(* test calculation of values for function constants

   (c) Walther Neuper 2000

use"../smltest/Scripts/calculate.sml";

use"calculate.sml";

*)

" ================= calculate.sml: calculate_ ======================== ";

" ================= calculate.sml: aus script ======================== ";

" ================= calculate.sml: 2.8.02 check test-root-equ ======== ";

"--------------(4): check bottom up: ---------------------------";

" ================= calculate.sml:10.8.02 2002:///->/ ======== ";

" ================= calculate.sml: calculate_ 2002 =================== ";

"----------- get_pair with 3 args --------------------------------";

" ================= eval_binop Float  =================== ";

"------------------ 3.6.03 (2 * x is_const) ---------------------------";

(*  [("Vars",("Tools.Vars",fn)),("Length",("Tools.Length",fn)),

     ("Nth",("Tools.Nth",fn)),

   ("power_",("Atools.pow",fn)),("plus",("op +",fn)),("times",("op *",fn)),

   ("is_const",("Atools.is'_const",fn)),

   ("le",("op <",fn)),("leq",("op <=",fn)),

   ("ident",("Atools.ident",fn))]                                                      *)

val thy' = "Isac.thy";

" ================= calculate.sml: calculate_ ======================== ";

" ================= calculate.sml: calculate_ ======================== ";

" ================= calculate.sml: calculate_ ======================== ";

val thy = Test.thy;

val t = (term_of o the o (parse thy)) "1+2";

val Some (thmID,thm) = get_calculation_ thy (the(assoc(calclist,"plus"))) t;

val t = (term_of o the o (parse thy)) "((1+2)*4/3)^^^2";

val Some (thmID,thm) = get_calculation_ thy (the(assoc(calclist,"plus"))) t;

val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t;

Sign.string_of_term (sign_of thy) t;

(*val it = "(#3 * #4 // #3) ^^^ #2" : string*)

val Some (thmID,thm) = get_calculation_ thy (the(assoc(calclist,"times"))) t;

val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t;

Sign.string_of_term (sign_of thy) t;

(*val it = "(#12 // #3) ^^^ #2" : string*)

val Some (thmID,thm) = get_calculation_ thy(the(assoc(calclist,"divide_")))t;

val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t;

Sign.string_of_term (sign_of thy) t;

(*it = "#4 ^^^ #2" : string*)

val Some (thmID,thm) = get_calculation_ thy(the(assoc(calclist,"power_")))t;

val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t;

Sign.string_of_term (sign_of thy) t;

(*val it = "#16" : string*)

if it <> "16" then raise error "calculate.sml: new behaviour in calculate_"

else ();

" ================= calculate.sml: aus script ======================== ";

" ================= calculate.sml: aus script ======================== ";

" ================= calculate.sml: aus script ======================== ";

store_pbt

 (prep_pbt Test.thy "pbl_ttest" [] e_pblID

 (["test"],

  [],

  e_rls, None, []));

store_pbt

 (prep_pbt Test.thy "pbl_ttest_calc" [] e_pblID

 (["calculate","test"],

  [("#Given" ,["realTestGiven t_"]),

   ("#Find"  ,["realTestFind s_"])

   ],

  e_rls, None, [["Test","test_calculate"]]));

store_met

 (prep_met Test.thy "met_testcal" [] e_metID

 (["Test","test_calculate"]:metID,

  [("#Given" ,["realTestGiven t_"]),

   ("#Find"  ,["realTestFind s_"])

   ],

  {rew_ord'="sqrt_right",rls'=tval_rls,srls=e_rls,prls=e_rls,

   calc=[("plus"    ,("op +"        ,eval_binop "#add_")),

	 ("times"   ,("op *"        ,eval_binop "#mult_")),

	 ("divide_" ,("HOL.divide"  ,eval_cancel "#divide_")),

	 ("power_"  ,("Atools.pow"  ,eval_binop "#power_"))],

   crls=tval_rls, nrls=e_rls(*,

   asm_rls=[],asm_thm=[]*)},

  "Script STest_simplify (t_::real) =          \

  \(Repeat                                        \

  \ ((Try (Repeat (Calculate plus))) @@   \

  \  (Try (Repeat (Calculate times))) @@  \

  \  (Try (Repeat (Calculate divide_))) @@ \

  \  (Try (Repeat (Calculate power_))))) t_"

   ));

val fmz = ["realTestGiven (((1+2)*4/3)^^^2)","realTestFind s"];

val (dI',pI',mI') =

  ("Test.thy",["calculate","test"],["Test","test_calculate"]);

(*val p = e_pos'; val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c  EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt =("Add_Given",Add_Given "realTestGiven (((#1 + #2) * #4 // #3) ^^^#2)")*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt = ("Add_Find",Add_Find "realTestFind s") : string * tac*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt = ("Specify_Theory",Specify_Theory "Test.thy") : string * tac*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt = ("Specify_Problem",Specify_Problem ["calculate","test"])*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt = ("Specify_Method",Specify_Method ("Test.thy","test_calculate"))*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt = ("Apply_Method",Apply_Method ("Test.thy","test_calculate"))*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt = ("Calculate",Calculate "plus")*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt = ("Calculate",Calculate "times")*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt = ("Calculate",Calculate "divide_")*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt = ("Calculate",Calculate "power_")*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt = ("Check_Postcond",Check_Postcond ["calculate","test"])*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt = ("End_Proof'",End_Proof')*)

if f = Form' (FormKF (~1,EdUndef,0,Nundef,"16")) then ()

else raise error "calculate.sml: script test_calculate changed behaviour";

" ================= calculate.sml: 2.8.02 check test-root-equ ======== ";

" ================= calculate.sml: 2.8.02 check test-root-equ ======== ";

" ================= calculate.sml: 2.8.02 check test-root-equ ======== ";

(*(1): 2nd Test_simplify didn't work:

val ct =

  "sqrt (x ^^^ 2 + -3 * x) = (-3 + 2 * x + -1 * (9 + 4 * x)) / (-1 * 2)"

> val rls = ("Test_simplify");

> val (ct,_) = the (rewrite_set thy' ("tval_rls") false rls ct);

val ct = "sqrt (x ^^^ 2 + -3 * x) =

(-9) / (-2) + (-3 / (-2) + (x * ((-4) / (-2)) + x * (2 / (-2))))";

ie. cancel does not work properly

*)

 val thy = "Test.thy";

 val op_ = "divide_";

 val ct = "sqrt (x ^^^ 2 + -3 * x) =\

 \(-9) / (-2) + (-3 / (-2) + (x * ((-4) / (-2)) + x * (2 / (-2))))";

 val Some (ct,_) = calculate thy (the(assoc(calclist,op_))) ct;

 writeln ct;

(*

           sqrt (x ^^^ 2 + -3 * x) =\

 \(-9) / (-2) + (-3 / (-2) + (x * ((-4) / (-2)) + x * (2 / (-2))))

............... does not work *)

(*--------------(2): does divide work in Test_simplify ?: ------*)

 val thy = Test.thy;

 val t = (term_of o the o (parse thy)) "6 / 2";

 val rls = Test_simplify;

 val (t,_) = the (rewrite_set_ thy false rls t);

(*val t = Free ("3","RealDef.real") : term*)

 val thy = "Test.thy";

 val t = "6 / 2";

 val rls = "Test_simplify";

 val (t,_) = the (rewrite_set thy false rls t);

(*val t = "3" : string

      ....... works, thus: which rule in SqRoot_simplify works differently ?*)

(*--------------(3): is_const works ?: -------------------------------------*)

 val t = (term_of o the o (parse Test.thy)) "2 is_const";

 atomty t;

 rewrite_set_ Test.thy false tval_rls t;

(*val it = Some (Const ("True","bool"),[]) ... works*)

 val t = str2term "2 * x is_const";

 val Some (str,t') = eval_const "" "" t Isac.thy;

 term2str t';

"--------------(4): check bottom up: ---------------------------";

(*-------------- eval_cancel works: *)

 trace_rewrite:=true;

 val thy = Test.thy;

 val t = (term_of o the o (parse thy)) "(-4) / 2";

 val Some (_,t) = eval_cancel "xxx" "HOL.divide" t thy;

 term2str t;

"-4 / 2 = (-2)";

(*-------------- but ... *)

 val ct = "x + (-4) / 2";

 val (ct,_) = the (rewrite_set thy' false rls ct);

"(-2) + x";

(*-------------- while ... *)

 val ct = "(-4) / 2";

 val (ct,_) = the (rewrite_set thy'  false rls ct);

"-2";

(*--------------(5): reproduce (1) with simpler term: ------------*)

 val thy = "Test.thy";

 val t = "(3+5)/2";

 val (t,_) = the (rewrite_set thy false rls t);

(*val t = "4" ... works*)

 val t = "(3+1+2*x)/2";

 val (t,_) = the (rewrite_set thy false rls t);

(*val t = "2 + x" ... works*)

 trace_rewrite:=true; (*3.6.03*)

 val thy = "Test.thy";

 val rls = "Test_simplify";

 val t = "(3+(1+2*x))/2";

 val (t,_) = the (rewrite_set thy false rls t);

(*val t = "2 + x" ... works: give up----------------------------------------*)

 trace_rewrite:=false; 

 trace_rewrite:=true; (*3.6.03*)

 val thy = Test.thy;

 val rls = Test_simplify;

 val t = str2term "(3+(1+2*x))/2";

 val Some (t',asm) = rewrite_set_ thy false rls t;

 term2str t';

(*val t = "2 + x" ... works: give up----------------------------------------*)

 trace_rewrite:=false; 

(*--- trace_rewrite before correction of ... --------------------

 val ct = "(-3 + 2 * x + -1) / 2";

 val (ct,_) = the (rewrite_set thy'  false rls ct);

:

### trying thm 'root_ge0_2'

### rewrite_set_: x + (-1 + -3) / 2

### trying thm 'radd_real_const_eq'

### trying thm 'radd_real_const'

### rewrite_set_: x + (-4) / 2

### trying thm 'rcollect_right'

:

"x + (-4) / 2"

-------------------------------------while before Isabelle20002:

 val ct = "(#-3 + #2 * x + #-1) // #2";

 val (ct,_) = the (rewrite_set thy'  false rls ct);

:

### trying thm 'root_ge0_2'

### rewrite_set_: x + (#-1 + #-3) // #2

### trying thm 'radd_real_const_eq'

### trying thm 'radd_real_const'

### rewrite_set_: x + #-4 // #2

### rewrite_set_: x + #-2

### trying thm 'rcollect_right'

:

"#-2 + x"

-----------------------------------------------------------------*)

 toggle trace_rewrite;

(*===================*)

 trace_rewrite:=true;

 val thy' = "Test.thy";

 val rls = "Test_simplify";		

 val ct = "x + (-1 + -3) / 2";

 val (ct,_) = the (rewrite_set thy'  false rls ct);	

"x + (-4) / 2";						

(*

### trying calc. 'cancel'

@@@ get_pair: binop, t = x + (-4) / 2

@@@ get_pair: t else

@@@ get_pair: t else -> None

@@@ get_pair: binop, t = (-4) / 2

@@@ get_pair: then 1

@@@ get_pair: t -> None

@@@ get_pair: t1 -> None

@@@ get_calculation: None

### trying calc. 'pow'

*)

 trace_rewrite:=true;

 val thy' = "Test.thy";

 val rls = "Test_simplify";		

 val ct = "x + (-4) / 2";

 val (ct,_) = the (rewrite_set thy'  false rls ct);	

"(-2) + x";

(*

### trying calc. 'cancel'

@@@ get_pair: binop, t = x + -4 / 2

@@@ get_pair: t else

@@@ get_pair: t else -> None

@@@ get_pair: binop, t = -4 / 2

@@@ get_pair: then 1

@@@ get_calculation: Some #cancel_-4_2

### calc. to: x + (-2)

### trying calc. 'cancel'

*)

 trace_rewrite:=false;

" ================= calculate.sml:10.8.02 2002:///->/ ======== ";

" ================= calculate.sml:10.8.02 2002:///->/ ======== ";

" ================= calculate.sml:10.8.02 2002:///->/ ======== ";

" ----------------- rewriting works ? -----------------------";

 val thy = Isac.thy;

 val prop = (#prop o rep_thm) real_divide_1;

 atomty prop;

(*** -------------

*** Const ( Trueprop, bool => prop)

*** . Const ( op =, [real, real] => bool)

*** . . Const ( HOL.divide, [real, real] => real)

*** . . . Var ((x, 0), real)

*** . . . Const ( 1, real)

*** . . Var ((x, 0), real) *)

 val prop' = (#prop o rep_thm o num_str) real_divide_1;

 atomty prop';

(*** -------------

*** Const ( Trueprop, bool => prop)

*** . Const ( op =, [real, real] => bool)

*** . . Const ( HOL.divide, [real, real] => real)

*** . . . Var ((x, 0), real)

*** . . . Free ( 1, real)   (*app_num_tr'*)

*** . . Var ((x, 0), real)*)

 val t = (term_of o the o (parseold thy)) "aaa/1";

 atomty t;

(*** -------------

*** Const ( HOL.divide, ['a, 'a] => 'a)

*** . Free ( aaa, 'a)

*** . Free ( 1, 'a) *)

 val t = (term_of o the o (parse thy)) "aaa/1";

 atomty t;

(*** -------------

*** Const ( HOL.divide, [real, real] => real)

*** . Free ( aaa, real)

*** . Free ( 1, real)  *)

 val thm = num_str real_divide_1;

 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t;

(*val t = Free ("aaa","RealDef.real") : term*)

 val prop = (#prop o rep_thm) realpow_eq_one;

 atomty prop;

(*** -------------

*** Const ( Trueprop, bool => prop)

*** . Const ( op =, [real, real] => bool)

*** . . Const ( Nat.power, [real, nat] => real)

*** . . . Const ( 1, real)

*** . . . Var ((n, 0), nat)

*** . . Const ( 1, real) *)

 val prop' = (#prop o rep_thm o num_str) realpow_eq_one;

 atomty prop';

(*** -------------

*** Const ( Trueprop, bool => prop)

*** . Const ( op =, [real, real] => bool)

*** . . Const ( Nat.power, [real, nat] => real)

*** . . . Free ( 1, real)

*** . . . Var ((n, 0), nat)

*** . . Free ( 1, real)*)

 val t = (term_of o the o (parseold thy)) "1 ^ aaa";

 atomty t;

(*** -------------

*** Const ( Nat.power, ['a, nat] => 'a)

*** . Free ( 1, 'a)

*** . Free ( aaa, nat) *)

 val t = (term_of o the o (parse thy)) "1 ^ aaa";

 atomty t;

(*** -------------

*** Const ( Nat.power, [real, nat] => real)

*** . Free ( 1, real)

*** . Free ( aaa, nat) .......................... nat !!! *)

 val thm = num_str realpow_eq_one;

 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t;

(*val t = Free ("1","RealDef.real") : term*)

" ================= calculate.sml: calculate_ 2002 =================== ";

" ================= calculate.sml: calculate_ 2002 =================== ";

" ================= calculate.sml: calculate_ 2002 =================== ";

val thy = Test.thy;

val t = (term_of o the o (parse thy)) "12 / 3";

val Some (thmID,thm) = get_calculation_ thy(the(assoc(calclist,"divide_")))t;

val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t;

"12 / 3 = 4";

val thy = Test.thy;

val t = (term_of o the o (parse thy)) "4 ^^^ 2";

val Some (thmID,thm) = get_calculation_ thy(the(assoc(calclist,"power_"))) t;

val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t;

"4 ^ 2 = 16";

 val t = (term_of o the o (parse thy)) "((1 + 2) * 4 / 3) ^^^ 2";

 val Some (thmID,thm) = get_calculation_ thy (the(assoc(calclist,"plus"))) t;

"1 + 2 = 3";

 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t;

 Sign.string_of_term (sign_of thy) t;

"(3 * 4 / 3) ^^^ 2";

 val Some (thmID,thm) = get_calculation_ thy (the(assoc(calclist,"times")))t;

"3 * 4 = 12";

 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t;

 Sign.string_of_term (sign_of thy) t;

"(12 / 3) ^^^ 2";

 val Some (thmID,thm) =get_calculation_ thy(the(assoc(calclist,"divide_")))t;

"12 / 3 = 4";

 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t;

 Sign.string_of_term (sign_of thy) t;

"4 ^^^ 2";

 val Some (thmID,thm) = get_calculation_ thy(the(assoc(calclist,"power_")))t;

"4 ^^^ 2 = 16";

 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t;

 Sign.string_of_term (sign_of thy) t;

"16";

 if it <> "16" then raise error "calculate.sml: new behaviour in calculate_"

 else ();

(*13.9.02 *** calc: operator = pow not defined*)

  val t = (term_of o the o (parse thy)) "3^^^2";

  val Some (thmID,thm) = 

      get_calculation_ thy (the(assoc(calclist,"power_"))) t;

(*** calc: operator = pow not defined*)

  val (op_, eval_fn) = the (assoc(calclist,"power_"));

  (*

val op_ = "Atools.pow" : string

val eval_fn = fn : string -> term -> theory -> (string * term) option*)

  val Some (thmid,t') = get_pair thy op_ eval_fn t;

(*** calc: operator = pow not defined*)

  val Some (id,t') = eval_fn op_ t thy;

(*** calc: operator = pow not defined*)

  val (thmid, (Const (op0,t0) $ Free (n1,t1) $ Free(n2,t2))) = (op_, t);

  val Some (id,t') = eval_binop thmid op_ t thy;

(*** calc: operator = pow not defined*)

"----------- get_pair with 3 args --------------------------------";

"----------- get_pair with 3 args --------------------------------";

"----------- get_pair with 3 args --------------------------------";

val (thy, op_, ef, arg) =

    (thy, "EqSystem.occur'_exactly'_in", 

     snd (the (assoc(!calclist',"occur_exactly_in"))),

     str2term

      "[] from_ [c, c_2, c_3, c_4] occur_exactly_in -1 * (q_0 * L ^^^ 2) / 2"

      );

val Some (str, simpl) = get_pair thy op_ ef arg;

if str = 

"[] from_ [c, c_2, c_3, c_4] occur_exactly_in -1 * (q_0 * L ^^^ 2) / 2 = True"

then () else raise error "calculate.sml get_pair with 3 args:occur_exactly_in";

" ================= eval_binop Float  =================== ";

val t = str2term "Float ((1,2),(0,0))";

atomty t;

val Const ("Float.Float",_) $

	  (Const ("Pair",_) $ 

		 (Const ("Pair",_) $ Free (i1,_) $ Free (i2,_)) $ _) = t;

val t = str2term "Float ((1,2),(0,0)) * Float ((3,4),(0,0))";

atomty t;

(*WN.10.4.03 eval_binop Float *)

"------------------ 3.6.03 (2 * x is_const) ---------------------------";

"------------------ 3.6.03 (2 * x is_const) ---------------------------";

"------------------ 3.6.03 (2 * x is_const) ---------------------------";

val t = str2term "2 * x is_const";

val Some (str, t') = eval_const "" "" t Test.thy;

term2str t';

"(2 * x is_const) = False";

val Some (t',_) = rewrite_set_ Test.thy false tval_rls t;

term2str t';

"False";