(* Title: extends Isabelle/src/Pure/term.ML

   Author: Walther Neuper 1999, Mathias Lehnfeld

   (c) due to copyright terms

*)

signature TERMC =

  sig

  (*val bool \<longrightarrow> HOLogic.boolT*)

    val const_in: string -> term -> bool

    val contains_Var: term -> bool

    val dest_binop_typ: typ -> typ * typ * typ

    val (*dest_equals'*) dest_equals: term -> term * term

    val free2str: term -> string

    val ids2str: term -> string list

    val ins_concl: term -> term -> term

    val inst_abs: term -> term

    val inst_bdv: (term * term) list -> term -> term

    val term_of_num: typ -> int -> term

    val (*num_of_term \<longrightarrow>*) num_of_term: term -> int

    val (*int_of_str \<longrightarrow>*) int_of_str_opt: string -> int option

    val (*int_of_str' int2str \<longrightarrow>*)int_of_str: string -> int

    val isastr_of_int: int -> string

    val isalist2list: term -> term list

    val list2isalist: typ -> term list -> term

    val isapair2pair: term -> term * term

    val is_atom: term -> bool

    val is_bdv: string -> bool

    val is_bdv_subst: term -> bool

    val is_equality: term -> bool

    val is_expliceq: term -> bool

    val is_f_x: term -> bool

    val is_list: term -> bool

    val is_num: term -> bool

    val (*is_no  is_numeral \<longrightarrow>*)is_num': string -> bool

    val mk_add: term -> term -> term

    val mk_free: typ -> string -> term

    val mk_equality: term * term -> term

    val mk_factroot: string -> typ -> int -> int -> term

    val mk_Free: string * typ -> term

    val mk_thmid: string -> string -> string -> string

    val mk_num_op_num(*<-- num_op_num*): typ -> typ -> string * typ -> int -> int -> term

    val mk_num_op_var(*<-- num_op_var*): term -> string -> typ -> typ -> int -> term

    val mk_var_op_num(*<-- var_op_num*): term -> string -> typ -> typ -> int -> term

  (*val list_implies: term list * term -> term  --> Logic.list_implies*)

    val matches: theory -> term -> term -> bool

    val parse: theory -> string -> cterm option

    val parseN: theory -> string -> cterm option

    val parseNEW: Proof.context -> string -> term option

    val parseold: theory -> string -> cterm option

    val parse_patt: theory -> string -> term

    val perm: term -> term -> bool

    val calc_equ: string -> int * int -> bool

    val power: int -> int -> int

    val sign_mult: int -> int -> int

    val squfact: int -> int

    val gcd: int -> int -> int

    val str_of_free_opt: term -> string option

    val str_of_int: int -> string

    val str2term: string -> term

    val strip_imp_prems': term -> term option

    val subst_atomic_all: (term * term) list -> term -> bool * term

    val term_detail2str: term -> string

    val num_str: thm -> thm

    val pairt: term -> term -> term

    val pairT: typ -> typ -> typ

    val strip_trueprop: term -> term

    val uminus_to_string: term -> term

    val var2free: term -> term

    val vars: term -> term list

(* ---- for tests only: shifted from below to remove the Warning "unused" at fun.def. --------- *)

    val atomtyp(*<-- atom_typ TODO*): typ -> unit

    val scala_of_term: term -> string

    val atomty: term -> unit

    val atomw: term -> unit

    val atomwy: term -> unit

    val atomty_thy: thyID -> term -> unit

    val free2var: term -> term

    val sign: int -> int

    val sqrt: int -> int

(*/-------------------------------------------------------- ! aktivate for Test_Isac BEGIN ---\* )

(*============================================= shift up during Test_Isac ======================

    val --->: typ list * typ -> typ

    val -->: typ * typ -> typ

    val PairT: typ -> typ -> typ

    val T_a2real: typ -> typ

    val add_term_vars: term * term list -> term list

    val atless: term * term -> bool

    val atomt: term -> unit

    val atomthm: thm -> unit

    val contains_term: term -> term -> bool

    val divisors: int -> int list

    val doubles: ''a list -> ''a list

    val dvd: int * int -> bool

    val eq_set_term: term list * term list -> bool

    val insert_aterm: term * term list -> term list

    val is_Free: term -> bool

    val is_fun_id: term -> bool

    val list_const: typ -> term

    val mem_term: term * term list -> bool

    val mk_listT: typ -> typ

    val mk_subs: ((string * int) * (typ * term)) list -> (term * term) list

    val numbers_to_string: term -> term

    val raw_pp_typ: typ -> Pretty.T

    val scala_of_typ: typ -> string

    val str2termN: string -> term

    val str2term_: theory -> string -> term

    val str_of_int: int -> string

    val strs2terms: string list -> term list

    val subset_term: term list * term list -> bool

    val subst_bound: term * term -> term

    val term_detail2str_thy: thyID -> term -> string

    val term_of_num: typ -> int -> term

    val term_vars: term -> term list

    val typ_a2real: term -> term

    val var_perm: term * term -> bool

    val vperm: term * term -> bool

    val xless: (string * int) * indexname -> bool

*============================================= shift up during Test_Isac ======================*)

( *\--- ! aktivate for Test_Isac END ----------------------------------------------------------/*)

  end

(**)

structure TermC(**): TERMC(**) =

struct

(**)

fun isastr_of_int i = if i >= 0 then string_of_int i else "-" ^ string_of_int (abs i)

fun matches thy tm pa = 

    (Pattern.match thy (pa, tm) (Vartab.empty, Vartab.empty); true)

    handle Pattern.MATCH => false

(** transform  typ / term to a String to be parsed by Scala after transport via libisabelle **)

fun scala_of_typ (Type (s, typs)) =

    enclose "Type(" ")" (quote s ^ ", " ^

      (typs |> map scala_of_typ |> commas |> enclose "List(" ")"))

  | scala_of_typ (TFree (s, sort)) =

    enclose "TFree(" ")" (quote s ^ ", " ^ (sort |> map quote |> commas |> enclose "List(" ")"))

  | scala_of_typ (TVar ((s, i), sort)) =

    enclose "TVar(" ")" (

      enclose "(" ")," (quote s ^ "," ^ quote (string_of_int i)) ^ 

      (sort |> map quote |> commas |> enclose "List(" ")"))

fun scala_of_term (Const (s, T)) =

    enclose "Const(" ")" (quote s ^ ", " ^ scala_of_typ T)

  | scala_of_term (Free (s, T)) =

    enclose "Free(" ")" (quote s ^ ", " ^ scala_of_typ T)

  | scala_of_term (Var ((s, i), T)) =

    enclose "TVar(" ")" (

      enclose "(" ")," (quote s ^ "," ^ quote (string_of_int i)) ^ 

      scala_of_typ T)

  | scala_of_term (Bound i) = enclose "Bound(" ")" (string_of_int i)

  | scala_of_term (Abs (s, T, t)) =

    enclose "Abs(" ")" (

      quote s ^ ", " ^

      scala_of_typ T ^ ", " ^

      scala_of_term t)

  | scala_of_term (t1 $ t2) =

    enclose "App(" ")" (scala_of_term t1 ^ ", " ^ scala_of_term t2)

(* see structure's bare bones.

   for Isabelle standard output compare 2017 "structure ML_PP" *)

fun atomtyp t =

  let

    fun ato n (Type (s, [])) = "\n*** " ^ indent n ^ "Type (" ^ s ^",[])"

      | ato n (Type (s, Ts)) = "\n*** " ^ indent n ^ "Type (" ^ s ^ ",[" ^ atol (n + 1) Ts

      | ato n (TFree (s, sort)) = "\n*** " ^ indent n ^ "TFree (" ^ s ^ "," ^ strs2str' sort

      | ato n (TVar ((s, i), sort)) =

        "\n*** " ^ indent n ^ "TVar ((" ^ s ^ "," ^ string_of_int i ^ strs2str' sort

    and atol n [] = "\n*** " ^ indent n ^ "]"

      | atol n (T :: Ts) = (ato n T ^ atol n Ts)

in tracing (ato 0 t ^ "\n") end;

local 

  fun ato (Const (a, _)) n = "\n*** " ^ indent n ^ "Const (" ^ a ^ ", _)"

	  | ato (Free (a, _)) n = "\n*** " ^ indent n ^ "Free (" ^ a ^ ", _)"

	  | ato (Var ((a, i), _)) n =

	    "\n*** " ^ indent n ^ "Var (" ^ a ^ ", " ^ string_of_int i ^ "), _)"

	  | ato (Bound i) n = "\n*** " ^ indent n ^ "Bound " ^ string_of_int i

	  | ato (Abs (a, _, body)) n = "\n*** " ^ indent n ^ "Abs(" ^ a ^ ", _" ^ ato body (n+1)

	  | ato (f $ t) n = (ato f n ^ ato t (n + 1))

in

  fun atomw t = writeln ("\n*** -------------" ^ ato t 0 ^ "\n***");

  fun atomt t = tracing ("\n*** -------------" ^ ato t 0 ^ "\n***");

end;

fun term_detail2str t =

  let 

    fun ato (Const (a, T)) n = "\n*** " ^ indent n ^ "Const (" ^ a ^ ", " ^ string_of_typ T ^ ")"

      | ato (Free (a, T)) n = "\n*** " ^ indent n ^ "Free (" ^ a ^ ", " ^ string_of_typ T ^ ")"

      | ato (Var ((a, i), T)) n =

        "\n*** " ^ indent n ^ "Var ((" ^ a ^ ", " ^ string_of_int i ^ "), " ^ string_of_typ T ^ ")"

      | ato (Bound i) n = "\n*** " ^ indent n ^ "Bound " ^ string_of_int i

      | ato (Abs(a, T, body))  n = 

        "\n*** " ^ indent n ^ "Abs (" ^ a ^ ", " ^ string_of_typ T ^ ",.." ^ ato body (n + 1)

      | ato (f $ t) n = ato f n ^ ato t (n + 1)

  in "\n*** " ^ ato t 0 ^ "\n***" end;

fun term_detail2str_thy thy t =

  let

    fun ato (Const (a, T)) n =

        "\n*** " ^ indent n ^ "Const (" ^ a ^ ", " ^ string_of_typ_thy thy T ^ ")"

  	  | ato (Free (a, T)) n =

  	     "\n*** " ^ indent n ^ "Free (" ^ a ^ ", " ^ string_of_typ_thy thy T ^ ")"

  	  | ato (Var ((a, i), T)) n =

  	    "\n*** " ^ indent n ^ "Var ((" ^ a ^ ", " ^ string_of_int i ^ "), " ^

  	    string_of_typ_thy thy T ^ ")"

  	  | ato (Bound i) n = 

  	    "\n*** " ^ indent n ^ "Bound " ^ string_of_int i

  	  | ato (Abs(a, T, body))  n = 

  	    "\n*** " ^ indent n ^ "Abs (" ^ a ^ ", " ^ string_of_typ_thy thy T ^ ",.." ^

  	    ato body (n + 1)

  	  | ato (f $ t) n = ato f n ^ ato t (n + 1)

  in "\n*** " ^ ato t 0 ^ "\n***" end;

fun atomwy t = (writeln o term_detail2str) t;

fun atomty t = (tracing o term_detail2str) t;

fun atomty_thy thy t = (tracing o (term_detail2str_thy thy)) t;

(* contains the term a VAR(("*",_),_) ? *)

fun contains_Var (Abs(_,_,body)) = contains_Var body

  | contains_Var (f $ f') = contains_Var f orelse contains_Var f'

  | contains_Var (Var _) = true

  | contains_Var _ = false;

fun str_of_int n = 

  if n < 0 then "-" ^ ((string_of_int o abs) n)

  else string_of_int n;

val int_of_str = Thy_Output.integer;

fun int_of_str_opt str = 

  let

    val ss = Symbol.explode str

    val ss' = case ss of "(" :: s => drop_last s | _ => ss

    val (sign, istr) = case ss' of "-" :: istr => (~1, istr) | _ => (1, ss')

  in

    case Library.read_int istr of (i, []) => SOME (sign * i) | _ => NONE

  end;

fun is_num' str = case int_of_str_opt str of SOME _ => true | NONE => false;

fun is_num (Free (s, _)) = if is_num' s then true else false | is_num _ = false;

fun term_of_num ntyp n = Free (str_of_int n, ntyp);

fun num_of_term (t as (Free (istr, _))) = 

    (case int_of_str_opt istr of SOME i => i | NONE => raise TERM ("num_of_term: NOT int ", [t]))

  | num_of_term t = raise TERM ("num_of_term: NOT Free ", [t])

fun is_Free (Free _) = true | is_Free _ = false;

fun is_fun_id (Const _) = true

  | is_fun_id (Free _) = true

  | is_fun_id _ = false;

fun is_f_x (f $ x) = is_fun_id f andalso is_Free x

  | is_f_x _ = false;

fun vars t =

  let

    fun scan vs (Const _) = vs

      | scan vs (t as Free (s, _)) = if is_num' s then vs else t :: vs

      | scan vs (t as Var _) = t :: vs

      | scan vs (Bound _) = vs 

      | scan vs (Abs (_, _, t)) = scan vs t

      | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)

  in (distinct o (scan [])) t end;

(* bypass Isabelle's Pretty, which requires ctxt *)

fun ids2str t =

  let

    fun scan vs (Const (s, _)) = if is_num' s then vs else s :: vs

      | scan vs (Free (s, _)) = if is_num' s then vs else s :: vs

      | scan vs (Var ((s, i), _)) = (s ^ "_" ^ string_of_int i) :: vs

      | scan vs (Bound _) = vs 

      | scan vs (Abs (s, _, t)) = scan (s :: vs) t

      | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)

  in (distinct o (scan [])) t end;

fun is_bdv str = case Symbol.explode str of "b"::"d"::"v"::_ => true | _ => false;

(* instantiate #prop thm with bound variables (as Free) *)

fun inst_bdv [] t = t

  | inst_bdv (instl: (term*term) list) t =

    let

      fun subst (v as Var((s, _), T)) = 

          (case Symbol.explode s of

            "b"::"d"::"v"::_ => if_none (assoc(instl,Free(s,T))) (Free(s,T))

          | _ => v)

        | subst (Abs(a, T, body)) = Abs(a, T, subst body)

        | subst (f $ t') = subst f $ subst t'

        | subst t = if_none (assoc (instl, t)) t

    in  subst t  end;

(* is a term a substitution for a bdv as found in programs *)

fun is_bdv_subst (Const ("List.list.Cons", _) $

      (Const ("Product_Type.Pair", _) $ Free (str, _) $ _) $ _) = is_bdv str

  | is_bdv_subst _ = false;

fun free2str (Free (s, _)) = s

  | free2str t = error ("free2str not for " ^ term2str t);

fun str_of_free_opt (Free (s, _)) = SOME s

  | str_of_free_opt _ = NONE

(* compare Logic.unvarify_global, which rejects Free *)

fun var2free (t as Const _) = t

  | var2free (t as Free _) = t

  | var2free (Var((s, _), T)) = Free (s,T)

  | var2free (t as Bound _) = t 

  | var2free (Abs(s, T, t)) = Abs(s, T, var2free t)

  | var2free (t1 $ t2) = (var2free t1) $ (var2free t2);

(* Logic.varify does NOT take care of 'Free ("1", _)'*)

fun free2var (t as Const _) = t

  | free2var (t as Free (s, T)) = if is_num' s then t else Var ((s, 0), T)

  | free2var (t as Var _) = t

  | free2var (t as Bound _) = t 

  | free2var (Abs (s, T, t)) = Abs (s, T, free2var t)

  | free2var (t1 $ t2) = (free2var t1) $ (free2var t2);

fun mk_listT T = Type ("List.list", [T]);

fun list_const T = Const ("List.list.Cons", [T, mk_listT T] ---> mk_listT T);

fun list2isalist T [] = Const ("List.list.Nil", mk_listT T)

  | list2isalist T (t :: ts) = (list_const T) $ t $ (list2isalist T ts);

fun isapair2pair (Const ("Product_Type.Pair",_) $ a $ b) = (a, b)

  | isapair2pair t = 

    error ("isapair2pair called with "^term2str t);

fun isalist2list ls =

  let

    fun get es (Const("List.list.Cons", _) $ t $ ls) = get (t :: es) ls

      | get es (Const("List.list.Nil", _)) = es

      | get _ t = error ("isalist2list applied to NON-list '"^term2str t^"'")

  in (rev o (get [])) ls end;

fun is_list ((Const ("List.list.Cons", _)) $ _ $ _) = true

  | is_list _ = false;

fun dest_binop_typ (Type ("fun", [range, Type ("fun", [arg2, arg1])])) = (arg1, arg2, range)

  | dest_binop_typ _ = raise ERROR "dest_binop_typ: not binary";

fun dest_equals (Const("HOL.eq", _) $ t $ u)  =  (t, u) (* Pure/logic.ML: Const ("==", ..*)

  | dest_equals t = raise TERM ("dest_equals'", [t]);

fun is_equality (Const("HOL.eq",_) $ _ $ _)  =  true  (* logic.ML: Const("=="*)

  | is_equality _ = false;

fun mk_equality (t, u) = (Const("HOL.eq", [type_of t, type_of u] ---> HOLogic.boolT) $ t $ u); 

fun is_expliceq (Const("HOL.eq",_) $ (Free _) $ _)  =  true

  | is_expliceq _ = false;

fun strip_trueprop (Const ("HOL.Trueprop", _) $ t) = t

  | strip_trueprop t = t;

(* (A1==>...An==>B) goes to (A1==>...An==>)   Pure/logic.ML: term -> term list*)

fun strip_imp_prems' (Const ("==>", _) $ A $ t) = 

    let

      fun coll_prems As (Const("==>", _) $ A $ t) = 

          coll_prems (As $ (Logic.implies $ A)) t

        | coll_prems As _ = SOME As

    in coll_prems (Logic.implies $ A) t end

  | strip_imp_prems' _ = NONE;  (* *)

(* (A1==>...An==>) (B) goes to (A1==>...An==>B), where B is lowest branch, 2002 Pure/thm.ML *)

fun ins_concl (Const ("==>", _) $ A $ t) B = Logic.implies $ A $ (ins_concl t B)

  | ins_concl (Const ("==>", _) $ A    ) B = Logic.implies $ A $ B

  | ins_concl t B =  raise TERM ("ins_concl", [t, B]);

fun vperm (Var _, Var _) = true  (* 2002 Pure/thm.ML *)

  | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)

  | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)

  | vperm (t, u) = (t = u);

(*2002 cp from Pure/term.ML --- since 2009 in Pure/old_term.ML*)

fun mem_term (_, []) = false

  | mem_term (t, t' :: ts) = t aconv t' orelse mem_term (t, ts);

fun subset_term ([], _) = true

  | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term (xs, ys);

fun eq_set_term (xs, ys) =

    xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));

(*a total, irreflexive ordering on index names*)

fun xless ((a, i), (b, j): indexname) = i<j  orelse  (i = j andalso a < b);

(*a partial ordering (not reflexive) for atomic terms*)

fun atless (Const (a, _), Const (b, _)) = a < b

  | atless (Free (a, _), Free (b, _)) = a < b

  | atless (Var (v, _), Var (w, _)) = xless (v, w)

  | atless (Bound i, Bound j) =  i < j

  | atless _ = false;

(*insert atomic term into partially sorted list, suppressing duplicates (?)*)

fun insert_aterm (t,us) =

  let fun inserta [] = [t]

        | inserta (us as u::us') =

              if atless(t,u) then t::us

              else if t=u then us (*duplicate*)

              else u :: inserta us'

  in inserta us end;

(* Accumulates the Vars in the term, suppressing duplicates *)

fun add_term_vars (t, vars: term list) = case t of

    Var   _ => insert_aterm (t, vars)

  | Abs (_, _, body) => add_term_vars (body, vars)

  | f$t =>  add_term_vars (f, add_term_vars (t, vars))

  | _ => vars;

fun term_vars t = add_term_vars (t, []);

(*2002 Pure/thm.ML *)

fun var_perm (t, u) = vperm (t, u) andalso eq_set_term (term_vars t, term_vars u);

(*2002 fun decomp_simp, Pure/thm.ML *)

fun perm lhs rhs = var_perm (lhs, rhs) andalso not (lhs aconv rhs) andalso not (is_Var lhs);

(* TODO: shift to calculate.sml? *)

fun calc_equ "less"  (n1, n2) = n1 < n2

  | calc_equ "less_eq" (n1, n2) = n1 <= n2

  | calc_equ op_ _ = error ("calc_equ: operator = " ^ op_ ^ " not defined");

fun sqrt (n:int) = if n < 0 then 0 else (trunc o Math.sqrt o Real.fromInt (*FIXME*)) n;

fun power _ 0 = 1

  | power b n = 

    if n > 0 then b* (power b (n - 1))

    else error ("power " ^ str_of_int b ^ " " ^ str_of_int n);

fun gcd 0 b = b

  | gcd a b = if a < b then gcd (b mod a) a else gcd (a mod b) b;

fun sign n =

  if n < 0 then ~1

	else if n = 0 then 0 else 1;

fun sign_mult n1 n2 = (sign n1) * (sign n2);

infix dvd;

fun d dvd n = n mod d = 0;

fun divisors n =

  let fun pdiv ds d n = 

    if d = n then d :: ds

    else if d dvd n then pdiv (d :: ds) d (n div d)

	 else pdiv ds (d + 1) n

  in pdiv [] 2 n end;

fun doubles ds = (* ds is ordered *)

  let fun dbls ds [] = ds

	| dbls ds [ _ ] = ds

	| dbls ds (i :: i' :: is) = if i = i' then dbls (i :: ds) is

				else dbls ds (i'::is)

  in dbls [] ds end;

fun squfact 0 = 0

  | squfact 1 = 1

  | squfact n = foldl op* (1, (doubles o divisors) n);

fun pairT T1 T2 = Type ("*", [T1, T2]);

fun PairT T1 T2 = ([T1, T2] ---> Type ("*", [T1, T2]));

fun pairt t1 t2 = Const ("Product_Type.Pair", PairT (type_of t1) (type_of t2)) $ t1 $ t2;

fun mk_factroot op_(*=thy.sqrt*) T fact root = 

  Const ("Groups.times_class.times", [T, T] ---> T) $ (term_of_num T fact) $

    (Const (op_, T --> T) $ term_of_num T root);

fun mk_var_op_num v op_ optype ntyp n = Const (op_, optype) $ v $ Free (str_of_int  n, ntyp);

fun mk_num_op_var v op_ optype ntyp n = Const (op_, optype) $ Free (str_of_int n, ntyp) $ v;

fun mk_num_op_num T1 T2 (op_, Top) n1 n2 =

  Const (op_, Top) $ Free (str_of_int n1, T1) $ Free (str_of_int n2, T2);

fun mk_thmid thmid n1 n2 = 

  thmid ^ (strip_thy n1) ^ "_" ^ (strip_thy n2);

fun mk_add t1 t2 =

  let

    val (T1, T2) = (type_of t1, type_of t2)

  in

    if T1 <> T2 then raise TYPE ("mk_add gets ", [T1, T2], [t1,t2])

    else (Const ("Groups.plus_class.plus", [T1, T2] ---> T1) $ t1 $ t2)

  end;

fun const_in _ (Const _) = false

  | const_in str (Free (s, _)) = if strip_thy s = str then true else false

  | const_in _ (Bound _) = false

  | const_in _ (Var _) = false

  | const_in str (Abs (_, _, body)) = const_in str body

  | const_in str (f $ u) = const_in str f orelse const_in str u;

(** transform binary numeralsstrings **)

(*Makarius 100308, hacked by WN*)

val numbers_to_string =

  let

    fun dest_num t =

      (case try HOLogic.dest_number t of

        SOME (T, i) =>

          (*if T = @{typ int} orelse T = @{typ real} then WN*)

            SOME (Free (signed_string_of_int i, T))

          (*else NONE  WN*)

      | NONE => NONE);

    fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)

      | to_str (t as (u1 $ u2)) =

          (case dest_num t of

            SOME t' => t'

          | NONE => to_str u1 $ to_str u2)

      | to_str t = perhaps dest_num t;

  in to_str end

val uminus_to_string =

  let

	  fun dest_num t =

	    case t of

	      (Const ("Groups.uminus_class.uminus", _) $ Free (s, T)) => 

	        (case int_of_str_opt s of

	          SOME i => SOME (Free (signed_string_of_int (~1 * i), T))

	        | NONE => NONE)

	    | _ => NONE;

    fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)

      | to_str (t as (u1 $ u2)) =

          (case dest_num t of SOME t' => t' | NONE => to_str u1 $ to_str u2)

      | to_str t = perhaps dest_num t;

  in to_str end;

fun num_str thm =

  let

    val (deriv, 

	   {cert = cert, tags = tags, maxidx = maxidx, shyps = shyps, 

	    hyps = hyps, tpairs = tpairs, prop = prop}) = Thm.rep_thm_G thm

    val prop' = numbers_to_string prop;

  in Thm.assbl_thm deriv cert tags maxidx shyps hyps tpairs prop' end;

fun mk_Free (s,T) = Free (s, T);

fun mk_free T s =  Free (s, T);

(*Special case: one argument cp from Isabelle2002/src/Pure/term.ML*)

fun subst_bound (arg, t) =

  let

    fun subst (t as Bound i, lev) =

        if i < lev then t (*var is locally bound*)

        else if i = lev then incr_boundvars lev arg

        else Bound (i - 1) (*loose: change it*)

      | subst (Abs(a, T, body), lev) = Abs (a, T, subst (body, lev + 1))

      | subst (f$t, lev) =  subst(f, lev)  $  subst(t, lev)

      | subst (t, _) = t

  in subst (t, 0)  end;

(* instantiate let; necessary for ass_up *)

fun inst_abs (Const sT) = Const sT

  | inst_abs (Free sT) = Free sT

  | inst_abs (Bound n) = Bound n

  | inst_abs (Var iT) = Var iT

  | inst_abs (Const ("HOL.Let",T1) $ e $ (Abs (v, T2, b))) = 

    let val b' = subst_bound (Free (v, T2), b); (*fun variant_abs: term.ML*)

    in Const ("HOL.Let", T1) $ inst_abs e $ (Abs (v, T2, inst_abs b')) end

  | inst_abs (t1 $ t2) = inst_abs t1 $ inst_abs t2

  | inst_abs t = t;

(* for parse and parse_patt: fix all types to real *)

fun T_a2real (Type (s, [])) = 

    if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else Type (s, [])

  | T_a2real (Type (s, Ts)) = Type (s, map T_a2real Ts)

  | T_a2real (TFree (s, srt)) = 

    if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else TFree (s, srt)

  | T_a2real (TVar (("DUMMY", _), _)) = HOLogic.realT

  | T_a2real (TVar ((s, i), srt)) = 

    if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else TVar ((s, i), srt)

fun typ_a2real (Const( s, T)) = (Const( s, T_a2real T)) 

  | typ_a2real (Free( s, T)) = (Free( s, T_a2real T))

  | typ_a2real (Var( n, T)) = (Var( n, T_a2real T))

  | typ_a2real (Bound i) = (Bound i)

  | typ_a2real (Abs(s,T,t)) = Abs(s, T, typ_a2real t)

  | typ_a2real (t1 $ t2) = (typ_a2real t1) $ (typ_a2real t2);

(* TODO clarify parse with Test_Isac *)

fun parseold thy str = (* before 2002 *)

  (let val t = ((*typ_a2real o*) numbers_to_string) (Syntax.read_term_global thy str)

   in SOME (Thm.global_cterm_of thy t) end)

  handle _(*EXN? ..Inner syntax error Failed to parse term*) => NONE;

fun parseN thy str = (* introduced 2002 *)

  (let val t = (*(typ_a2real o numbers_to_string)*) (Syntax.read_term_global thy str)

   in SOME (Thm.global_cterm_of thy t) end)

  handle _(*EXN? ..Inner syntax error Failed to parse term*) => NONE;

fun parse thy str = (* introduced 2010 *)

  (let val t = (typ_a2real o numbers_to_string) (Syntax.read_term_global thy str)

   in SOME (Thm.global_cterm_of thy t) end)

  handle _(*EXN? ..Inner syntax error Failed to parse term*) => NONE;

(*WN110317 parseNEW will replace parse after introduction of ctxt completed*)

fun parseNEW ctxt str = SOME (Syntax.read_term ctxt str |> numbers_to_string)

   handle _ => NONE;

(* parse term patterns; Var ("v",_), i.e. "?v", are required for instantiation

  WN130613 probably compare to 

  http://www.mail-archive.com/isabelle-dev@mailbroy.informatik.tu-muenchen.de/msg04249.html*)

fun parse_patt thy str =

  (thy, str) |>> thy2ctxt 

             |-> Proof_Context.read_term_pattern

             |> numbers_to_string (*TODO drop*)

             |> typ_a2real;       (*TODO drop*)

fun str2term str = parse_patt (Thy_Info_get_theory "Isac") str

(* TODO decide with Test_Isac *)

fun is_atom t = length (vars t) = 1

fun is_atom (Const ("Float.Float",_) $ _) = true

  | is_atom (Const ("ComplexI.I'_'_",_)) = true

  | is_atom (Const ("Groups.times_class.times",_) $ t $ Const ("ComplexI.I'_'_",_)) = is_atom t

  | is_atom (Const ("Groups.plus_class.plus",_) $ t1 $ Const ("ComplexI.I'_'_",_)) = is_atom t1

  | is_atom (Const ("Groups.plus_class.plus",_) $ t1 $ 

		   (Const ("Groups.times_class.times",_) $ t2 $ Const ("ComplexI.I'_'_",_))) = 

    is_atom t1 andalso is_atom t2

  | is_atom (Const _) = true

  | is_atom (Free _) = true

  | is_atom (Var _) = true

  | is_atom _ = false;

(* from Pure/term.ML; reports if ALL Free's have found a substitution

   (required for evaluating the preconditions of _incomplete_ models) *)

fun subst_atomic_all [] t = (false (*TODO may be 'true' for some terms ?*), t)

  | subst_atomic_all instl t =

    let

      fun subst (Abs (a, T, body)) = 

          let

            val (all, body') = subst body

          in (all, Abs(a, T, body')) end

        | subst (f$tt) = 

	        let

	          val (all1, f') = subst f

	          val (all2, tt') = subst tt

	        in (all1 andalso all2, f' $ tt') end

        | subst (t as Free _) = 

	        if is_num t then (true, t) (*numerals cannot be subst*)

	        else (case assoc (instl, t) of

					  SOME t' => (true, t')

				  | NONE => (false, t))

        | subst t = (true, if_none (assoc(instl,t)) t)

    in subst t end;

end