src/Pure/Isar/local_defs.ML
author wenzelm
Thu Dec 14 15:31:21 2006 +0100 (2006-12-14 ago)
changeset 21844 e10b8bd7a886
parent 21801 c77bc21b3eef
child 22568 ed7aa5a350ef
permissions -rw-r--r--
added trans_terms/props;
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(*  Title:      Pure/Isar/local_defs.ML
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    ID:         $Id$
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    Author:     Makarius
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Local definitions.
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*)
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signature LOCAL_DEFS =
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sig
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  val cert_def: Proof.context -> term -> (string * typ) * term
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  val abs_def: term -> (string * typ) * term
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  val mk_def: Proof.context -> (string * term) list -> term list
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  val expand: cterm list -> thm -> thm
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  val def_export: Assumption.export
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  val add_defs: ((string * mixfix) * ((bstring * attribute list) * term)) list -> Proof.context ->
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    (term * (bstring * thm)) list * Proof.context
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  val export: Proof.context -> Proof.context -> thm -> thm list * thm
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  val trans_terms: Proof.context -> thm list -> thm
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  val trans_props: Proof.context -> thm list -> thm
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  val print_rules: Proof.context -> unit
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  val defn_add: attribute
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  val defn_del: attribute
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  val meta_rewrite_rule: Proof.context -> thm -> thm
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  val unfold: Proof.context -> thm list -> thm -> thm
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  val unfold_goals: Proof.context -> thm list -> thm -> thm
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  val unfold_tac: Proof.context -> thm list -> tactic
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  val fold: Proof.context -> thm list -> thm -> thm
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  val fold_tac: Proof.context -> thm list -> tactic
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  val derived_def: Proof.context -> bool -> term ->
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    ((string * typ) * term) * (Proof.context -> thm -> thm)
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end;
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structure LocalDefs: LOCAL_DEFS =
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struct
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(** primitive definitions **)
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(* prepare defs *)
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fun cert_def ctxt eq =
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  let
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    val pp = ProofContext.pp ctxt;
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    val display_term = quote o Pretty.string_of_term pp;
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    fun err msg = cat_error msg ("The error(s) above occurred in definition: " ^ display_term eq);
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    val ((lhs, _), eq') = eq
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      |> Sign.no_vars pp
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      |> Logic.dest_def pp Term.is_Free (Variable.is_fixed ctxt) (K true)
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      handle TERM (msg, _) => err msg | ERROR msg => err msg;
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  in (Term.dest_Free (Term.head_of lhs), eq') end;
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val abs_def = Logic.abs_def #>> Term.dest_Free;
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fun mk_def ctxt args =
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  let
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    val (xs, rhss) = split_list args;
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    val (bind, _) = ProofContext.bind_fixes xs ctxt;
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    val lhss = map (fn (x, rhs) => bind (Free (x, Term.fastype_of rhs))) args;
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  in map Logic.mk_equals (lhss ~~ rhss) end;
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(* export defs *)
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val head_of_def =
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  #1 o Term.dest_Free o Term.head_of o #1 o Logic.dest_equals o Term.strip_all_body;
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(*
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  [x, x == a]
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       :
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      B x
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  -----------
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      B a
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*)
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fun expand defs =
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  Drule.implies_intr_list defs
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  #> Drule.generalize ([], map (head_of_def o Thm.term_of) defs)
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  #> funpow (length defs) (fn th => Drule.reflexive_thm RS th);
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val expand_term = Envir.expand_term_frees o map (abs_def o Thm.term_of);
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fun def_export _ defs = (expand defs, expand_term defs);
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(* add defs *)
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fun add_defs defs ctxt =
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  let
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    val ((xs, mxs), specs) = defs |> split_list |>> split_list;
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    val ((names, atts), rhss) = specs |> split_list |>> split_list;
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    val names' = map2 Thm.def_name_optional xs names;
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    val eqs = mk_def ctxt (xs ~~ rhss);
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    val lhss = map (fst o Logic.dest_equals) eqs;
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  in
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    ctxt
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    |> ProofContext.add_fixes_i (map2 (fn x => fn mx => (x, NONE, mx)) xs mxs) |> #2
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    |> fold Variable.declare_term eqs
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    |> ProofContext.add_assms_i def_export
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      (map2 (fn a => fn eq => (a, [(eq, [])])) (names' ~~ atts) eqs)
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    |>> map2 (fn lhs => fn (name, [th]) => (lhs, (name, th))) lhss
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  end;
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(* specific export -- result based on educated guessing *)
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fun export inner outer th =
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  let
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    val th' = Assumption.export false inner outer th;
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    val still_fixed = map #1 (Drule.fold_terms Term.add_frees th' []);
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    val defs = Assumption.prems_of inner |> filter_out (fn prem =>
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      (case try (head_of_def o Thm.prop_of) prem of
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        SOME x => member (op =) still_fixed x
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      | NONE => true));
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  in (map Drule.abs_def defs, th') end;
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(* basic transitivity reasoning -- modulo beta-eta *)
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local
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val is_trivial = Pattern.aeconv o Logic.dest_equals o Thm.prop_of;
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fun trans_list _ _ [] = raise Empty
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  | trans_list trans ctxt (th :: raw_eqs) =
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      (case filter_out is_trivial raw_eqs of
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        [] => th
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      | eqs =>
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          let val ((_, th' :: eqs'), ctxt') = Variable.import true (th :: eqs) ctxt
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          in singleton (Variable.export ctxt' ctxt) (fold trans eqs' th') end);
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in
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val trans_terms = trans_list (fn eq2 => fn eq1 => eq2 COMP (eq1 COMP Drule.transitive_thm));
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val trans_props = trans_list (fn eq => fn th => th COMP (eq COMP Drule.equal_elim_rule1));
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end;
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(** defived definitions **)
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(* transformation rules *)
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structure Rules = GenericDataFun
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(
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  val name = "Pure/derived_defs";
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  type T = thm list;
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  val empty = []
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  val extend = I;
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  fun merge _ = Drule.merge_rules;
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  fun print context rules =
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    Pretty.writeln (Pretty.big_list "definitional transformations:"
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      (map (ProofContext.pretty_thm (Context.proof_of context)) rules));
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);
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val _ = Context.add_setup Rules.init;
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val print_rules = Rules.print o Context.Proof;
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val defn_add = Thm.declaration_attribute (Rules.map o Drule.add_rule);
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val defn_del = Thm.declaration_attribute (Rules.map o Drule.del_rule);
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(* meta rewrite rules *)
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val equals_ss =
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  MetaSimplifier.theory_context ProtoPure.thy MetaSimplifier.empty_ss
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    addeqcongs [Drule.equals_cong];    (*protect meta-level equality*)
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fun meta_rewrite ctxt =
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  MetaSimplifier.rewrite_cterm (false, false, false) (K (K NONE))
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    (equals_ss addsimps (Rules.get (Context.Proof ctxt)));
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val meta_rewrite_rule = Drule.fconv_rule o meta_rewrite;
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fun meta_rewrite_tac ctxt i =
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  PRIMITIVE (Drule.fconv_rule (Drule.goals_conv (equal i) (meta_rewrite ctxt)));
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(* rewriting with object-level rules *)
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fun meta f ctxt = f o map (meta_rewrite_rule ctxt);
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val unfold       = meta MetaSimplifier.rewrite_rule;
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val unfold_goals = meta MetaSimplifier.rewrite_goals_rule;
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val unfold_tac   = meta MetaSimplifier.rewrite_goals_tac;
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val fold         = meta MetaSimplifier.fold_rule;
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val fold_tac     = meta MetaSimplifier.fold_goals_tac;
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(* derived defs -- potentially within the object-logic *)
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fun derived_def ctxt conditional prop =
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  let
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    val ((c, T), rhs) = prop
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      |> Thm.cterm_of (ProofContext.theory_of ctxt)
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      |> meta_rewrite ctxt
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      |> (snd o Logic.dest_equals o Thm.prop_of)
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      |> conditional ? Logic.strip_imp_concl
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      |> (abs_def o #2 o cert_def ctxt);
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    fun prove ctxt' def =
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      let
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        val frees = Term.fold_aterms (fn Free (x, _) =>
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          if Variable.is_fixed ctxt' x then I else insert (op =) x | _ => I) prop [];
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      in
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        Goal.prove ctxt' frees [] prop (K (ALLGOALS
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          (meta_rewrite_tac ctxt' THEN'
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            Goal.rewrite_goal_tac [def] THEN'
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            resolve_tac [Drule.reflexive_thm])))
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        handle ERROR msg => cat_error msg "Failed to prove definitional specification."
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      end;
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  in (((c, T), rhs), prove) end;
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end;