(*  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 def_export: Assumption.export

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

  val print_rules: Context.generic -> unit

  val defn_add: attribute

  val defn_del: attribute

  val meta_rewrite_rule: Context.generic -> 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 -> term -> 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 #> apfst 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 o Thm.term_of;

(*

  [x, x == t]

       :

      B x

  -----------

      B t

*)

fun def_export _ defs thm =

  thm

  |> Drule.implies_intr_list defs

  |> Drule.generalize ([], map head_of_def defs)

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

(* add defs *)

fun add_def (x, t) ctxt =

  let

    val [eq] = mk_def ctxt [(x, t)];

    val x' = Term.dest_Free (fst (Logic.dest_equals eq));

  in

    ctxt

    |> ProofContext.add_fixes_i [(x, NONE, NoSyn)] |> snd

    |> ProofContext.add_assms_i def_export [(("", []), [(eq, [])])]

    |>> (fn [(_, [th])] => (x', th))

  end;

(** defived definitions **)

(* transformation rules *)

structure Rules = GenericDataFun

(

  val name = "Pure/derived_defs";

  type T = thm list;

  val empty = []

  val extend = I;

  fun merge _ = Drule.merge_rules;

  fun print context rules =

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

      (map (ProofContext.pretty_thm (Context.proof_of context)) rules));

);

val _ = Context.add_setup Rules.init;

val print_rules = Rules.print;

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 context =

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

    (equals_ss addsimps (Rules.get context));

val meta_rewrite_rule = Drule.fconv_rule o meta_rewrite;

fun meta_rewrite_tac ctxt i =

  PRIMITIVE (Drule.fconv_rule (Drule.goals_conv (equal i) (meta_rewrite (Context.Proof ctxt))));

(* rewriting with object-level rules *)

fun meta f ctxt = f o map (meta_rewrite_rule (Context.Proof ctxt));

val unfold       = meta Tactic.rewrite_rule;

val unfold_goals = meta Tactic.rewrite_goals_rule;

val unfold_tac   = meta Tactic.rewrite_goals_tac;

val fold         = meta Tactic.fold_rule;

val fold_tac     = meta Tactic.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 (Context.Proof ctxt)

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

      |> K conditional ? Logic.strip_imp_concl

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

    fun prove ctxt' t def =

      let

        val prop' = Term.subst_atomic [(Free (c, T), t)] prop;

        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

          (meta_rewrite_tac ctxt' THEN'

            Tactic.rewrite_goal_tac [def] THEN'

            Tactic.resolve_tac [Drule.reflexive_thm])))

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

      end;

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

end;