theory NewParser
imports "../Nominal-General/Nominal2_Base" 
        "../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 ((fv, fvbn), info, 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)
*}

atom_decl name

nominal_datatype lam =
  Var name
| App lam lam
| Lam x::name t::lam  bind_set x in t
| Let p::pt t::lam bind_set "bn p" in t
and pt =
  P1 name
| P2 pt pt
binder
 bn::"pt \<Rightarrow> atom set"
where
  "bn (P1 x) = {atom x}"
| "bn (P2 p1 p2) = bn p1 \<union> bn p2"

thm fv_lam_raw.simps fv_pt_raw.simps fv_bn_raw.simps

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 *)

nominal_datatype lam2 =
  Var2 "name"
| App2 "lam2" "lam2 list"
| Lam2 x::"name" t::"lam2" bind x in t

nominal_datatype ty =
  Var "name"
| Fun "ty" "ty"

nominal_datatype tys =
  All xs::"name fset" ty::"ty_raw" bind xs in ty



end