(*  Nominal Mutual Functions
    Author:  Christian Urban

    heavily based on the code of Alexander Krauss
    (code forked on 14 January 2011)

Main entry points to the nominal function package.
*)

signature NOMINAL_FUNCTION =
sig
  include FUNCTION_DATA

  val add_nominal_function: (binding * typ option * mixfix) list ->
    (Attrib.binding * term) list -> Function_Common.function_config ->
    (Proof.context -> tactic) -> local_theory -> info * local_theory

  val add_nominal_function_cmd: (binding * string option * mixfix) list ->
    (Attrib.binding * string) list -> Function_Common.function_config ->
    (Proof.context -> tactic) -> local_theory -> info * local_theory

  val nominal_function: (binding * typ option * mixfix) list ->
    (Attrib.binding * term) list -> Function_Common.function_config ->
    local_theory -> Proof.state

  val nominal_function_cmd: (binding * string option * mixfix) list ->
    (Attrib.binding * string) list -> Function_Common.function_config ->
    local_theory -> Proof.state

  val setup : theory -> theory
  val get_congs : Proof.context -> thm list

  val get_info : Proof.context -> term -> info
end


structure Nominal_Function : NOMINAL_FUNCTION =
struct

open Function_Lib
open Function_Common

val simp_attribs = map (Attrib.internal o K)
  [Simplifier.simp_add,
   Code.add_default_eqn_attribute,
   Nitpick_Simps.add]

val psimp_attribs = map (Attrib.internal o K)
  [Nitpick_Psimps.add]

fun mk_defname fixes = fixes |> map (fst o fst) |> space_implode "_"

fun add_simps fnames post sort extra_qualify label mod_binding moreatts
  simps lthy =
  let
    val spec = post simps
      |> map (apfst (apsnd (fn ats => moreatts @ ats)))
      |> map (apfst (apfst extra_qualify))

    val (saved_spec_simps, lthy) =
      fold_map Local_Theory.note spec lthy

    val saved_simps = maps snd saved_spec_simps
    val simps_by_f = sort saved_simps

    fun add_for_f fname simps =
      Local_Theory.note
        ((mod_binding (Binding.qualify true fname (Binding.name label)), []), simps)
      #> snd
  in
    (saved_simps, fold2 add_for_f fnames simps_by_f lthy)
  end

(* nominal *)
fun prepare_nominal_function is_external prep default_constraint fixspec eqns config lthy =
  let
    val constrn_fxs = map (fn (b, T, mx) => (b, SOME (the_default default_constraint T), mx))
    val ((fixes0, spec0), ctxt') = prep (constrn_fxs fixspec) eqns lthy
    val fixes = map (apfst (apfst Binding.name_of)) fixes0;
    val spec = map (fn (bnd, prop) => (bnd, [prop])) spec0;
    val (eqs, post, sort_cont, cnames) = get_preproc lthy config ctxt' fixes spec

    val defname = mk_defname fixes
    val FunctionConfig {partials, default, ...} = config
    val _ =
      if is_some default then Output.legacy_feature
        "'function (default)'. Use 'partial_function'."
      else ()

    val ((goal_state, cont), lthy') =
      Nominal_Function_Mutual.prepare_nominal_function_mutual config defname fixes eqs lthy

    fun afterqed [[proof]] lthy =
      let
        val FunctionResult {fs, R, psimps, simple_pinducts,
          termination, domintros, cases, ...} =
          cont (Thm.close_derivation proof)

        val fnames = map (fst o fst) fixes
        fun qualify n = Binding.name n
          |> Binding.qualify true defname
        val conceal_partial = if partials then I else Binding.conceal

        val addsmps = add_simps fnames post sort_cont

        val (((psimps', pinducts'), (_, [termination'])), lthy) =
          lthy
          |> addsmps (conceal_partial o Binding.qualify false "partial")
               "psimps" conceal_partial psimp_attribs psimps
          ||>> Local_Theory.note ((conceal_partial (qualify "pinduct"),
                 [Attrib.internal (K (Rule_Cases.case_names cnames)),
                  Attrib.internal (K (Rule_Cases.consumes 1)),
                  Attrib.internal (K (Induct.induct_pred ""))]), simple_pinducts)
          ||>> Local_Theory.note ((Binding.conceal (qualify "termination"), []), [termination])
          ||> (snd o Local_Theory.note ((qualify "cases",
                 [Attrib.internal (K (Rule_Cases.case_names cnames))]), [cases]))
          ||> (case domintros of NONE => I | SOME thms => 
                   Local_Theory.note ((qualify "domintros", []), thms) #> snd)

        val info = { add_simps=addsmps, case_names=cnames, psimps=psimps',
          pinducts=snd pinducts', simps=NONE, inducts=NONE, termination=termination',
          fs=fs, R=R, defname=defname, is_partial=true }

        val _ =
          if not is_external then ()
          else Specification.print_consts lthy (K false) (map fst fixes)
      in
        (info, 
         lthy |> Local_Theory.declaration false (add_function_data o morph_function_data info))
      end
  in
    ((goal_state, afterqed), lthy')
  end

fun gen_add_nominal_function is_external prep default_constraint fixspec eqns config tac lthy =
  let
    val ((goal_state, afterqed), lthy') =
      prepare_nominal_function is_external prep default_constraint fixspec eqns config lthy
    val pattern_thm =
      case SINGLE (tac lthy') goal_state of
        NONE => error "pattern completeness and compatibility proof failed"
      | SOME st => Goal.finish lthy' st
  in
    lthy'
    |> afterqed [[pattern_thm]]
  end

val add_nominal_function =
  gen_add_nominal_function false Specification.check_spec (Type_Infer.anyT HOLogic.typeS)
val add_nominal_function_cmd = gen_add_nominal_function true Specification.read_spec "_::type"

fun gen_nominal_function is_external prep default_constraint fixspec eqns config lthy =
  let
    val ((goal_state, afterqed), lthy') =
      prepare_nominal_function is_external prep default_constraint fixspec eqns config lthy
  in
    lthy'
    |> Proof.theorem NONE (snd oo afterqed) [[(Logic.unprotect (concl_of goal_state), [])]]
    |> Proof.refine (Method.primitive_text (K goal_state)) |> Seq.hd
  end

val nominal_function =
  gen_nominal_function false Specification.check_spec (Type_Infer.anyT HOLogic.typeS)
val nominal_function_cmd = gen_nominal_function true Specification.read_spec "_::type"

fun add_case_cong n thy =
  let
    val cong = #case_cong (Datatype.the_info thy n)
      |> safe_mk_meta_eq
  in
    Context.theory_map
      (Function_Ctx_Tree.map_function_congs (Thm.add_thm cong)) thy
  end

val setup_case_cong = Datatype.interpretation (K (fold add_case_cong))


(* setup *)

val setup =
  Attrib.setup @{binding fundef_cong}
    (Attrib.add_del Function_Ctx_Tree.cong_add Function_Ctx_Tree.cong_del)
    "declaration of congruence rule for function definitions"
  #> setup_case_cong
  #> Function_Relation.setup
  #> Function_Common.Termination_Simps.setup

val get_congs = Function_Ctx_Tree.get_function_congs

fun get_info ctxt t = Item_Net.retrieve (get_function ctxt) t
  |> the_single |> snd


(* outer syntax *)

(* nominal *)
val _ =
  Outer_Syntax.local_theory_to_proof "nominal_primrec" "define general recursive nominal functions"
  Keyword.thy_goal
  (function_parser default_config
     >> (fn ((config, fixes), statements) => nominal_function_cmd fixes statements config))


end