theory NewParser

        "../Nominal-General/Nominal2_Eqvt" 

        "../Nominal-General/Nominal2_Supp" 

        "Perm" "NewFv"

begin

section{* Interface for nominal_datatype *}

ML {* 

(* nominal datatype parser *)

local

  structure P = OuterParse;

  structure S = Scan

  fun triple1 ((x, y), z) = (x, y, z)

  fun triple2 (x, (y, z)) = (x, y, z)

  fun tuple ((x, y, z), u) = (x, y, z, u)

  fun tswap (((x, y), z), u) = (x, y, u, z)

in

val _ = OuterKeyword.keyword "bind"

val _ = OuterKeyword.keyword "bind_set"

val _ = OuterKeyword.keyword "bind_res"

val anno_typ = S.option (P.name --| P.$$$ "::") -- P.typ

val bind_mode = P.$$$ "bind" || P.$$$ "bind_set" || P.$$$ "bind_res"

val bind_clauses = 

  P.enum "," (bind_mode -- S.repeat1 P.term -- (P.$$$ "in" |-- S.repeat1 P.name) >> triple1)

val cnstr_parser =

  P.binding -- S.repeat anno_typ -- bind_clauses -- P.opt_mixfix >> tswap

(* datatype parser *)

val dt_parser =

  (P.type_args -- P.binding -- P.opt_mixfix >> triple1) -- 

    (P.$$$ "=" |-- P.enum1 "|" cnstr_parser) >> tuple

(* binding function parser *)

val bnfun_parser = 

  S.optional (P.$$$ "binder" |-- P.fixes -- SpecParse.where_alt_specs) ([], [])

(* main parser *)

val main_parser =

  P.and_list1 dt_parser -- bnfun_parser >> triple2

end

*}

ML {*

fun get_cnstrs dts =

  map (fn (_, _, _, constrs) => constrs) dts

fun get_typed_cnstrs dts =

  flat (map (fn (_, bn, _, constrs) => 

   (map (fn (bn', _, _) => (Binding.name_of bn, Binding.name_of bn')) constrs)) dts)

fun get_cnstr_strs dts =

  map (fn (bn, _, _) => Binding.name_of bn) (flat (get_cnstrs dts))

fun get_bn_fun_strs bn_funs =

  map (fn (bn_fun, _, _) => Binding.name_of bn_fun) bn_funs

*}

ML {* 

fun add_primrec_wrapper funs eqs lthy = 

  if null funs then (([], []), lthy)

  else 

   let 

     val eqs' = map (fn (_, eq) => (Attrib.empty_binding, eq)) eqs

     val funs' = map (fn (bn, ty, mx) => (bn, SOME ty, mx)) funs

   in 

     Primrec.add_primrec funs' eqs' lthy

   end

*}

ML {*

fun add_datatype_wrapper dt_names dts =

let

  val conf = Datatype.default_config

in

  Local_Theory.theory_result (Datatype.add_datatype conf dt_names dts)

end

*}

text {* Infrastructure for adding "_raw" to types and terms *}

ML {*

fun add_raw s = s ^ "_raw"

fun add_raws ss = map add_raw ss

fun raw_bind bn = Binding.suffix_name "_raw" bn

fun replace_str ss s = 

  case (AList.lookup (op=) ss s) of 

     SOME s' => s'

   | NONE => s

fun replace_typ ty_ss (Type (a, Ts)) = Type (replace_str ty_ss a, map (replace_typ ty_ss) Ts)

  | replace_typ ty_ss T = T  

fun raw_dts ty_ss dts =

let

  fun raw_dts_aux1 (bind, tys, mx) =

    (raw_bind bind, map (replace_typ ty_ss) tys, mx)

  fun raw_dts_aux2 (ty_args, bind, mx, constrs) =

    (ty_args, raw_bind bind, mx, map raw_dts_aux1 constrs)

in

  map raw_dts_aux2 dts

end

fun replace_aterm trm_ss (Const (a, T)) = Const (replace_str trm_ss a, T)

  | replace_aterm trm_ss (Free (a, T)) = Free (replace_str trm_ss a, T)

  | replace_aterm trm_ss trm = trm

fun replace_term trm_ss ty_ss trm =

  trm |> Term.map_aterms (replace_aterm trm_ss) |> map_types (replace_typ ty_ss) 

*}

ML {*

fun rawify_dts dt_names dts dts_env =

let

  val raw_dts = raw_dts dts_env dts

  val raw_dt_names = add_raws dt_names

in

  (raw_dt_names, raw_dts)

end 

*}

ML {*

fun rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs =

let

  val bn_funs' = map (fn (bn, ty, mx) => 

    (raw_bind bn, replace_typ dts_env ty, mx)) bn_funs

  val bn_eqs' = map (fn (attr, trm) => 

    (attr, replace_term (cnstrs_env @ bn_fun_env) dts_env trm)) bn_eqs

in

  (bn_funs', bn_eqs') 

end 

*}

ML {* 

fun rawify_bclauses dts_env cnstrs_env bn_fun_env bclauses =

let

  fun rawify_bnds bnds = 

    map (apfst (Option.map (replace_term (cnstrs_env @ bn_fun_env) dts_env))) bnds

  fun rawify_bclause (BEmy n) = BEmy n

    | rawify_bclause (BLst (bnds, bdys)) = BLst (rawify_bnds bnds, bdys)

    | rawify_bclause (BSet (bnds, bdys)) = BSet (rawify_bnds bnds, bdys)

    | rawify_bclause (BRes (bnds, bdys)) = BRes (rawify_bnds bnds, bdys)

in

  map (map (map rawify_bclause)) bclauses

end

*}

text {* What does the prep_bn code do? Cezary's Function? *}

ML {*

fun strip_bn_fun t =

  case t of

    Const (@{const_name sup}, _) $ l $ r => strip_bn_fun l @ strip_bn_fun r

  | Const (@{const_name append}, _) $ l $ r => strip_bn_fun l @ strip_bn_fun r

  | Const (@{const_name insert}, _) $ (Const (@{const_name atom}, _) $ Bound i) $ y =>

      (i, NONE) :: strip_bn_fun y

  | Const (@{const_name Cons}, _) $ (Const (@{const_name atom}, _) $ Bound i) $ y =>

      (i, NONE) :: strip_bn_fun y

  | Const (@{const_name bot}, _) => []

  | Const (@{const_name Nil}, _) => []

  | (f as Free _) $ Bound i => [(i, SOME f)]

  | _ => error ("Unsupported binding function: " ^ (PolyML.makestring t))

*}

ML {*

fun find [] _ = error ("cannot find element")

  | find ((x, z)::xs) y = if (Long_Name.base_name x) = y then z else find xs y

*}

ML {*

fun prep_bn dt_names dts eqs = 

let

  fun aux eq = 

  let

    val (lhs, rhs) = eq

      |> strip_qnt_body "all" 

      |> HOLogic.dest_Trueprop

      |> HOLogic.dest_eq

    val (bn_fun, [cnstr]) = strip_comb lhs

    val (_, ty) = dest_Free bn_fun

    val (ty_name, _) = dest_Type (domain_type ty)

    val dt_index = find_index (fn x => x = ty_name) dt_names

    val (cnstr_head, cnstr_args) = strip_comb cnstr

    val rhs_elements = strip_bn_fun rhs

    val included = map (apfst (fn i => length (cnstr_args) - i - 1)) rhs_elements

  in

    (dt_index, (bn_fun, (cnstr_head, included)))

  end 

  fun order dts i ts = 

  let

    val dt = nth dts i

    val cts = map (fn (x, _, _) => Binding.name_of x) ((fn (_, _, _, x) => x) dt)

    val ts' = map (fn (x, y) => (fst (dest_Const x), y)) ts

  in

    map (find ts') cts

  end

  val unordered = AList.group (op=) (map aux eqs)

  val unordered' = map (fn (x, y) =>  (x, AList.group (op=) y)) unordered

  val ordered = map (fn (x, y) => (x, map (fn (v, z) => (v, order dts x z)) y)) unordered' 

in

  ordered

end

*}

ML {*

fun raw_nominal_decls dts bn_funs bn_eqs binds lthy =

let

  val thy = ProofContext.theory_of lthy

  val thy_name = Context.theory_name thy

  val dt_names = map (fn (_, s, _, _) => Binding.name_of s) dts

  val dt_full_names = map (Long_Name.qualify thy_name) dt_names 

  val dt_full_names' = add_raws dt_full_names

  val dts_env = dt_full_names ~~ dt_full_names'

  val cnstrs = get_cnstr_strs dts

  val cnstrs_ty = get_typed_cnstrs dts

  val cnstrs_full_names = map (Long_Name.qualify thy_name) cnstrs

  val cnstrs_full_names' = map (fn (x, y) => Long_Name.qualify thy_name 

    (Long_Name.qualify (add_raw x) (add_raw y))) cnstrs_ty

  val cnstrs_env = cnstrs_full_names ~~ cnstrs_full_names'

  val bn_fun_strs = get_bn_fun_strs bn_funs

  val bn_fun_strs' = add_raws bn_fun_strs

  val bn_fun_env = bn_fun_strs ~~ bn_fun_strs'

  val bn_fun_full_env = map (pairself (Long_Name.qualify thy_name)) 

    (bn_fun_strs ~~ bn_fun_strs')

  val (raw_dt_names, raw_dts) = rawify_dts dt_names dts dts_env

  val (raw_bn_funs, raw_bn_eqs) = rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs 

  val raw_bclauses = rawify_bclauses dts_env cnstrs_env bn_fun_full_env binds 

  val raw_bns = prep_bn dt_full_names' raw_dts (map snd raw_bn_eqs)

in

  lthy 

  |> add_datatype_wrapper raw_dt_names raw_dts 

  ||>> add_primrec_wrapper raw_bn_funs raw_bn_eqs

  ||>> pair raw_bclauses

  ||>> pair raw_bns

end

*}

ML {*

fun nominal_datatype2 dts bn_funs bn_eqs bclauses lthy =

let

  val ((((raw_dt_names, (raw_bn_funs_loc, raw_bn_eqs_loc)), raw_bclauses), raw_bns), lthy1) =

    raw_nominal_decls dts bn_funs bn_eqs bclauses lthy

  val dtinfo = Datatype.the_info (ProofContext.theory_of lthy1) (hd raw_dt_names);

  val {descr, sorts, ...} = dtinfo;

  val ((raw_perm_def, raw_perm_simps, perms), lthy2) =

    Local_Theory.theory_result (define_raw_perms dtinfo (length dts)) lthy1;

  val morphism_2_0 = ProofContext.export_morphism lthy2 lthy

  fun export_fun f (t, l) = (f t, map (map (apsnd (Option.map f))) l);

  val raw_bns_exp = map (apsnd (map (export_fun (Morphism.term morphism_2_0)))) raw_bns;

  val bn_funs_decls = flat (map (fn (ith, l) => map (fn (bn, data) => (bn, ith, data)) l) raw_bns_exp);

  val thy = Local_Theory.exit_global lthy2;

  val lthy3 = Theory_Target.init NONE thy;

  val (_, lthy4) = define_raw_fv dtinfo bn_funs_decls raw_bclauses lthy3;

in

  ((raw_dt_names, raw_bn_funs_loc, raw_bn_eqs_loc, raw_bclauses, raw_bns), lthy4)

end

*}

section {* Preparing and parsing of the specification *}

ML {* 

(* parsing the datatypes and declaring *)

(* constructors in the local theory    *)

fun prepare_dts dt_strs lthy = 

let

  val thy = ProofContext.theory_of lthy

  fun mk_type full_tname tvrs =

    Type (full_tname, map (fn a => TVar ((a, 0), [])) tvrs)

  fun prep_cnstr full_tname tvs (cname, anno_tys, mx, _) =

  let

    val tys = map (Syntax.read_typ lthy o snd) anno_tys

    val ty = mk_type full_tname tvs

  in

    ((cname, tys ---> ty, mx), (cname, tys, mx))

  end

  fun prep_dt (tvs, tname, mx, cnstrs) = 

  let

    val full_tname = Sign.full_name thy tname

    val (cnstrs', cnstrs'') = 

      split_list (map (prep_cnstr full_tname tvs) cnstrs)

  in

    (cnstrs', (tvs, tname, mx, cnstrs''))

  end 

  val (cnstrs, dts) = split_list (map prep_dt dt_strs)

in

  lthy

  |> Local_Theory.theory (Sign.add_consts_i (flat cnstrs))

  |> pair dts

end

*}

ML {*

(* parsing the binding function specification and *)

(* declaring the functions in the local theory    *)

fun prepare_bn_funs bn_fun_strs bn_eq_strs lthy =

let

  val ((bn_funs, bn_eqs), _) = 

    Specification.read_spec bn_fun_strs bn_eq_strs lthy

  fun prep_bn_fun ((bn, T), mx) = (bn, T, mx) 

  val bn_funs' = map prep_bn_fun bn_funs

in

  lthy

  |> Local_Theory.theory (Sign.add_consts_i bn_funs')

  |> pair (bn_funs', bn_eqs) 

end 

*}

text {* associates every SOME with the index in the list; drops NONEs *}

ML {*

fun indexify xs =

let

  fun mapp _ [] = []

    | mapp i (NONE :: xs) = mapp (i + 1) xs

    | mapp i (SOME x :: xs) = (x, i) :: mapp (i + 1) xs

in 

  mapp 0 xs 

end

fun index_lookup xs x =

  case AList.lookup (op=) xs x of

    SOME x => x

  | NONE => error ("Cannot find " ^ x ^ " as argument annotation.");

*}

ML {*

fun prepare_bclauses dt_strs lthy = 

let

  val annos_bclauses =

    get_cnstrs dt_strs

    |> map (map (fn (_, antys, _, bns) => (map fst antys, bns)))

  fun prep_binder env bn_str =

    case (Syntax.read_term lthy bn_str) of

      Free (x, _) => (NONE, index_lookup env x)

    | Const (a, T) $ Free (x, _) => (SOME (Const (a, T)), index_lookup env x)

    | _ => error ("The term " ^ bn_str ^ " is not allowed as binding function.")

  fun prep_body env bn_str = index_lookup env bn_str

  fun prep_mode "bind"     = BLst 

    | prep_mode "bind_set" = BSet 

    | prep_mode "bind_res" = BRes 

  fun prep_bclause env (mode, binders, bodies) = 

  let

    val binders' = map (prep_binder env) binders

    val bodies' = map (prep_body env) bodies

  in  

    prep_mode mode (binders', bodies')

  end

  fun prep_bclauses (annos, bclause_strs) = 

  let

    val env = indexify annos (* for every label, associate the index *)

  in

    map (prep_bclause env) bclause_strs

  end

in

  map (map prep_bclauses) annos_bclauses

end

*}

text {* 

  adds an empty binding clause for every argument

  that is not already part of a binding clause

*}

ML {*

fun included i bcs = 

let

  fun incl (BEmy j) = i = j

    | incl (BLst (bns, bds)) = (i mem (map snd bns)) orelse (i mem bds) 

    | incl (BSet (bns, bds)) = (i mem (map snd bns)) orelse (i mem bds) 

    | incl (BRes (bns, bds)) = (i mem (map snd bns)) orelse (i mem bds) 

in

  exists incl bcs 

end

*}

ML {* 

fun complete dt_strs bclauses = 

let

  val args = 

    get_cnstrs dt_strs

    |> map (map (fn (_, antys, _, _) => length antys))

  fun complt n bcs = 

  let

    fun add bcs i = (if included i bcs then [] else [BEmy i]) 

  in

    bcs @ (flat (map_range (add bcs) n))

  end

in

  map2 (map2 complt) args bclauses

end

*}

ML {*

fun nominal_datatype2_cmd (dt_strs, bn_fun_strs, bn_eq_strs) lthy = 

let

  fun prep_typ (tvs, tname, mx, _) = (tname, length tvs, mx)

  val lthy0 = 

    Local_Theory.theory (Sign.add_types (map prep_typ dt_strs)) lthy

  val (dts, lthy1) = prepare_dts dt_strs lthy0

  val ((bn_funs, bn_eqs), lthy2) = prepare_bn_funs bn_fun_strs bn_eq_strs lthy1

  val bclauses = prepare_bclauses dt_strs lthy2

  val bclauses' = complete dt_strs bclauses 

in

  nominal_datatype2 dts bn_funs bn_eqs bclauses' lthy |> snd

end

(* Command Keyword *)

val _ = OuterSyntax.local_theory "nominal_datatype" "test" OuterKeyword.thy_decl

  (main_parser >> nominal_datatype2_cmd)

*}

nominal_datatype exp =

  EVar name

| EUnit

| EPair q1::exp q2::exp      bind_set q1 q2 in q1 q2

| ELetRec l::lrbs e::exp     bind "b_lrbs l" in e l

and fnclause =

  K x::name p::pat f::exp    bind_res "b_pat p" in f 

and fnclauses =

  S fnclause

| ORs fnclause fnclauses

and lrb =

  Clause fnclauses

and lrbs =

  Single lrb

| More lrb lrbs

and pat =

  PVar name

| PUnit

| PPair pat pat

binder

  b_lrbs      :: "lrbs \<Rightarrow> atom set" and

  b_pat       :: "pat \<Rightarrow> atom set" and

  b_fnclauses :: "fnclauses \<Rightarrow> atom set" and

  b_fnclause  :: "fnclause \<Rightarrow> atom set" and

  b_lrb       :: "lrb \<Rightarrow> atom set"

where

  "b_lrbs (Single l) = b_lrb l"

| "b_lrbs (More l ls) = b_lrb l \<union> b_lrbs ls"

| "b_pat (PVar x) = {atom x}"

| "b_pat (PUnit) = {}"

| "b_pat (PPair p1 p2) = b_pat p1 \<union> b_pat p2"

| "b_fnclauses (S fc) = (b_fnclause fc)"

| "b_fnclauses (ORs fc fcs) = (b_fnclause fc) \<union> (b_fnclauses fcs)"

| "b_lrb (Clause fcs) = (b_fnclauses fcs)"

| "b_fnclause (K x pat exp) = {atom x}"

typ exp_raw 

typ pat_raw 

thm exp_raw_fnclause_raw_fnclauses_raw_lrb_raw_lrbs_raw_pat_raw.induct[no_vars]

thm b_fnclause_raw_b_fnclauses_raw_b_lrb_raw_b_lrbs_raw_b_pat_raw.simps[no_vars]

thm permute_exp_raw_permute_fnclause_raw_permute_fnclauses_raw_permute_lrb_raw_permute_lrbs_raw_permute_pat_raw.simps[no_vars]

thm fv_exp_raw.simps fv_fnclause_raw.simps fv_fnclauses_raw.simps fv_lrb_raw.simps fv_lrbs_raw.simps fv_pat_raw.simps fv_b_lrbs_raw.simps fv_b_pat_raw.simps fv_b_fnclauses_raw.simps fv_b_lrb_raw.simps fv_b_fnclause_raw.simps

(* some further tests *)