(*  Title:      HOL/HOLCF/Tools/Domain/domain.ML

    Author:     David von Oheimb

    Author:     Brian Huffman

Theory extender for domain command, including theory syntax.

*)

signature DOMAIN =

sig

  val add_domain_cmd:

      ((string * string option) list * binding * mixfix *

       (binding * (bool * binding option * string) list * mixfix) list) list

      -> theory -> theory

  val add_domain:

      ((string * sort) list * binding * mixfix *

       (binding * (bool * binding option * typ) list * mixfix) list) list

      -> theory -> theory

  val add_new_domain_cmd:

      ((string * string option) list * binding * mixfix *

       (binding * (bool * binding option * string) list * mixfix) list) list

      -> theory -> theory

  val add_new_domain:

      ((string * sort) list * binding * mixfix *

       (binding * (bool * binding option * typ) list * mixfix) list) list

      -> theory -> theory

end

structure Domain : DOMAIN =

struct

open HOLCF_Library

fun first  (x,_,_) = x

fun second (_,x,_) = x

(* ----- calls for building new thy and thms -------------------------------- *)

type info =

     Domain_Take_Proofs.iso_info list * Domain_Take_Proofs.take_induct_info

fun add_arity ((b, sorts, mx), sort) thy : theory =

  thy

  |> Sign.add_types_global [(b, length sorts, mx)]

  |> AxClass.axiomatize_arity (Sign.full_name thy b, sorts, sort)

fun gen_add_domain

    (prep_sort : theory -> 'a -> sort)

    (prep_typ : theory -> (string * sort) list -> 'b -> typ)

    (add_isos : (binding * mixfix * (typ * typ)) list -> theory -> info * theory)

    (arg_sort : bool -> sort)

    (raw_specs : ((string * 'a) list * binding * mixfix *

               (binding * (bool * binding option * 'b) list * mixfix) list) list)

    (thy : theory) =

  let

    val dtnvs : (binding * typ list * mixfix) list =

      let

        fun prep_tvar (a, s) = TFree (a, prep_sort thy s)

      in

        map (fn (vs, dbind, mx, _) =>

                (dbind, map prep_tvar vs, mx)) raw_specs

      end

    fun thy_arity (dbind, tvars, mx) =

      ((dbind, map (snd o dest_TFree) tvars, mx), arg_sort false)

    (* this theory is used just for parsing and error checking *)

    val tmp_thy = thy

      |> Theory.copy

      |> fold (add_arity o thy_arity) dtnvs

    val dbinds : binding list =

        map (fn (_,dbind,_,_) => dbind) raw_specs

    val raw_rhss :

        (binding * (bool * binding option * 'b) list * mixfix) list list =

        map (fn (_,_,_,cons) => cons) raw_specs

    val dtnvs' : (string * typ list) list =

        map (fn (dbind, vs, _) => (Sign.full_name thy dbind, vs)) dtnvs

    val all_cons = map (Binding.name_of o first) (flat raw_rhss)

    val _ =

      case duplicates (op =) all_cons of 

        [] => false | dups => error ("Duplicate constructors: " 

                                      ^ commas_quote dups)

    val all_sels =

      (map Binding.name_of o map_filter second o maps second) (flat raw_rhss)

    val _ =

      case duplicates (op =) all_sels of

        [] => false | dups => error("Duplicate selectors: "^commas_quote dups)

    fun test_dupl_tvars s =

      case duplicates (op =) (map(fst o dest_TFree)s) of

        [] => false | dups => error("Duplicate type arguments: " 

                                    ^commas_quote dups)

    val _ = exists test_dupl_tvars (map snd dtnvs')

    val sorts : (string * sort) list =

      let val all_sorts = map (map dest_TFree o snd) dtnvs'

      in

        case distinct (eq_set (op =)) all_sorts of

          [sorts] => sorts

        | _ => error "Mutually recursive domains must have same type parameters"

      end

    (* a lazy argument may have an unpointed type *)

    (* unless the argument has a selector function *)

    fun check_pcpo (lazy, sel, T) =

      let val sort = arg_sort (lazy andalso is_none sel) in

        if Sign.of_sort tmp_thy (T, sort) then ()

        else error ("Constructor argument type is not of sort " ^

                    Syntax.string_of_sort_global tmp_thy sort ^ ": " ^

                    Syntax.string_of_typ_global tmp_thy T)

      end

    (* test for free type variables, illegal sort constraints on rhs,

       non-pcpo-types and invalid use of recursive type

       replace sorts in type variables on rhs *)

    val rec_tab = Domain_Take_Proofs.get_rec_tab thy

    fun check_rec _ (T as TFree (v,_))  =

        if AList.defined (op =) sorts v then T

        else error ("Free type variable " ^ quote v ^ " on rhs.")

      | check_rec no_rec (T as Type (s, Ts)) =

        (case AList.lookup (op =) dtnvs' s of

          NONE =>

            let val no_rec' =

                  if no_rec = NONE then

                    if Symtab.defined rec_tab s then NONE else SOME s

                  else no_rec

            in Type (s, map (check_rec no_rec') Ts) end

        | SOME typevars =>

          if typevars <> Ts

          then error ("Recursion of type " ^ 

                      quote (Syntax.string_of_typ_global tmp_thy T) ^ 

                      " with different arguments")

          else (case no_rec of

                  NONE => T

                | SOME c =>

                  error ("Illegal indirect recursion of type " ^ 

                         quote (Syntax.string_of_typ_global tmp_thy T) ^

                         " under type constructor " ^ quote c)))

      | check_rec _ (TVar _) = error "extender:check_rec"

    fun prep_arg (lazy, sel, raw_T) =

      let

        val T = prep_typ tmp_thy sorts raw_T

        val _ = check_rec NONE T

        val _ = check_pcpo (lazy, sel, T)

      in (lazy, sel, T) end

    fun prep_con (b, args, mx) = (b, map prep_arg args, mx)

    fun prep_rhs cons = map prep_con cons

    val rhss : (binding * (bool * binding option * typ) list * mixfix) list list =

        map prep_rhs raw_rhss

    fun mk_arg_typ (lazy, _, T) = if lazy then mk_upT T else T

    fun mk_con_typ (_, args, _) =

        if null args then oneT else foldr1 mk_sprodT (map mk_arg_typ args)

    fun mk_rhs_typ cons = foldr1 mk_ssumT (map mk_con_typ cons)

    val absTs : typ list = map Type dtnvs'

    val repTs : typ list = map mk_rhs_typ rhss

    val iso_spec : (binding * mixfix * (typ * typ)) list =

        map (fn ((dbind, _, mx), eq) => (dbind, mx, eq))

          (dtnvs ~~ (absTs ~~ repTs))

    val ((iso_infos, take_info), thy) = add_isos iso_spec thy

    val (constr_infos, thy) =

        thy

          |> fold_map (fn ((dbind, cons), info) =>

                Domain_Constructors.add_domain_constructors dbind cons info)

             (dbinds ~~ rhss ~~ iso_infos)

    val (_, thy) =

        Domain_Induction.comp_theorems

          dbinds take_info constr_infos thy

  in

    thy

  end

fun define_isos (spec : (binding * mixfix * (typ * typ)) list) =

  let

    fun prep (dbind, mx, (lhsT, rhsT)) =

      let val (_, vs) = dest_Type lhsT

      in (map (fst o dest_TFree) vs, dbind, mx, rhsT, NONE) end

  in

    Domain_Isomorphism.domain_isomorphism (map prep spec)

  end

fun pcpo_arg lazy = if lazy then @{sort cpo} else @{sort pcpo}

fun rep_arg lazy = if lazy then @{sort predomain} else @{sort "domain"}

fun read_sort thy (SOME s) = Syntax.read_sort_global thy s

  | read_sort thy NONE = Sign.defaultS thy

(* Adapted from src/HOL/Tools/Datatype/datatype_data.ML *)

fun read_typ thy sorts str =

  let

    val ctxt = Proof_Context.init_global thy

      |> fold (Variable.declare_typ o TFree) sorts

  in Syntax.read_typ ctxt str end

fun cert_typ sign sorts raw_T =

  let

    val T = Type.no_tvars (Sign.certify_typ sign raw_T)

      handle TYPE (msg, _, _) => error msg

    val sorts' = Term.add_tfreesT T sorts

    val _ =

      case duplicates (op =) (map fst sorts') of

        [] => ()

      | dups => error ("Inconsistent sort constraints for " ^ commas dups)

  in T end

val add_domain =

    gen_add_domain (K I) cert_typ Domain_Axioms.add_axioms pcpo_arg

val add_new_domain =

    gen_add_domain (K I) cert_typ define_isos rep_arg

val add_domain_cmd =

    gen_add_domain read_sort read_typ Domain_Axioms.add_axioms pcpo_arg

val add_new_domain_cmd =

    gen_add_domain read_sort read_typ define_isos rep_arg

(** outer syntax **)

val dest_decl : (bool * binding option * string) parser =

  @{keyword "("} |-- Scan.optional (@{keyword "lazy"} >> K true) false --

    (Parse.binding >> SOME) -- (@{keyword "::"} |-- Parse.typ)  --| @{keyword ")"} >> Parse.triple1

    || @{keyword "("} |-- @{keyword "lazy"} |-- Parse.typ --| @{keyword ")"}

    >> (fn t => (true, NONE, t))

    || Parse.typ >> (fn t => (false, NONE, t))

val cons_decl =

  Parse.binding -- Scan.repeat dest_decl -- Parse.opt_mixfix

val domain_decl =

  (Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix) --

    (@{keyword "="} |-- Parse.enum1 "|" cons_decl)

val domains_decl =

  Scan.optional (@{keyword "("} |-- (@{keyword "unsafe"} >> K true) --| @{keyword ")"}) false --

    Parse.and_list1 domain_decl

fun mk_domain

    (unsafe : bool,

     doms : ((((string * string option) list * binding) * mixfix) *

             ((binding * (bool * binding option * string) list) * mixfix) list) list ) =

  let

    val specs : ((string * string option) list * binding * mixfix *

                 (binding * (bool * binding option * string) list * mixfix) list) list =

        map (fn (((vs, t), mx), cons) =>

                (vs, t, mx, map (fn ((c, ds), mx) => (c, ds, mx)) cons)) doms

  in

    if unsafe

    then add_domain_cmd specs

    else add_new_domain_cmd specs

  end

val _ =

  Outer_Syntax.command "domain" "define recursive domains (HOLCF)"

    Keyword.thy_decl (domains_decl >> (Toplevel.theory o mk_domain))

end