(*  Title:      Pure/Isar/local_defs.ML

    ID:         $Id$

    Author:     Makarius

Local definitions.

*)

signature LOCAL_DEFS =

sig

  val cert_def: ProofContext.context -> term -> string * term

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

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

  val def_export: ProofContext.export

  val add_def: string * term -> ProofContext.context ->

    ((string * typ) * thm) * ProofContext.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: ProofContext.context -> thm list -> thm -> thm

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

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

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

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

  val derived_def: ProofContext.context -> term ->

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

end;

structure LocalDefs: LOCAL_DEFS =

struct

(** primitive definitions **)

(* prepare defs *)

(*c x == t[x] to !!x. c x == t[x]*)

fun cert_def ctxt eq =

  let

    fun err msg = cat_error msg

      ("The error(s) above occurred in definition: " ^ ProofContext.string_of_term ctxt eq);

    val (lhs, rhs) = Logic.dest_equals (Term.strip_all_body eq)

      handle TERM _ => err "Not a meta-equality (==)";

    val (f, xs) = Term.strip_comb (Pattern.beta_eta_contract lhs);

    val (c, _) = Term.dest_Free f handle TERM _ =>

      err "Head of lhs must be a free/fixed variable";

    fun check_arg (Bound _) = true

      | check_arg (Free (x, _)) = not (ProofContext.is_fixed ctxt x)

      | check_arg t = (case try Logic.dest_type t of SOME (TFree _) => true | _ => false);

    fun close_arg (Bound _) t = t

      | close_arg x t = Term.all (Term.fastype_of x) $ lambda x t;

    val extra_frees = Term.fold_aterms (fn v as Free (x, _) =>

      if ProofContext.is_fixed ctxt x orelse member (op aconv) xs v then I

      else insert (op =) x | _ => I) rhs [];

  in

    if not (forall check_arg xs) orelse has_duplicates (op aconv) xs then

      err "Arguments of lhs must be distinct free/bound variables"

    else if not (null extra_frees) then

      err ("Extra free variables on rhs: " ^ commas_quote extra_frees)

    else if Term.exists_subterm (fn t => t = f) rhs then

      err "Element to be defined occurs on rhs"

    else (c, fold_rev close_arg xs eq)

  end;

(*!!x. c x == t[x] to c == %x. t[x]*)

fun abs_def eq =

  let

    val body = Term.strip_all_body eq;

    val vars = map Free (Term.rename_wrt_term body (Term.strip_all_vars eq));

    val (lhs, rhs) = Logic.dest_equals (Term.subst_bounds (vars, body));

    val (f, xs) = Term.strip_comb (Pattern.beta_eta_contract lhs);

    val eq' = Term.list_abs_free (map Term.dest_Free xs, rhs);

  in (Term.dest_Free f, eq') end;

(*c == t*)

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 *)

fun head_of_def cprop =

  #1 (Term.strip_comb (#1 (Logic.dest_equals (Term.strip_all_body (Thm.term_of cprop)))))

  |> Thm.cterm_of (Thm.theory_of_cterm cprop);

(*

  [x]

  [x == t]

     :

    B x

  --------

    B t

*)

fun def_export _ cprops thm =

  thm

  |> Drule.implies_intr_list cprops

  |> Drule.forall_intr_list (map head_of_def cprops)

  |> Drule.forall_elim_vars 0

  |> RANGE (replicate (length cprops) (Tactic.rtac Drule.reflexive_thm)) 1;

(* 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 prop =

  let

    val thy = ProofContext.theory_of ctxt;

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

      |> Thm.cterm_of thy

      |> meta_rewrite (Context.Proof ctxt)

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

      |> Logic.strip_imp_concl

      |> (snd o cert_def ctxt)

      |> abs_def;

    fun prove ctxt' t def =

      let

        val thy' = ProofContext.theory_of ctxt';

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

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

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

      in

        Goal.prove thy' 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;