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

   Author: Walther Neuper 1999, Mathias Lehnfeld

   (c) due to copyright terms

*)

infix contains_one_of

(* TERM_C extends Isabelle's naming conventions: "C" indicates Isac add-ons to an Isabelle module *)

signature TERM_ISAC =

sig

  type as_string

  val empty: term

  val typ_empty: typ

  datatype lrd = D | L | R

  type path

  val string_of_path: path -> string

  val sub_at: path -> term -> term

  val go_up: path -> term -> term

  val contains_Var: term -> bool

  val dest_binop_typ: typ -> typ * typ * typ

  val 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 lhs: term -> term

  val rhs: term -> term

  val mk_frac: typ -> int * (int * int) -> term

  val numerals_to_Free: term -> term

  val term_of_num: typ -> int -> term

  val num_of_term: term -> int

  val to_string: term -> string

  val int_of_str: string -> int

  val isastr_of_int: int -> string

  val int_opt_of_string: string -> int option

  val isalist2list: term -> term list

  val list2isalist: typ -> term list -> term

  val isapair2pair: term -> term * term (* rename to dest_pair, compare HOLogic.dest_string *)

  val is_atom: term -> bool

  val string_of_atom: term -> string

  val is_variable: term -> bool

  val is_bdv: string -> bool

  val is_bdv_subst: term -> bool

  val guess_bdv_typ: term -> typ

  val is_equality: term -> bool

  val is_expliceq: term -> bool

  val is_f_x: term -> bool

  val is_list: term -> bool

  val is_bool_list: term -> bool

  val dest_listT: typ -> typ

  val is_num: term -> bool

  val is_num': string -> bool

  val string_of_num: term -> string

  val variable_constant_pair: term * term -> 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: typ -> typ -> string * typ -> int -> int -> term

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

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

  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 parseNEW': Proof.context -> string -> term

  val parseNEW'': theory -> string -> term

  val parseold: theory -> string -> cterm option

  val parse_strict: theory -> string -> term

  val parse_patt: theory -> string -> term

  val perm: term -> term -> bool

  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 pairt: term -> term -> term

  val pairT: typ -> typ -> typ

  val raise_type_conflicts: term list -> unit

  val strip_trueprop: term -> term

  val var2free: term -> term

  val vars: term -> term list  (* recognises numerals, should replace "fun vars_of" TODOO*)

  val vars': term list -> term list

  val vars_of: term -> term list   (* deprecated TODOO: see differences in test/../termC.sml*)

  val dest_list': term -> term list

  val negates: term -> term -> bool

\<^isac_test>\<open>

  val mk_negative: typ -> term -> term

  val scala_of_term: term -> string

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

  val atomty: term -> unit

  val atomw: term -> unit

  val atomt: term -> unit

  val atomwy: term -> unit

  val atomty_thy: ThyC.id -> term -> unit

  val free2var: term -> term

  val typ_a2real: term -> term

\<close>

  val contains_one_of: thm * (string * typ) list -> bool

  val contains_Const_typeless: term list -> term -> bool

(*----- unused code, kept as hints to design ideas ---------------------------------------------*)

  val sym_trm : term -> term

end

(**)

structure TermC(**): TERM_ISAC(**) =

struct

(**)

type as_string = UnparseC.term_as_string

val empty = UnparseC.term_empty

val typ_empty = UnparseC.typ_empty

datatype lrd = L (*t1 in "t1$t2"*)

             | R (*t2 in "t1$t2"*) | D; (*b in Abs(_,_,b*)

type path = lrd list; 

fun ldr2str L = "L"

  | ldr2str R = "R"

  | ldr2str D = "D";

fun string_of_path k = (strs2str' o (map ldr2str)) k;

(*go to a location in a term and fetch the resective sub-term*)

fun sub_at [] t = t

  | sub_at (D :: p) (Abs(_, _, body)) = sub_at p body

  | sub_at (L :: p) (t1 $ _) = sub_at p t1

  | sub_at (R :: p) (_ $ t2) = sub_at p t2

  | sub_at l t = raise TERM ("sub_at: no " ^ string_of_path l ^ " for ", [t]);

fun go_up l t =

  if length l > 1 then sub_at (drop_last l) t else raise ERROR ("go_up [] " ^ UnparseC.term t)

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 **)

\<^isac_test>\<open>

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;

\<close>

fun term_detail2str t =

  let 

    fun ato (Const (a, T)) n = "\n*** " ^ indent n ^ "Const (" ^ a ^ ", " ^ UnparseC.typ T ^ ")"

      | ato (Free (a, T)) n = "\n*** " ^ indent n ^ "Free (" ^ a ^ ", " ^ UnparseC.typ T ^ ")"

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

        "\n*** " ^ indent n ^ "Var ((" ^ a ^ ", " ^ string_of_int i ^ "), " ^ UnparseC.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 ^ ", " ^ UnparseC.typ T ^ ",.." ^ ato body (n + 1)

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

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

\<^isac_test>\<open>

fun term_detail2str_thy thy t =

  let

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

        "\n*** " ^ indent n ^ "Const (" ^ a ^ ", " ^ UnparseC.typ_by_thyID thy T ^ ")"

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

  	     "\n*** " ^ indent n ^ "Free (" ^ a ^ ", " ^ UnparseC.typ_by_thyID thy T ^ ")"

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

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

  	    UnparseC.typ_by_thyID 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 ^ ", " ^ UnparseC.typ_by_thyID 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;

\<close>

(* 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 = Value.parse_int;

val int_opt_of_string = ThmC_Def.int_opt_of_string

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

fun is_num (Const (\<^const_name>\<open>numeral\<close>, _) $ _) = true

  | is_num (Const (\<^const_name>\<open>uminus\<close>, _) $

    (Const (\<^const_name>\<open>numeral\<close>, _) $ _)) = true

  | is_num (Const (\<^const_name>\<open>one_class.one\<close>, _)) = true

  | is_num (Const (\<^const_name>\<open>uminus\<close>, _) $ Const (\<^const_name>\<open>one_class.one\<close>, _)) = true

  | is_num (Const (\<^const_name>\<open>zero_class.zero\<close>, _)) = true

  | is_num (Const (\<^const_name>\<open>uminus\<close>, _) $ Const (\<^const_name>\<open>zero_class.zero\<close>, _)) = true

  | is_num _ = false;

fun string_of_num n = (n |> HOLogic.dest_number |> snd |> string_of_int)

(* refer to Thm.lhs_of *)

fun lhs (Const (\<^const_name>\<open>HOL.eq\<close>,_) $ l $ _) = l

  | lhs t = raise ERROR("lhs called with (" ^ UnparseC.term t ^ ")");

fun rhs (Const (\<^const_name>\<open>HOL.eq\<close>,_) $ _ $ r) = r

  | rhs t = raise ERROR("rhs called with (" ^ UnparseC.term t ^ ")");

fun mk_negative T t = Const (\<^const_name>\<open>uminus\<close>, T --> T) $ t

fun mk_frac T (sg, (i1, i2)) =

  if sg = 1 then

    if i2 = 1 then HOLogic.mk_number T i1

    else Const (\<^const_name>\<open>divide_class.divide\<close>, T --> T --> T) $

      HOLogic.mk_number T i1 $ HOLogic.mk_number T i2

  else (*take negative*)

    if i2 = 1 then mk_negative T (HOLogic.mk_number T i1)

    else Const (\<^const_name>\<open>divide_class.divide\<close>, T --> T --> T) $

      mk_negative T (HOLogic.mk_number T i1) $ HOLogic.mk_number T i2

val numerals_to_Free = (* Makarius 100308 *)

  let

    fun dest_num t =

      (case try HOLogic.dest_number t of

        SOME (T, i) => SOME (Free (signed_string_of_int i, T))

      | 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 term_of_num = HOLogic.mk_number;

fun num_of_term t = t |> HOLogic.dest_number |> snd;

(* accomodate string-representation for int to term-orders *)

fun to_string t = t |> num_of_term |> signed_string_of_int

fun is_variable (t as Free _) = not (is_num t)

  | is_variable _ = false;

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;

(* precondition: TermC.is_atom v andalso TermC.is_atom c *)

fun is_const (Const _) = true | is_const _ = false;

fun variable_constant_pair (v, c) =

  if (is_variable v andalso (is_const c orelse is_num c)) orelse

     (is_variable c andalso (is_const v orelse is_num v))

  then true

  else false

fun vars t =

  let

    fun scan vs (Const _) = vs

      | scan vs (t as Free _) = (*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 op =) o (scan [])) t end;

fun vars' ts = ts |> map vars |> flat |> distinct op =

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

fun ids2str t =

  let

    fun scan vs (t as Const (s, _) $ arg) =

        if is_num t then vs else scan (s :: vs) arg

      | scan vs (Const (s as "Partial_Fractions.AA", _)) = s :: vs (*how get rid of spec.case?*)

      | scan vs (Const (s as "Partial_Fractions.BB", _)) = s :: vs (*how get rid of spec.case?*)

      | scan vs (Const _) = 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 op =) 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 and tactics *)

fun is_bdv_subst (Const (\<^const_name>\<open>Cons\<close>, _) $

      (Const (\<^const_name>\<open>Pair\<close>, _) $ str $ _) $ _) = is_bdv (HOLogic.dest_string str)

  | is_bdv_subst _ = false;

(* this shall be improved due to future requirements *)

fun guess_bdv_typ t = t |> vars |> hd |> type_of

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

  | free2str t = raise ERROR ("free2str not for " ^ UnparseC.term 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);

\<^isac_test>\<open>

(* 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);

\<close>

fun mk_listT T = Type (\<^type_name>\<open>list\<close>, [T]);

fun list_const T = Const (\<^const_name>\<open>Cons\<close>, [T, mk_listT T] ---> mk_listT T);

fun list2isalist T [] = Const (\<^const_name>\<open>Nil\<close>, mk_listT T)

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

fun isapair2pair (Const (\<^const_name>\<open>Pair\<close>,_) $ a $ b) = (a, b)

  | isapair2pair t = 

    raise ERROR ("isapair2pair called with " ^ UnparseC.term t);

fun isalist2list ls =

  let

    fun get es (Const(\<^const_name>\<open>Cons\<close>, _) $ t $ ls) = get (t :: es) ls

      | get es (Const(\<^const_name>\<open>Nil\<close>, _)) = es

      | get _ t = raise TERM ("isalist2list applied to NON-list: ", [t])

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

fun is_list ((Const (\<^const_name>\<open>Cons\<close>, _)) $ _ $ _) = true

  | is_list _ = false;

fun dest_listT (Type (\<^type_name>\<open>list\<close>, [T])) = T

  | dest_listT T = raise TYPE ("dest_listT: list type expected", [T], []);

fun is_bool_list t =

  (if dest_listT (Term.type_of t) = HOLogic.boolT then true else false)

  handle TYPE _ => false

fun dest_binop_typ (Type (\<^type_name>\<open>fun\<close>, [range, Type (\<^type_name>\<open>fun\<close>, [arg2, arg1])])) = (arg1, arg2, range)

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

fun dest_equals (Const(\<^const_name>\<open>HOL.eq\<close>, _) $ t $ u)  =  (t, u) (* Pure/logic.ML: Const ("==", ..*)

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

fun is_equality (Const(\<^const_name>\<open>HOL.eq\<close>,_) $ _ $ _)  =  true  (* logic.ML: Const ("=="*)

  | is_equality _ = false;

fun mk_equality (t, u) = (Const(\<^const_name>\<open>HOL.eq\<close>, [type_of t, type_of u] ---> HOLogic.boolT) $ t $ u); 

fun is_expliceq (Const(\<^const_name>\<open>HOL.eq\<close>,_) $ (Free _) $ _)  =  true

  | is_expliceq _ = false;

fun strip_trueprop (Const (\<^const_name>\<open>Trueprop\<close>, _) $ t) = t

  | strip_trueprop t = t;

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

fun strip_imp_prems' (Const (\<^const_name>\<open>Pure.imp\<close>, _) $ A $ t) = 

    let

      fun coll_prems As (Const(\<^const_name>\<open>Pure.imp\<close>, _) $ 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 (\<^const_name>\<open>Pure.imp\<close>, _) $ A $ t) B = Logic.implies $ A $ (ins_concl t B)

  | ins_concl (Const (\<^const_name>\<open>Pure.imp\<close>, _) $ 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);

fun pairT T1 T2 = Type (\<^type_name>\<open>prod\<close>, [T1, T2]);

fun PairT T1 T2 = ([T1, T2] ---> Type (\<^type_name>\<open>prod\<close>, [T1, T2]));

fun pairt t1 t2 = Const (\<^const_name>\<open>Pair\<close>, PairT (type_of t1) (type_of t2)) $ t1 $ t2;

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

  Const (\<^const_name>\<open>times\<close>, [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 $ HOLogic.mk_number ntyp n;

fun mk_num_op_var v op_ optype ntyp n = Const (op_, optype) $ HOLogic.mk_number ntyp n $ v;

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

  Const (op_, Top) $ HOLogic.mk_number T1 n1 $ HOLogic.mk_number T2 n2;

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 (\<^const_name>\<open>plus\<close>, [T1, T2] ---> T1) $ t1 $ t2)

  end;

(** transform binary numeralsstrings **)

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 scan_up1 *)

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 (\<^const_name>\<open>Let\<close>,T1) $ e $ (Abs (v, T2, b))) = 

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

    in Const (\<^const_name>\<open>Let\<close>, 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 *)

  \<^try>\<open>

    let val t = Syntax.read_term_global thy str

    in Thm.global_cterm_of thy t end\<close>;

fun parseN thy str = (* introduced 2002 *)

  \<^try>\<open>

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

    in Thm.global_cterm_of thy t end\<close>;

fun parse_strict thy str = typ_a2real (Syntax.read_term_global thy str);

fun parse thy str = (* introduced 2010 *)

  \<^try>\<open>

    let val t = parse_strict thy str

    in Thm.global_cterm_of thy t end\<close>;

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

fun parseNEW ctxt str = \<^try>\<open>Syntax.read_term ctxt str\<close>;

fun parseNEW' ctxt str = 

  case parseNEW ctxt str of

    SOME t => t

  | NONE => raise TERM ("NO parseNEW' for " ^ str, [])

fun parseNEW'' thy str =

  case parseNEW (Proof_Context.init_global thy) str of

    SOME t => t

  | NONE => raise TERM ("NO parseNEW'' for " ^ str, [])

(* 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)

  |>> Proof_Context.init_global

  |-> Proof_Context.read_term_pattern

(*|> numbers_to_string   TODO drop*)

  |> typ_a2real;       (*TODO drop*)

fun str2term str = parse_patt (ThyC.get_theory "Isac_Knowledge") str

fun is_atom (Const _) = true

  | is_atom (Free _) = true

  | is_atom (Var _) = true

  | is_atom t = is_num t;

fun string_of_atom (t as Const (\<^const_name>\<open>numeral\<close>, _) $ _) = to_string t

  | string_of_atom (t as Const (\<^const_name>\<open>one_class.one\<close>, _)) = to_string t

  | string_of_atom (t as Const (\<^const_name>\<open>zero_class.zero\<close>, _)) = to_string t

  | string_of_atom (Const (str, _)) = str

  | string_of_atom (Free (str, _)) = str

  | string_of_atom (Var ((str, int), _)) = str ^ "_" ^ string_of_int int

  | string_of_atom _ = "DUMMY-string_of_atom";

(* 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;

fun op contains_one_of (thm, ids) =

  Term.exists_Const (fn id => member op= ids id) (Thm.prop_of thm)

fun var_for vs (t as Const (str, _)) id =

    if is_num t then vs

    else if id = strip_thy str then t :: vs else vs

  | var_for vs (t as Free (str, _)) id = if id = str then t :: vs else vs

  | var_for vs (t as Var (idn, _)) id = if id = Term.string_of_vname idn then t :: vs else vs

  | var_for vs (Bound _) _ = vs

  | var_for vs (Abs (_, _, t)) id = var_for vs t id

  | var_for vs (t1 $ t2) id = (var_for vs t1 id) @ (var_for vs t2 id)

val poly_consts = (* TODO: adopt syntax-const from Isabelle*)

  [\<^const_name>\<open>plus\<close>, \<^const_name>\<open>minus\<close>,

  \<^const_name>\<open>divide\<close>, \<^const_name>\<open>times\<close>,

  \<^const_name>\<open>realpow\<close>];

(* treat Free, Const, Var as variables in polynomials *)

fun vars_of t =

  let

    val var_ids = t |> ids2str |> subtract op = poly_consts |> map strip_thy |> sort string_ord

  in (map (var_for [] t) var_ids) |> flat |> distinct op = end

(* this may decompose an object-language isa-list;

   use only, if description is not available, eg. not input ?WN:14.5.03 ??!?*)

fun dest_list' t = if is_list t then isalist2list t  else [t];

fun negat (Const (\<^const_name>\<open>Not\<close>, _) $ P, P') = P = P'

  | negat _ = false

fun negates p1 p2 = negat (p1, p2) orelse negat (swap (p1, p2));

fun raise_type_conflicts ts =

  let

    val dups = duplicates (op =) (map (fst o dest_Free) ts)

    val confl = filter (fn Free (str, _) => member op = dups str

                         | _ => false) ts

  in

    if confl = []

    then ()

    else raise TYPE ("formalisation inconsistent w.r.t. type inference: ",

      map (snd o dest_Free)confl, confl)

  end

(* expects t as Const *)

fun contains_Const_typeless ts t = (t

  |> strip_comb |> fst

  |> member (fn (t1, t2) => fst (dest_Const t1) = fst (dest_Const t2)) ts

) handle TERM("dest_Const", _) => raise TERM ("contains_Const_typeless", [t])

(* WN100910 weaker than fun sym_thm for Theory.axioms_of in isa02 *)

fun sym_trm trm =

  let

    val (lhs, rhs) = (dest_equals o strip_trueprop o Logic.strip_imp_concl) trm

    val trm' = case strip_imp_prems' trm of

	      NONE => mk_equality (rhs, lhs)

	    | SOME cs => ins_concl cs (mk_equality (rhs, lhs))

  in trm' end

end