(*  Title:      Pure/Isar/local_defs.ML

    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: ((binding * mixfix) * (Thm.binding * term)) list -> Proof.context ->

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

  val add_def: (binding * mixfix) * term -> Proof.context -> (term * thm) * Proof.context

  val fixed_abbrev: (binding * mixfix) * term -> Proof.context ->

    (term * term) * Proof.context

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

  val export_cterm: Proof.context -> Proof.context -> cterm -> cterm * 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

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

      quote (Syntax.string_of_term ctxt eq));

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

      |> Sign.no_vars (Syntax.pp ctxt)

      |> PrimitiveDefs.dest_def ctxt 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 = PrimitiveDefs.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 ((bvars, mxs), specs) = defs |> split_list |>> split_list;

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

    val xs = map Name.of_binding bvars;

    val names = map2 Thm.def_binding_optional bvars bfacts;

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

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

  in

    ctxt

    |> ProofContext.add_fixes (map2 (fn x => fn mx => (x, NONE, mx)) bvars 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;

fun add_def (var, rhs) ctxt =

  let val ([(lhs, (_, th))], ctxt') = add_defs [(var, (Thm.empty_binding, rhs))] ctxt

  in ((lhs, th), ctxt') end;

(* fixed_abbrev *)

fun fixed_abbrev ((x, mx), rhs) ctxt =

  let

    val T = Term.fastype_of rhs;

    val ([x'], ctxt') = ctxt

      |> Variable.declare_term rhs

      |> ProofContext.add_fixes [(x, SOME T, mx)];

    val lhs = Free (x', T);

    val _ = cert_def ctxt' (Logic.mk_equals (lhs, rhs));

    fun abbrev_export _ _ = (I, Envir.expand_term_frees [((x', T), rhs)]);

    val (_, ctxt'') = Assumption.add_assms abbrev_export [] ctxt';

  in ((lhs, rhs), ctxt'') end;

(* specific export -- result based on educated guessing *)

(*

  [xs, xs == as]

        :

       B xs

  --------------

       B as

*)

fun export inner outer =    (*beware of closure sizes*)

  let

    val exp = Assumption.export false inner outer;

    val prems = Assumption.all_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;

(*

  [xs, xs == as]

        :

     TERM b xs

  --------------  and  --------------

     TERM b as          b xs == b as

*)

fun export_cterm inner outer ct =

  let val (defs, ct') = export inner outer (Drule.mk_term ct) ||> Drule.dest_term

  in (ct', MetaSimplifier.rewrite true defs ct) 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 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 _ = Thm.merge_thms;

);

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 Thm.add_thm);

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

(* meta rewrite rules *)

fun meta_rewrite_conv ctxt =

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

    (MetaSimplifier.context ctxt MetaSimplifier.empty_ss

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

      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;