(*  Title:      Pure/Isar/local_defs.ML

    ID:         $Id$

    Author:     Makarius

Local definitions.

*)

signature LOCAL_DEFS =

sig

  val cert_def: Proof.context -> term -> (string * typ) * term

  val abs_def: term -> (string * typ) * term

  val mk_def: Proof.context -> (string * term) list -> term list

  val expand: cterm list -> thm -> thm

  val def_export: Assumption.export

  val add_defs: ((string * mixfix) * ((bstring * attribute list) * term)) list -> Proof.context ->

    (term * (bstring * thm)) list * Proof.context

  val export: Proof.context -> Proof.context -> thm -> thm list * thm

  val trans_terms: Proof.context -> thm list -> thm

  val trans_props: Proof.context -> thm list -> thm

  val print_rules: Proof.context -> unit

  val defn_add: attribute

  val defn_del: attribute

  val meta_rewrite_conv: Proof.context -> conv

  val meta_rewrite_rule: Proof.context -> thm -> thm

  val unfold: Proof.context -> thm list -> thm -> thm

  val unfold_goals: Proof.context -> thm list -> thm -> thm

  val unfold_tac: Proof.context -> thm list -> tactic

  val fold: Proof.context -> thm list -> thm -> thm

  val fold_tac: Proof.context -> thm list -> tactic

  val derived_def: Proof.context -> bool -> term ->

    ((string * typ) * term) * (Proof.context -> thm -> thm)

end;

structure LocalDefs: LOCAL_DEFS =

struct

(** primitive definitions **)

(* prepare defs *)

fun cert_def ctxt eq =

  let

    val pp = ProofContext.pp ctxt;

    val display_term = quote o Pretty.string_of_term pp;

    fun err msg = cat_error msg ("The error(s) above occurred in definition: " ^ display_term eq);

    val ((lhs, _), eq') = eq

      |> Sign.no_vars pp

      |> Logic.dest_def pp Term.is_Free (Variable.is_fixed ctxt) (K true)

      handle TERM (msg, _) => err msg | ERROR msg => err msg;

  in (Term.dest_Free (Term.head_of lhs), eq') end;

val abs_def = Logic.abs_def #>> Term.dest_Free;

fun mk_def ctxt args =

  let

    val (xs, rhss) = split_list args;

    val (bind, _) = ProofContext.bind_fixes xs ctxt;

    val lhss = map (fn (x, rhs) => bind (Free (x, Term.fastype_of rhs))) args;

  in map Logic.mk_equals (lhss ~~ rhss) end;

(* export defs *)

val head_of_def =

  #1 o Term.dest_Free o Term.head_of o #1 o Logic.dest_equals o Term.strip_all_body;

(*

  [x, x == a]

       :

      B x

  -----------

      B a

*)

fun expand defs =

  Drule.implies_intr_list defs

  #> Drule.generalize ([], map (head_of_def o Thm.term_of) defs)

  #> funpow (length defs) (fn th => Drule.reflexive_thm RS th);

val expand_term = Envir.expand_term_frees o map (abs_def o Thm.term_of);

fun def_export _ defs = (expand defs, expand_term defs);

(* add defs *)

fun add_defs defs ctxt =

  let

    val ((xs, mxs), specs) = defs |> split_list |>> split_list;

    val ((names, atts), rhss) = specs |> split_list |>> split_list;

    val names' = map2 Thm.def_name_optional xs names;

    val eqs = mk_def ctxt (xs ~~ rhss);

    val lhss = map (fst o Logic.dest_equals) eqs;

  in

    ctxt

    |> ProofContext.add_fixes_i (map2 (fn x => fn mx => (x, NONE, mx)) xs mxs) |> #2

    |> fold Variable.declare_term eqs

    |> ProofContext.add_assms_i def_export

      (map2 (fn a => fn eq => (a, [(eq, [])])) (names' ~~ atts) eqs)

    |>> map2 (fn lhs => fn (name, [th]) => (lhs, (name, th))) lhss

  end;

(* specific export -- result based on educated guessing (beware of closure sizes) *)

fun export inner outer =

  let

    val exp = Assumption.export false inner outer;

    val prems = Assumption.prems_of inner;

  in fn th =>

    let

      val th' = exp th;

      val still_fixed = map #1 (Thm.fold_terms Term.add_frees th' []);

      val defs = prems |> filter_out (fn prem =>

        (case try (head_of_def o Thm.prop_of) prem of

          SOME x => member (op =) still_fixed x

        | NONE => true));

    in (map Drule.abs_def defs, th') end

  end;

(* basic transitivity reasoning -- modulo beta-eta *)

local

val is_trivial = Pattern.aeconv o Logic.dest_equals o Thm.prop_of;

fun trans_list _ _ [] = raise Empty

  | trans_list trans ctxt (th :: raw_eqs) =

      (case filter_out is_trivial raw_eqs of

        [] => th

      | eqs =>

          let val ((_, th' :: eqs'), ctxt') = Variable.import_thms true (th :: eqs) ctxt

          in singleton (Variable.export ctxt' ctxt) (fold trans eqs' th') end);

in

val trans_terms = trans_list (fn eq2 => fn eq1 => eq2 COMP (eq1 COMP Drule.transitive_thm));

val trans_props = trans_list (fn eq => fn th => th COMP (eq COMP Drule.equal_elim_rule1));

end;

(** defived definitions **)

(* transformation rules *)

structure Rules = GenericDataFun

(

  type T = thm list;

  val empty = []

  val extend = I;

  fun merge _ = Drule.merge_rules;

);

fun print_rules ctxt =

  Pretty.writeln (Pretty.big_list "definitional transformations:"

    (map (ProofContext.pretty_thm ctxt) (Rules.get (Context.Proof ctxt))));

val defn_add = Thm.declaration_attribute (Rules.map o Drule.add_rule);

val defn_del = Thm.declaration_attribute (Rules.map o Drule.del_rule);

(* meta rewrite rules *)

val equals_ss =

  MetaSimplifier.theory_context ProtoPure.thy MetaSimplifier.empty_ss

    addeqcongs [Drule.equals_cong];    (*protect meta-level equality*)

fun meta_rewrite_conv ctxt =

  MetaSimplifier.rewrite_cterm (false, false, false) (K (K NONE))

    (equals_ss addsimps (Rules.get (Context.Proof ctxt)));

val meta_rewrite_rule = Conv.fconv_rule o meta_rewrite_conv;

(* rewriting with object-level rules *)

fun meta f ctxt = f o map (meta_rewrite_rule ctxt);

val unfold       = meta MetaSimplifier.rewrite_rule;

val unfold_goals = meta MetaSimplifier.rewrite_goals_rule;

val unfold_tac   = meta MetaSimplifier.rewrite_goals_tac;

val fold         = meta MetaSimplifier.fold_rule;

val fold_tac     = meta MetaSimplifier.fold_goals_tac;

(* derived defs -- potentially within the object-logic *)

fun derived_def ctxt conditional prop =

  let

    val ((c, T), rhs) = prop

      |> Thm.cterm_of (ProofContext.theory_of ctxt)

      |> meta_rewrite_conv ctxt

      |> (snd o Logic.dest_equals o Thm.prop_of)

      |> conditional ? Logic.strip_imp_concl

      |> (abs_def o #2 o cert_def ctxt);

    fun prove ctxt' def =

      let

        val frees = Term.fold_aterms (fn Free (x, _) =>

          if Variable.is_fixed ctxt' x then I else insert (op =) x | _ => I) prop [];

      in

        Goal.prove ctxt' frees [] prop (K (ALLGOALS

          (CONVERSION (meta_rewrite_conv ctxt') THEN'

            MetaSimplifier.rewrite_goal_tac [def] THEN'

            resolve_tac [Drule.reflexive_thm])))

        handle ERROR msg => cat_error msg "Failed to prove definitional specification."

      end;

  in (((c, T), rhs), prove) end;

end;