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

   Author: Walther Neuper 1999, Mathias Lehnfeld

   (c) due to copyright terms

*)

(*

> (cterm_of thy) a_term; 

val it = "empty" : cterm        *)

(*2003 fun match thy t pat =

    (snd (Pattern.match (Sign.tsig_of (sign_of thy)) (pat, t)))

    handle _ => [];

fn : theory ->

     Term.term -> Term.term -> (Term.indexname * Term.term) list*)

(*see src/Tools/eqsubst.ML fun clean_match*)

(*2003 fun matches thy tm pa = if match thy tm pa = [] then false else true;*)

fun matches thy tm pa = 

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

    handle _ => false

fun atomtyp t = (*WN10 see raw_pp_typ*)

  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;

(*

> val T = (type_of o term_of o the o (parse thy)) "a::[real,int] => nat";

> atomtyp T;

*** Type (fun,[

***   Type (RealDef.real,[])

***   Type (fun,[

***     Type (IntDef.int,[])

***     Type (nat,[])

***     ]

***   ]

*)

(*Prog.Tutorial.p.34, Makarius 1005 does the above like this..*)

local

   fun pp_pair (x, y) = Pretty.list "(" ")" [x, y]

   fun pp_list xs = Pretty.list "[" "]" xs

   fun pp_str s   = Pretty.str s

   fun pp_qstr s = Pretty.quote (pp_str s)

   fun pp_int i   = pp_str (string_of_int i)

   fun pp_sort S = pp_list (map pp_qstr S)

   fun pp_constr a args = Pretty.block [pp_str a, Pretty.brk 1, args]

in

fun raw_pp_typ (TVar ((a, i), S)) =

       pp_constr "TVar" (pp_pair (pp_pair (pp_qstr a, pp_int i), pp_sort S))

   | raw_pp_typ (TFree (a, S)) =

       pp_constr "TFree" (pp_pair (pp_qstr a, pp_sort S))

   | raw_pp_typ (Type (a, tys)) =

       pp_constr "Type" (pp_pair (pp_qstr a, pp_list (map raw_pp_typ tys)))

end

(* install

PolyML.addPrettyPrinter

  (fn _ => fn _ => ml_pretty o Pretty.to_ML o raw_pp_typ);

de-install

PolyML.addPrettyPrinter

  (fn _ => fn _ => ml_pretty o Pretty.to_ML o Proof_Display.pp_typ Pure.thy);

*)

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;

fun term_str thy (Const(s,_)) = s

  | term_str thy (Free(s,_)) = s

  | term_str thy (Var((s,i),_)) = s^(string_of_int i)

  | term_str thy (Bound i) = "B."^(string_of_int i)

  | term_str thy (Abs(s,_,_)) = s

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

(*.contains the fst argument the second argument (a leave! of term).*)

fun contains_term (Abs(_,_,body)) t = contains_term body t 

  | contains_term (f $ f') t = 

    contains_term f t orelse contains_term f' t

  | contains_term s t = t = s;

(*.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;

(* contains_Var (str2term "?z = 3") (*true*);

   contains_Var (str2term "z = 3")  (*false*);

   *)

(*fun int_of_str str =

    let val ss = Symbol.explode str

	val str' = case ss of

	   "("::s => drop_last s | _ => ss

    in case BasisLibrary.Int.fromString (implode str') of

	     SOME i => SOME i

	   | NONE => NONE end;*)

fun int_of_str str =

    let val ss = Symbol.explode str

	val str' = case ss of

	   "("::s => drop_last s | _ => ss

    in (SOME (Thy_Output.integer (implode str'))) handle _ => NONE end;

(*

> int_of_str "123";

val it = SOME 123 : int option

> int_of_str "(-123)";

val it = SOME 123 : int option

> int_of_str "#123";

val it = NONE : int option

> int_of_str "-123";

val it = SOME ~123 : int option

*)

fun int_of_str' str = 

    case int_of_str str of

	SOME i => i

      | NONE => raise TERM ("int_of_string: no int-string",[]);

val str2int = int_of_str';

fun is_numeral str = case int_of_str str of

			 SOME _ => true

		       | NONE => false;

val is_no = is_numeral;

(* see /home/neuper/repos/FHpoly/src/HOL/Decision_Procs/Approximation.thy:

  val mk_int = HOLogic.mk_number @{typ int} o @{code integer_of_int};

  val dest_int = @{code int_of_integer} o snd o HOLogic.dest_number;

  fun nat_of_term t = @{code nat_of_integer}

    (HOLogic.dest_nat t handle TERM _ => snd (HOLogic.dest_number t));

  etc...

*)

fun is_num (Free (s,_)) = if is_numeral s then true else false

  | is_num _ = false;

(*>

> is_num ((term_of o the o (parse thy)) "#1");

val it = true : bool

> is_num ((term_of o the o (parse thy)) "#-1");

val it = true : bool

> is_num ((term_of o the o (parse thy)) "a123");

val it = false : bool

*)

(*fun int_of_Free (Free (intstr, _)) =

    (case BasisLibrary.Int.fromString intstr of

	     SOME i => i

	   | NONE => error ("int_of_Free ( "^ intstr ^", _)"))

  | int_of_Free t = error ("int_of_Free ( "^ term2str t ^" )");*)

fun int_of_Free (Free (intstr, _)) = (Thy_Output.integer intstr

    handle _ => error ("int_of_Free ( "^ intstr ^", _)"))

  | int_of_Free t = error ("int_of_Free ( "^ term2str t ^" )");

fun vars t =

  let

    fun scan vs (Const(s,T)) = vs

      | scan vs (t as Free(s,T)) = if is_no s then vs else t::vs

      | scan vs (t as Var((s,i),T)) = t::vs

      | scan vs (Bound i) = vs 

      | scan vs (Abs(s,T,t)) = scan vs t

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

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

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;

(* is_f_x (str2term "q_0/2 * L * x") (*false*);

   is_f_x (str2term "M_b x") (*true*);

  *)

fun vars_str t =

  let

    fun scan vs (Const(s,T)) = vs

      | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs

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

      | scan vs (Bound i) = vs 

      | scan vs (Abs(s,T,t)) = scan vs t

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

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

fun ids2str t =

  let

    fun scan vs (Const(s,T)) = if is_no s then vs else s::vs

      | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs

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

      | scan vs (Bound i) = vs 

      | scan vs (Abs(s,T,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;

fun is_bdv_ (Free (s,_)) = is_bdv s

  | is_bdv_ _ = false;

(* 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 free2int (t as Free (s, _)) = ((str2int s)

    handle _ => error ("free2int: "^term_detail2str t))

  | free2int t = error ("free2int: "^term_detail2str t);

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

fun var2free (t as Const(s,T)) = t

  | var2free (t as Free(s,T)) = t

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

  | var2free (t as Bound i) = t 

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

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

(*27.8.01: doesn't find some subterm ???!???*)

(*2010 free2var -> Logic.varify, but take care of 'Free ("1",_)'*)

fun free2var (t as Const (s, T)) = t

  | free2var (t as Free (s, T)) = if is_no s then t else Var ((s, 0), T)

  | free2var (t as Var ((s, i), T)) = t

  | free2var (t as Bound i) = 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);

(*28.8.01: TODO: get type from head of list: 1 arg less!!!*)

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

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

(*

> val tt = (term_of o the o (parse thy)) "R=(R::real)";

> val TT = type_of tt;

> val ss = list2isalist TT [tt,tt,tt];

> (cterm_of thy) ss;

val it = "[R = R, R = R, R = R]" : cterm  *)

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

  | isapair2pair t = 

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

val listType = Type ("List.list",[Type ("bool",[])]);

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;

(*      

> val il = str2term "[a=b,c=d,e=f]";

> val l = isalist2list il;

> (tracing o terms2str) l;

["a = b","c = d","e = f"]

> val il = str2term "ss___::bool list";

> val l = isalist2list il;

[Free ("ss___", "bool List.list")]

*)

(*review Isabelle2009/src/HOL/Tools/hologic.ML*)

(*val prop = Type ("HOL.Trueprop",[]);      ~/Diss.99/Integers-Isa/tools.sml*)

val bool = Type ("HOL.bool",[]);     (* 2002 Integ.int *)

val Trueprop = HOLogic.Trueprop;

fun mk_prop t = HOLogic.mk_Trueprop t;

val true_as_cterm = cterm_of (Thy_Info.get_theory "HOL") @{term True};

val false_as_cterm = cterm_of (Thy_Info.get_theory "HOL") @{term False};

infixr 5 -->;                    (*2002 /Pure/term.ML *)

infixr --->;			 (*2002 /Pure/term.ML *)

fun S --> T = Type("fun",[S,T]); (*2002 /Pure/term.ML *)

val op ---> = foldr (op -->);    (*2002 /Pure/term.ML *)

fun list_implies ([], B) = B : term (*2002 /term.ML *)

  | list_implies (A::AS, B) = Logic.implies $ A $ list_implies(AS,B);

(** substitution **)

fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =      (* = thm.ML *)

      match_bvs(s, t, if x="" orelse y="" then al

                                          else (x,y)::al)

  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))

  | match_bvs(_,_,al) = al;

fun ren_inst(insts,prop,pat,obj) =              (* = thm.ML *)

  let val ren = match_bvs(pat,obj,[])

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

            Abs(case assoc_string(ren,x) of NONE => x 

	  | SOME(y) => y, T, renAbs(b))

        | renAbs(f$t) = renAbs(f) $ renAbs(t)

        | renAbs(t) = t

  in subst_vars insts (if null(ren) then prop else renAbs(prop)) end;

fun dest_equals' (Const("HOL.eq",_) $ t $ u)  =  (t,u)(* logic.ML: Const("=="*)

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

val lhs_ = (fst o dest_equals');

val rhs_ = (snd o dest_equals');

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

  | is_equality _ = false;

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

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

  | is_expliceq _ = false;

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

  | strip_trueprop t = t;

(*  | strip_trueprop t = raise TERM("strip_trueprop", [t]);

*)

(*.(A1==>...An==>B) goes to (A1==>...An==>).*)

fun strip_imp_prems' (Const("==>", T) $ 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;  (* logic.ML: term -> term list*)

(*

  val thm = real_mult_div_cancel1;

  val prop = (#prop o rep_thm) thm;

  atomt prop;

*** -------------

*** Const ( ==>)

*** . Const ( Trueprop)

*** . . Const ( Not)

*** . . . Const ( op =)

*** . . . . Var ((k, 0), )

*** . . . . Const ( 0)

*** . Const ( Trueprop)

*** . . Const ( op =)                                                          *** .............

  val SOME t = strip_imp_prems' ((#prop o rep_thm) thm);

  atomt t;

*** -------------

*** Const ( ==>)

*** . Const ( Trueprop)

*** . . Const ( Not)

*** . . . Const ( op =)

*** . . . . Var ((k, 0), )

*** . . . . Const ( 0)

  val thm = real_le_anti_sym;

  val prop = (#prop o rep_thm) thm;

  atomt prop;

*** -------------

*** Const ( ==>)

*** . Const ( Trueprop)

*** . . Const ( op <=)

*** . . . Var ((z, 0), )

*** . . . Var ((w, 0), )

*** . Const ( ==>)

*** . . Const ( Trueprop)

*** . . . Const ( op <=)

*** . . . . Var ((w, 0), )

*** . . . . Var ((z, 0), )

*** . . Const ( Trueprop)

*** . . . Const ( op =)

*** .............

  val SOME t = strip_imp_prems' ((#prop o rep_thm) thm);

  atomt t;

*** -------------

*** Const ( ==>)

*** . Const ( Trueprop)

*** . . Const ( op <=)

*** . . . Var ((z, 0), )

*** . . . Var ((w, 0), )

*** . Const ( ==>)

*** . . Const ( Trueprop)

*** . . . Const ( op <=)

*** . . . . Var ((w, 0), )

*** . . . . Var ((z, 0), )

*)

(*. (A1==>...An==>) (B) goes to (A1==>...An==>B), where B is lowest branch.*)

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

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

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

(*

  val thm = real_le_anti_sym;

  val prop = (#prop o rep_thm) thm;

  val concl = Logic.strip_imp_concl prop;

  val SOME prems = strip_imp_prems' prop;

  val prop' = ins_concl prems concl;

  prop = prop';

  atomt prop;

  atomt prop';

*)

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 ([], ys) = 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,[]);

fun var_perm (t, u) = (*2002 Pure/thm.ML *)

  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 str_of_int n = 

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

  else string_of_int n;

(*

> str_of_int 1;

val it = "1" : string                                                          > str_of_int ~1;

val it = "-1" : string

*)

fun power b 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));

(*

> power 2 3;

val it = 8 : int

> power ~2 3;

val it = ~8 : int

> power ~3 2;

val it = 9 : int

> power 3 ~2;

*)

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 sign2 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;

divisors 30;

divisors 32;

divisors 60;

divisors 11;

fun doubles ds = (* ds is ordered *)

  let fun dbls ds [] = ds

	| dbls ds [i] = ds

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

				else dbls ds (i'::is)

  in dbls [] ds end;

(*> doubles [2,3,4];

val it = [] : int list

> doubles [2,3,3,5,5,7];

val it = [5,3] : int list*)

fun squfact 0 = 0

  | squfact 1 = 1

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

(*> squfact 30;

val it = 1 : int

> squfact 32;

val it = 4 : int

> squfact 60;

val it = 2 : int

> squfact 11;

val it = 1 : int*)

fun dest_type (Type(T,[])) = T

  | dest_type T = 

    (atomtyp T;

     error ("... dest_type: not impl. for this type"));

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

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

(*> val t = str2term "(1,2)";

> type_of t = pairT HOLogic.realT HOLogic.realT;

val it = true : bool

*)

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

(*> val t = str2term "(1,2)";

> val Const ("Product_Type.Pair",pT) $ _ $ _ = t;

> pT = PairT HOLogic.realT HOLogic.realT;

val it = true : bool

*)

fun pairt t1 t2 =

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

(*> val t = str2term "(1,2)";

> val (t1, t2) = (str2term "1", str2term "2");

> t = pairt t1 t2;

val it = true : bool*)

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

    (case int_of_str s of

	 SOME s' => s'

       | NONE => error ("num_of_term not for "^ term2str t))

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

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);

(*

val T =  (type_of o term_of o the) (parse thy "#12::real");

val t = mk_factroot "SqRoot.sqrt" T 2 3;

(cterm_of thy) t;

val it = "#2 * sqrt #3 " : cterm

*)

fun var_op_num v op_ optype ntyp n =

  Const (op_, optype) $ v $ 

   Free (str_of_int  n, ntyp);

fun num_op_var v op_ optype ntyp n =

  Const (op_,optype) $  

   Free (str_of_int n, ntyp) $ v;

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

  Const (op_,Top) $ 

  Free (str_of_int n1, T1) $ Free (str_of_int n2, T2);

(*

> val t = num_op_num "Int" 3 4;

> atomty t;

> string_of_cterm ((cterm_of thy) t);

*)

fun const_in str (Const _) = false

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

  | const_in str (Bound _) = false

  | const_in str (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;

(*

> val t = (term_of o the o (parse thy)) "6 + 5 * sqrt 4 + 3";

> const_in "sqrt" t;

val it = true : bool

> val t = (term_of o the o (parse thy)) "6 + 5 * 4 + 3";

> const_in "sqrt" t;

val it = false : bool

*)

(*used for calculating built in binary operations in Isabelle2002->Float.ML*)

(*fun calc "Groups.plus_class.plus"  (n1, n2) = n1+n2

  | calc "Groups.minus_class.minus"  (n1, n2) = n1-n2

  | calc "Groups.times_class.times"  (n1, n2) = n1*n2

  | calc "Fields.inverse_class.divide"(n1, n2) = n1 div n2

  | calc "Atools.pow"(n1, n2) = power n1 n2

  | calc op_ _ = error ("calc: operator = "^op_^" not defined");-----*)

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

    (*FIXME ~~~*)  else (trunc o Math.sqrt o Real.fromInt) n;

fun mk_thmid thmid op_ n1 n2 = 

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

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

  (arg1,arg2,range)

  | dest_binop_typ _ = error "dest_binop_typ: not binary";

(* -----

> val t = (term_of o the o (parse thy)) "#3^#4";

> val hT = type_of (head_of t);

> dest_binop_typ hT;

val it = ("'a","nat","'a") : typ * typ * typ

 ----- *)

(** 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

(*.make uminus uniform: 

   Const ("uminus", _) $ Free ("2", "RealDef.real") --> Free ("-2", _)

to be used immediately before evaluation of numerals; 

see Scripts/calculate.sml .*)

(*2002 fun(*app_num_tr'2 (Const("0",T)) = Free("0",T)

  | app_num_tr'2 (Const("1",T)) = Free("1",T)

  |*)app_num_tr'2 (t as Const("uminus",_) $ Free(s,T)) = 

    (case int_of_str s of SOME i => 

			  if i > 0 then Free("-"^s,T) else Free(s,T)

		       | NONE => t)

(*| app_num_tr'2 (t as Const(s,T)) = t

  | app_num_tr'2 (Const("Numeral.number_of",Type ("fun", [_, T])) $ t) = 

    Free(NumeralSyntax.dest_bin_str t, T)

  | app_num_tr'2 (t as Free(s,T)) = t

  | app_num_tr'2 (t as Var(n,T)) = t

  | app_num_tr'2 (t as Bound i) = t

*)| app_num_tr'2 (Abs(s,T,body)) = Abs(s,T, app_num_tr'2 body)

  | app_num_tr'2 (t1 $ t2) = (app_num_tr'2 t1) $ (app_num_tr'2 t2)

  | app_num_tr'2 t = t;

*)

val uminus_to_string =

    let

	fun dest_num t =

	    (case t of

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

		 (case int_of_str 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;

(*2002 fun num_str thm =

  let 

    val {sign_ref = sign_ref, der = der, maxidx = maxidx,

	    shyps = shyps, hyps = hyps, (*tpairs = tpairs,*) prop = prop} = 

	rep_thm_G thm;

    val prop' = app_num_tr'1 prop;

  in assbl_thm sign_ref der maxidx shyps hyps (*tpairs*) prop' end;*)

fun num_str thm =

  let val (deriv, 

	   {thy_ref = thy_ref, tags = tags, maxidx = maxidx, shyps = shyps, 

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

    val prop' = numbers_to_string prop;

  in assbl_thm deriv thy_ref tags maxidx shyps hyps tpairs prop' end;

fun get_thm' xstring = (*?covers 2009 Thm?!, replaces 2002 fun get_thm :

val it = fn : theory -> xstring -> Thm.thm*)

    Thm (xstring, 

	 num_str (Proof_Context.get_thm (thy2ctxt' "Isac") xstring)); 

(** get types of Free and Abs for parse' **)

(*11.1.00: not used, fix-typed +,*,-,^ instead *)

val dummyT = Type ("dummy",[]);

val dummyT = TVar (("DUMMY",0),[]);

(* assumes only 1 type for numerals 

   and different identifiers for Const, Free and Abs *)

fun get_types t = 

  let

    fun get ts  (Const(s,T)) = (s,T)::ts

      | get ts  (Free(s,T)) = if is_no s 

				then ("#",T)::ts else (s,T)::ts

      | get ts  (Var(n,T)) = ts

      | get ts  (Bound i) = ts

      | get ts  (Abs(s,T,body)) = get ((s,T)::ts)  body

      | get ts  (t1 $ t2) = (get ts  t1) @ (get ts  t2)

  in distinct (get [] t) end;

(*

val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";

get_types t;

*)

(*11.1.00: not used, fix-typed +,*,-,^ instead *)

fun set_types al (Const(s,T)) = 

    (case assoc (al,s) of

       SOME T' => Const(s,T')

     | NONE => (warning ("set_types: no type for "^s); Const(s,dummyT)))

  | set_types al (Free(s,T)) = 

  if is_no s then

    (case assoc (al,"#") of

      SOME T' => Free(s,T')

    | NONE => (warning ("set_types: no type for numerals"); Free(s,T)))

  else (case assoc (al,s) of

	       SOME T' => Free(s,T')

	     | NONE => (warning ("set_types: no type for "^s); Free(s,T)))

  | set_types al (Var(n,T)) = Var(n,T)

  | set_types al (Bound i) = Bound i

  | set_types al (Abs(s,T,body)) = 

		 (case assoc (al,s) of

		    SOME T'  => Abs(s,T', set_types al body)

		  | NONE => (warning ("set_types: no type for "^s);

			     Abs(s,T, set_types al body)))

  | set_types al (t1 $ t2) = (set_types al t1) $ (set_types al t2);

(*

val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";

val al = get_types t;

val t = (term_of o the o (parse thy)) "x = #0 + #-1 * #-4";

atomty t;                         (* 'a *)

val t' = set_types al t;

atomty t';                        (*real*)

(cterm_of thy) t';

val it = "x = #0 + #-1 * #-4" : cterm

val t = (term_of o the o (parse thy)) 

  "#5 * x + x ^^^ #2 = (#2 + x) ^^^ #2";

atomty t;

val t' = set_types al t;

atomty t';

(cterm_of thy) t';

uncaught exception TYPE               (*^^^ is new, NOT in al*)

*)

(** from Descript.ML **)

(** decompose an isa-list to an ML-list 

    i.e. [] belong to the meta-language, too **)

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

  | is_list _ = false;

(* val (SOME ct) = parse thy "lll::real list";

> val ty = (#t o rep_cterm) ct;

> is_list ty;

val it = false : bool

> val (SOME ct) = parse thy "[lll]";

> val ty = (#t o rep_cterm) ct;

> is_list ty;

val it = true : bool *)

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) : term = (*WN100908 neglects 'raise Same.SAME'*)

  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,lev) = t

  in  subst (t,0)  end;

(*instantiate let; necessary for ass_up*)

fun inst_abs thy (Const sT) = Const sT  (*TODO.WN100907 drop thy*)

  | inst_abs thy (Free sT) = Free sT

  | inst_abs thy (Bound n) = Bound n

  | inst_abs thy (Var iT) = Var iT

  | inst_abs thy (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 thy e $ (Abs (v, T2, inst_abs thy b')) end

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

  | inst_abs thy t = t;

(*val scr =    

   "Script Make_fun_by_explicit (f_::real) (v_::real) (eqs_::bool list) = \

   \ (let h_ = (hd o (filterVar f_)) eqs_;                    \

   \      e_1 = hd (dropWhile (ident h_) eqs_);       \

   \      vs_ = dropWhile (ident f_) (Vars h_);                \

   \      v_1 = hd (dropWhile (ident v_) vs_);                \

   \      (s_1::bool list)=(SubProblem(DiffApp_,[univar,equation],[no_met])\

   \                          [BOOL e_1, REAL v_1])\

   \ in Substitute [(v_1 = (rhs o hd) s_1)] h_)";

> val ttt = (term_of o the o (parse thy)) scr;

> tracing(term2str ttt);

> atomt ttt;

*** -------------

*** Const ( DiffApp.Make'_fun'_by'_explicit)

*** . Free ( f_, )

*** . Free ( v_, )

*** . Free ( eqs_, )

*** . Const ( Let)

*** . . Const ( Fun.op o)

*** . . . Const ( List.hd)

*** . . . Const ( DiffApp.filterVar)

*** . . . . Free ( f_, )

*** . . . Free ( eqs_, )

*** . . Abs( h_,..

*** . . . Const ( Let)

*** . . . . Const ( List.hd)

*** . . . . . Const ( List.dropWhile)

*** . . . . . . Const ( Atools.ident)

*** . . . . . . . Bound 0                     <---- Free ( h_, )

*** . . . . . . Free ( eqs_, )

*** . . . . Abs( e_1,..

*** . . . . . Const ( Let)

*** . . . . . . Const ( List.dropWhile)

*** . . . . . . . Const ( Atools.ident)

*** . . . . . . . . Free ( f_, )

*** . . . . . . . Const ( Tools.Vars)

*** . . . . . . . . Bound 1                       <---- Free ( h_, )

*** . . . . . . Abs( vs_,..

*** . . . . . . . Const ( Let)

*** . . . . . . . . Const ( List.hd)

*** . . . . . . . . . Const ( List.dropWhile)

*** . . . . . . . . . . Const ( Atools.ident)

*** . . . . . . . . . . . Free ( v_, )

*** . . . . . . . . . . Bound 0                   <---- Free ( vs_, )

*** . . . . . . . . Abs( v_1,..

*** . . . . . . . . . Const ( Let)

*** . . . . . . . . . . Const ( Script.SubProblem)

*** . . . . . . . . . . . Const ( Pair)

*** . . . . . . . . . . . . Free ( DiffApp_, )

*** . . . . . . . . . . . . Const ( Pair)

*** . . . . . . . . . . . . . Const ( List.list.Cons)

*** . . . . . . . . . . . . . . Free ( univar, )

*** . . . . . . . . . . . . . . Const ( List.list.Cons)

*** . . . . . . . . . . . . . . . Free ( equation, )

*** . . . . . . . . . . . . . . . Const ( List.list.Nil)

*** . . . . . . . . . . . . . Const ( List.list.Cons)

*** . . . . . . . . . . . . . . Free ( no_met, )

*** . . . . . . . . . . . . . . Const ( List.list.Nil)

*** . . . . . . . . . . . Const ( List.list.Cons)

*** . . . . . . . . . . . . Const ( Script.BOOL)

*** . . . . . . . . . . . . . Bound 2                   <----- Free ( e_1, )

*** . . . . . . . . . . . . Const ( List.list.Cons)

*** . . . . . . . . . . . . . Const ( Script.real_)

*** . . . . . . . . . . . . . . Bound 0                 <----- Free ( v_1, )

*** . . . . . . . . . . . . . Const ( List.list.Nil)

*** . . . . . . . . . . Abs( s_1,..

*** . . . . . . . . . . . Const ( Script.Substitute)

*** . . . . . . . . . . . . Const ( List.list.Cons)

*** . . . . . . . . . . . . . Const ( Pair)

*** . . . . . . . . . . . . . . Bound 1                 <----- Free ( v_1, )

*** . . . . . . . . . . . . . . Const ( Fun.op o)

*** . . . . . . . . . . . . . . . Const ( Tools.rhs)

*** . . . . . . . . . . . . . . . Const ( List.hd)

*** . . . . . . . . . . . . . . . Bound 0               <----- Free ( s_1, )

*** . . . . . . . . . . . . . Const ( List.list.Nil)

*** . . . . . . . . . . . . Bound 4                     <----- Free ( h_, )

> val ttt' = inst_abs thy ttt;

> tracing(term2str ttt');

Script Make_fun_by_explicit f_ v_ eqs_ =  

  ... as above ...

> atomt ttt';

*** -------------

*** Const ( DiffApp.Make'_fun'_by'_explicit)

*** . Free ( f_, )

*** . Free ( v_, )

*** . Free ( eqs_, )

*** . Const ( Let)

*** . . Const ( Fun.op o)

*** . . . Const ( List.hd)

*** . . . Const ( DiffApp.filterVar)

*** . . . . Free ( f_, )

*** . . . Free ( eqs_, )

*** . . Abs( h_,..

*** . . . Const ( Let)

*** . . . . Const ( List.hd)

*** . . . . . Const ( List.dropWhile)

*** . . . . . . Const ( Atools.ident)

*** . . . . . . . Free ( h_, )                <---- Bound 0

*** . . . . . . Free ( eqs_, )

*** . . . . Abs( e_1,..

*** . . . . . Const ( Let)

*** . . . . . . Const ( List.dropWhile)

*** . . . . . . . Const ( Atools.ident)

*** . . . . . . . . Free ( f_, )

*** . . . . . . . Const ( Tools.Vars)

*** . . . . . . . . Free ( h_, )                  <---- Bound 1

*** . . . . . . Abs( vs_,..

*** . . . . . . . Const ( Let)

*** . . . . . . . . Const ( List.hd)

*** . . . . . . . . . Const ( List.dropWhile)

*** . . . . . . . . . . Const ( Atools.ident)

*** . . . . . . . . . . . Free ( v_, )

*** . . . . . . . . . . Free ( vs_, )             <---- Bound 0

*** . . . . . . . . Abs( v_1,..

*** . . . . . . . . . Const ( Let)

*** . . . . . . . . . . Const ( Script.SubProblem)

*** . . . . . . . . . . . Const ( Pair)

*** . . . . . . . . . . . . Free ( DiffApp_, )

*** . . . . . . . . . . . . Const ( Pair)

*** . . . . . . . . . . . . . Const ( List.list.Cons)

*** . . . . . . . . . . . . . . Free ( univar, )

*** . . . . . . . . . . . . . . Const ( List.list.Cons)

*** . . . . . . . . . . . . . . . Free ( equation, )

*** . . . . . . . . . . . . . . . Const ( List.list.Nil)

*** . . . . . . . . . . . . . Const ( List.list.Cons)

*** . . . . . . . . . . . . . . Free ( no_met, )

*** . . . . . . . . . . . . . . Const ( List.list.Nil)

*** . . . . . . . . . . . Const ( List.list.Cons)

*** . . . . . . . . . . . . Const ( Script.BOOL)

*** . . . . . . . . . . . . . Free ( e_1, )             <----- Bound 2

*** . . . . . . . . . . . . Const ( List.list.Cons)

*** . . . . . . . . . . . . . Const ( Script.real_)

*** . . . . . . . . . . . . . . Free ( v_1, )           <----- Bound 0

*** . . . . . . . . . . . . . Const ( List.list.Nil)

*** . . . . . . . . . . Abs( s_1,..

*** . . . . . . . . . . . Const ( Script.Substitute)

*** . . . . . . . . . . . . Const ( List.list.Cons)

*** . . . . . . . . . . . . . Const ( Pair)