conc, mss) of
berghofe@11371
   830
                    None => Some (None, thm)
berghofe@11371
   831
                  | Some (x, thm') => Some (x, transitive thm thm'))
berghofe@11371
   832
                end handle TERM _ => Some (None, thm))
berghofe@10413
   833
          | rebuild (Some thm2) =
berghofe@10413
   834
            let val thm = disch1 thm2
berghofe@10413
   835
            in (case rewritec (prover, sign, maxidx) mss (rhs_of thm) of
berghofe@10413
   836
                 None => Some (None, thm)
berghofe@10413
   837
               | Some (thm', _) =>
berghofe@10413
   838
                   let val (prem, conc) = Drule.dest_implies (rhs_of thm')
berghofe@10413
   839
                   in (case mut_impc (prems, prem, conc, mss) of
berghofe@10413
   840
                       None => Some (None, transitive thm thm')
berghofe@10413
   841
                     | Some (x, thm'') =>
berghofe@10413
   842
                         Some (x, transitive (transitive thm thm') thm''))
berghofe@10413
   843
                   end handle TERM _ => Some (None, transitive thm thm'))
berghofe@10413
   844
            end
berghofe@10413
   845
berghofe@10413
   846
        fun simpconc () =
berghofe@10413
   847
          let val (s, t) = Drule.dest_implies conc
berghofe@10413
   848
          in case mut_impc (prems @ [prem1], s, t, mss1) of
berghofe@10413
   849
               None => rebuild None
berghofe@10413
   850
             | Some (Some i, thm2) =>
berghofe@10413
   851
                  let
berghofe@10413
   852
                    val (prem, cC') = Drule.dest_implies (rhs_of thm2);
berghofe@10413
   853
                    val thm2' = transitive (disch1 thm2) (Thm.instantiate
berghofe@10413
   854
                      ([], [(cA, prem1), (cB, prem), (cC, cC')])
berghofe@10413
   855
                      Drule.swap_prems_eq)
berghofe@10413
   856
                  in if i=0 then apsome (apsnd (transitive thm2'))
berghofe@10413
   857
                       (mut_impc1 (prems, prem, mk_implies (prem1, cC'), mss))
berghofe@10413
   858
                     else Some (Some (i-1), thm2')
berghofe@10413
   859
                  end
berghofe@10413
   860
             | Some (None, thm) => rebuild (Some thm)
berghofe@10413
   861
          end handle TERM _ => rebuild (botc skel0 mss1 conc)
berghofe@10413
   862
berghofe@10413
   863
      in
berghofe@10413
   864
        let
berghofe@10413
   865
          val tsig = Sign.tsig_of sign
berghofe@10413
   866
          fun reducible t =
berghofe@10413
   867
            exists (fn lhs => Pattern.matches_subterm tsig (lhs, term_of t)) lhss1;
berghofe@10413
   868
        in case dropwhile (not o reducible) prems of
berghofe@10413
   869
            [] => simpconc ()
berghofe@10413
   870
          | red::rest => (trace_cterm false "Can now reduce premise:" red;
berghofe@10413
   871
              Some (Some (length rest), reflexive (mk_implies (prem1, conc))))
berghofe@10413
   872
        end
berghofe@10413
   873
      end
berghofe@10413
   874
berghofe@10413
   875
     (* legacy code - only for backwards compatibility *)
berghofe@10413
   876
     and nonmut_impc (prem, conc, mss) =
berghofe@10413
   877
       let val thm1 = if simprem then botc skel0 mss prem else None;
berghofe@10413
   878
           val prem1 = if_none (apsome rhs_of thm1) prem;
berghofe@10413
   879
           val maxidx1 = maxidx_of_term (term_of prem1)
berghofe@10413
   880
           val mss1 =
berghofe@10413
   881
             if not useprem then mss else
berghofe@10413
   882
             if maxidx1 <> ~1
berghofe@10413
   883
             then (trace_cterm true
berghofe@10413
   884
               "Cannot add premise as rewrite rule because it contains (type) unknowns:" prem1;
berghofe@10413
   885
                   mss)
berghofe@10413
   886
             else let val thm = assume prem1
berghofe@10413
   887
                  in add_safe_simp (add_prems (mss, [thm]), thm) end
berghofe@10413
   888
       in (case botc skel0 mss1 conc of
berghofe@10413
   889
           None => (case thm1 of
berghofe@10413
   890
               None => None
berghofe@10413
   891
             | Some thm1' => Some (combination
berghofe@10413
   892
                 (combination refl_implies thm1') (reflexive conc)))
berghofe@10413
   893
         | Some thm2 =>
berghofe@10413
   894
           let
berghofe@10413
   895
             val conc2 = rhs_of thm2;
berghofe@10413
   896
             val thm2' = implies_elim (Thm.instantiate
berghofe@10413
   897
               ([], [(cA, prem1), (cB, conc), (cC, conc2)]) Drule.imp_cong)
berghofe@10413
   898
               (implies_intr prem1 thm2)
berghofe@10413
   899
           in (case thm1 of
berghofe@10413
   900
               None => Some thm2'
berghofe@10413
   901
             | Some thm1' => Some (transitive (combination
berghofe@10413
   902
                 (combination refl_implies thm1') (reflexive conc)) thm2'))
berghofe@10413
   903
           end)
berghofe@10413
   904
       end
berghofe@10413
   905
berghofe@10413
   906
 in try_botc end;
berghofe@10413
   907
berghofe@10413
   908
berghofe@10413
   909
(*** Meta-rewriting: rewrites t to u and returns the theorem t==u ***)
berghofe@10413
   910
berghofe@10413
   911
(*
berghofe@10413
   912
  Parameters:
berghofe@10413
   913
    mode = (simplify A,
berghofe@10413
   914
            use A in simplifying B,
berghofe@10413
   915
            use prems of B (if B is again a meta-impl.) to simplify A)
berghofe@10413
   916
           when simplifying A ==> B
berghofe@10413
   917
    mss: contains equality theorems of the form [|p1,...|] ==> t==u
berghofe@10413
   918
    prover: how to solve premises in conditional rewrites and congruences
berghofe@10413
   919
*)
berghofe@10413
   920
berghofe@10413
   921
fun rewrite_cterm mode prover mss ct =
berghofe@10413
   922
  let val {sign, t, maxidx, ...} = rep_cterm ct
nipkow@11505
   923
      val Mss{depth, ...} = mss
nipkow@11505
   924
  in simp_depth := depth;
nipkow@11505
   925
     bottomc (mode, prover, sign, maxidx) mss ct
nipkow@11505
   926
  end
berghofe@10413
   927
  handle THM (s, _, thms) =>
berghofe@10413
   928
    error ("Exception THM was raised in simplifier:\n" ^ s ^ "\n" ^
wenzelm@11886
   929
      Pretty.string_of (Display.pretty_thms thms));
berghofe@10413
   930
berghofe@10413
   931
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
berghofe@10413
   932
(*Do not rewrite flex-flex pairs*)
berghofe@10413
   933
fun goals_conv pred cv =
berghofe@10413
   934
  let fun gconv i ct =
berghofe@10413
   935
        let val (A,B) = Drule.dest_implies ct
berghofe@10413
   936
            val (thA,j) = case term_of A of
berghofe@10413
   937
                  Const("=?=",_)$_$_ => (reflexive A, i)
berghofe@10413
   938
                | _ => (if pred i then cv A else reflexive A, i+1)
berghofe@10413
   939
        in  combination (combination refl_implies thA) (gconv j B) end
berghofe@10413
   940
        handle TERM _ => reflexive ct
berghofe@10413
   941
  in gconv 1 end;
berghofe@10413
   942
berghofe@11737
   943
(* Rewrite A in !!x1,...,xn. A *)
berghofe@11736
   944
fun forall_conv cv ct =
berghofe@11736
   945
  let val p as (ct1, ct2) = Thm.dest_comb ct
berghofe@11736
   946
  in (case pairself term_of p of
berghofe@11736
   947
      (Const ("all", _), Abs (s, _, _)) =>
berghofe@11736
   948
         let val (v, ct') = Thm.dest_abs (Some "@") ct2;
berghofe@11736
   949
         in Thm.combination (Thm.reflexive ct1)
berghofe@11736
   950
           (Thm.abstract_rule s v (forall_conv cv ct'))
berghofe@11736
   951
         end
berghofe@11736
   952
    | _ => cv ct)
berghofe@11736
   953
  end handle TERM _ => cv ct;
berghofe@11736
   954
berghofe@10413
   955
(*Use a conversion to transform a theorem*)
berghofe@10413
   956
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
berghofe@10413
   957
wenzelm@11760
   958
(*Rewrite a cterm*)
wenzelm@11767
   959
fun rewrite_aux _ _ [] = (fn ct => Thm.reflexive ct)
wenzelm@11767
   960
  | rewrite_aux prover full thms = rewrite_cterm (full, false, false) prover (mss_of thms);
wenzelm@11672
   961
berghofe@10413
   962
(*Rewrite a theorem*)
wenzelm@11767
   963
fun simplify_aux _ _ [] = (fn th => th)
wenzelm@11767
   964
  | simplify_aux prover full thms =
wenzelm@11767
   965
      fconv_rule (rewrite_cterm (full, false, false) prover (mss_of thms));
berghofe@10413
   966
berghofe@10413
   967
fun rewrite_thm mode prover mss = fconv_rule (rewrite_cterm mode prover mss);
berghofe@10413
   968
berghofe@10413
   969
(*Rewrite the subgoals of a proof state (represented by a theorem) *)
berghofe@10413
   970
fun rewrite_goals_rule_aux _ []   th = th
berghofe@10413
   971
  | rewrite_goals_rule_aux prover thms th =
berghofe@10413
   972
      fconv_rule (goals_conv (K true) (rewrite_cterm (true, true, false) prover
berghofe@10413
   973
        (mss_of thms))) th;
berghofe@10413
   974
berghofe@10413
   975
(*Rewrite the subgoal of a proof state (represented by a theorem) *)
berghofe@10413
   976
fun rewrite_goal_rule mode prover mss i thm =
berghofe@10413
   977
  if 0 < i  andalso  i <= nprems_of thm
berghofe@10413
   978
  then fconv_rule (goals_conv (fn j => j=i) (rewrite_cterm mode prover mss)) thm
berghofe@10413
   979
  else raise THM("rewrite_goal_rule",i,[thm]);
berghofe@10413
   980
berghofe@10413
   981
end;
berghofe@10413
   982
wenzelm@11672
   983
structure BasicMetaSimplifier: BASIC_META_SIMPLIFIER = MetaSimplifier;
wenzelm@11672
   984
open BasicMetaSimplifier;