(* Title:  "ProgLang/calculate.sml"

           test calculation of values for function constants

   Author: Walther Neuper 2000

   (c) copyright due to lincense terms.

*)

"--------------------------------------------------------";

"table of contents --------------------------------------";

"--------------------------------------------------------";

"-calculate.thy: provides 'setup' -----------------------";

"----------- fun norm -----------------------------------";

"----------- check return value of adhoc_thm  ----";

"----------- fun calculate_ --------------------------------------------------------------------";

"----------- calculate from Prog --------------------------------- -----------------------------";

"----------- calculate from script --requires 'setup'----";

"----------- calculate check test-root-equ --------------";

"----------- check calcul,ate bottom up -----------------";

"----------- Prog_Expr.pow Power.power_class.power ---------";

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

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

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

"----------- fun get_pair: examples ------------------------------------------------------------";

"----------- fun adhoc_thm: examples -----------------------------------------------------------";

"----------- fun power -------------------------------------------------------------------------";

"----------- fun divisors ----------------------------------------------------------------------";

"----------- fun doubles, fun squfact ----------------------------------------------------------";

"--------------------------------------------------------";

"--------------------------------------------------------";

"--------------------------------------------------------";

"----------- check return value of adhoc_thm  ----";

"----------- check return value of adhoc_thm  ----";

"----------- check return value of adhoc_thm  ----";

val thy = @{theory "Poly"};

val cal = snd (assoc_calc' thy "is_polyexp");

val t = @{term "(x / x) is_polyexp"};

val SOME (thmID, thm) = adhoc_thm thy cal t;

(HOLogic.dest_Trueprop (Thm.prop_of thm); writeln "all thms wrapped by Trueprop")

handle TERM _ => 

       error "calculate.sml: adhoc_thm must return Trueprop";

"----------- fun calculate_ --------------------------------------------------------------------";

"----------- fun calculate_ --------------------------------------------------------------------";

"----------- fun calculate_ --------------------------------------------------------------------";

(* fun rewrite__set_ \<longrightarrow> fun rew_once works the same way *)

val t = str2term "((1+2)*4/3)^^^2";

val thy = @{theory};

val times =  ("Groups.times_class.times", eval_binop "#mult_") : string * Exec_Def.eval_fn;

val plus =   ("Groups.plus_class.plus",eval_binop "#add_") : string * Exec_Def.eval_fn;

val divide = ("Rings.divide_class.divide"  ,eval_cancel "#divide_e") : string * Exec_Def.eval_fn;

val pow =    ("Prog_Expr.pow"  ,eval_binop "#power_") : string * Exec_Def.eval_fn;

"~~~~~ fun calculate_, args:"; val (thy, isa_fn, t) = (thy, plus, t);

val SOME ("#: 1 + 2 = 3", adh_thm) = adhoc_thm @{theory} isa_fn t;

val SOME (t', []) = rewrite__ thy 0 [] e_rew_ord Rule_Set.empty true adh_thm t;

if UnparseC.term t' = "(3 * 4 / 3) ^^^ 2" then () else error "calculate_  1 + 2 = 3  changed";

"~~~~~ fun calculate_, args:"; val (thy, isa_fn, t) = (thy, times, t');

val SOME ("#: 3 * 4 = 12", adh_thm) = adhoc_thm @{theory} isa_fn t';

val SOME (t'', []) = rewrite__ thy 0 [] e_rew_ord Rule_Set.empty true adh_thm t;

if UnparseC.term t'' = "(12 / 3) ^^^ 2" then () else error "calculate_  3 * 4 = 12  changed";

"~~~~~ fun calculate_, args:"; val (thy, isa_fn, t) = (thy, divide, t'');

val SOME ("#divide_e12_3", adh_thm) = adhoc_thm @{theory} isa_fn t;

val SOME (t''', []) = rewrite__ thy 0 [] e_rew_ord Rule_Set.empty true adh_thm t;

if UnparseC.term t''' = "4 ^^^ 2" then () else error "calculate_  12 / 3 = 4  changed";

"~~~~~ fun calculate_, args:"; val (thy, isa_fn, t) = (thy, pow, t''');

val SOME ("#: 4 ^^^ 2 = 16", adh_thm) = adhoc_thm @{theory} isa_fn t;

val SOME (t'''', []) = rewrite__ thy 0 [] e_rew_ord Rule_Set.empty true adh_thm t;

if UnparseC.term t'''' = "16" then () else error "calculate_  12 / 3 = 4  changed";

"----------- calculate from Prog --------------------------------- -----------------------------";

"----------- calculate from Prog --------------------------------- -----------------------------";

"----------- calculate from Prog --------------------------------- -----------------------------";

val thy = @{theory "Test"};

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

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

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

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") : 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","test_calculate"))*)

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

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

(*[1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; (*nxt = ("Calculate",Calculate "PLUS")*)

(*[1], Res*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; (*nxt = ("Calculate",Calculate "TIMES")*)

(*[2], Res*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; (*nxt = ("Calculate",Calculate "DIVIDE")*)

(*[3], Res*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; (*nxt = ("Calculate",Calculate "POWER")*)

(*[4], Res*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; (*nxt = ("Check_Postcond",Check_Postcond ["calculate","test"])*)

(*[], Res*)val (p,_,f,nxt,_,pt) = me nxt p [1] pt; (*nxt = ("End_Proof'",End_Proof')*)

case f of FormKF "16" => () | _ =>

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

"----------- calculate check test-root-equ --------------";

"----------- calculate check test-root-equ --------------";

"----------- calculate 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 = @{theory "Test"};

 val op_ = the (LibraryC.assoc (KEStore_Elems.get_calcs @{theory}, "DIVIDE"));

 val ct = ThmC_Def.num_to_Free @{term

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

case calculate_ thy op_ ct of

  SOME _ => ()

| NONE => error "calculate_ test-root-equ changed";

(*

           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 = @{theory Test};

 val t = (Thm.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","Real.real") : term*)

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

 val t = (Thm.term_of o the o (parse @{theory Test})) "2 is_const";

 atomty t;

 rewrite_set_ @{theory Test} false tval_rls t;

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

 val t = str2term "2 * x is_const";

 val SOME (str,t') = eval_const "" "" t (@{theory "Isac_Knowledge"});

 UnparseC.term t';

"----------- check calculate bottom up ------------------";

"----------- check calculate bottom up ------------------";

"----------- check calculate bottom up ------------------";

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

 trace_rewrite:=false;

 val thy = @{theory Test};

 val rls = Test_simplify;

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

val SOME (_, t) = eval_cancel "xxx" "Rings.divide_class.divide" t thy;

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

 val t = (Thm.term_of o the o (parse thy)) "(3+5)/2";

case rewrite_set_ thy false rls t of

  SOME (Free ("4", _), []) => ()

| _ => error "rewrite_set_ (3+5)/2 changed";

 val t = (Thm.term_of o the o (parse thy)) "(3+1+2*x)/2";

case rewrite_set_ thy false rls t of

  SOME (Const ("Groups.plus_class.plus", _) $ Free ("2", _) $ Free ("x", _), []) => ()

| _ => error "rewrite_set_ (3+1+2*x)/2 changed";

 trace_rewrite:=false; (*=true3.6.03*)

(*--- 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"

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

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

 trace_rewrite:=false; (*WN130722: =true stopped Test_Isac.thy*)

 val t = (Thm.term_of o the o (parse thy))  "x + (-1 + -3) / 2";

val SOME (res, []) = rewrite_set_ thy false rls t;

if UnparseC.term res = "-2 + x" then () else error "rewrite_set_  x + (-1 + -3) / 2  changed";

"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

@@@ adhoc_thm': NONE

### trying calc. 'pow'

*)

 trace_rewrite:=false; (*WN130722: =true stopped Test_Isac.thy*)

"----------- Prog_Expr.pow Power.power_class.power ---------";

"----------- Prog_Expr.pow Power.power_class.power ---------";

"----------- Prog_Expr.pow Power.power_class.power ---------";

val t = (Thm.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 = str2term "1 ^^^ aaa";

atomty t;

(**** 

*** Const (Prog_Expr.pow, real => real => real)

*** . Free (1, real)

*** . Free (aaa, real)

*** *);

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

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

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

val thy = @{theory Test};

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

val SOME (thmID,thm) = adhoc_thm thy(the(LibraryC.assoc(KEStore_Elems.get_calcs @{theory},"DIVIDE")))t;

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

"12 / 3 = 4";

val thy = @{theory Test};

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

val SOME (thmID,thm) = adhoc_thm thy(the(LibraryC.assoc(KEStore_Elems.get_calcs @{theory},"POWER"))) t;

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

"4 ^ 2 = 16";

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

 val SOME (thmID,thm) = adhoc_thm thy (the(LibraryC.assoc(KEStore_Elems.get_calcs @{theory},"PLUS"))) t;

"1 + 2 = 3";

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

 UnparseC.term t;

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

 val SOME (thmID,thm) = adhoc_thm thy (the(LibraryC.assoc(KEStore_Elems.get_calcs @{theory},"TIMES")))t;

"3 * 4 = 12";

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

 UnparseC.term t;

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

 val SOME (thmID,thm) =adhoc_thm thy(the(LibraryC.assoc(KEStore_Elems.get_calcs @{theory},"DIVIDE")))t;

"12 / 3 = 4";

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

 UnparseC.term t;

"4 ^^^ 2";

 val SOME (thmID,thm) = adhoc_thm thy(the(LibraryC.assoc(KEStore_Elems.get_calcs @{theory},"POWER")))t;

"4 ^^^ 2 = 16";

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

 UnparseC.term t;

"16";

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

 else ();

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

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

  val SOME (thmID,thm) = 

      adhoc_thm thy (the(LibraryC.assoc(KEStore_Elems.get_calcs @{theory},"POWER"))) t;

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

  val (op_, eval_fn) = the (LibraryC.assoc(KEStore_Elems.get_calcs @{theory},"POWER"));

  (*

val op_ = "Prog_Expr.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", 

     assoc_calc' (@{theory "EqSystem"}) "occur_exactly_in" |> snd |> snd,

     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 error "calculate.sml get_pair with 3 args:occur_exactly_in";

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

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

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

val t = str2term "2 * x is_const";

val SOME (str, t') = eval_const "" "" t @{theory Test};

UnparseC.term t';

"(2 * x is_const) = False";

val SOME (t',_) = rewrite_set_ @{theory Test} false tval_rls t;

UnparseC.term t';

"HOL.False";

"----------- fun get_pair: examples ------------------------------------------------------------";

"----------- fun get_pair: examples ------------------------------------------------------------";

"----------- fun get_pair: examples ------------------------------------------------------------";

val thy = @{theory};

val SOME (isa_str, eval_fn) = LibraryC.assoc (KEStore_Elems.get_calcs @{theory}, "PLUS");

val t = (Thm.term_of o the o (parse thy)) "3 + 4";

val SOME (str, term) = get_pair thy isa_str eval_fn t;

if str =  "#: 3 + 4 = 7" andalso UnparseC.term term = "3 + 4 = 7"

then () else error "get_pair  3 + 4  changed";

val t = (Thm.term_of o the o (parse thy)) "(a + 3) + 4";

val SOME (str, term) = get_pair thy isa_str eval_fn t;

if str =  "#: a + 3 + 4 = a + 7" andalso UnparseC.term term = "a + 3 + 4 = a + 7"

then () else error "get_pair  (a + 3) + 4  changed";

val t = (Thm.term_of o the o (parse thy)) "(a + 3) + 4";

val SOME (str, term) = get_pair thy isa_str eval_fn t;

if str =  "#: a + 3 + 4 = a + 7" andalso UnparseC.term term = "a + 3 + 4 = a + 7"

then () else error "get_pair  (a + 3) + 4  changed";

val t = (Thm.term_of o the o (parse thy)) "x = 5 * (3 + (4 + a))";

val SOME (str, term) = get_pair thy isa_str eval_fn t;

if str =  "#: 3 + (4 + a) = 7 + a" andalso UnparseC.term term = "3 + (4 + a) = 7 + a"

then ((* !!! gets subterm !!!*)) else error "get_pair  x = 5 * (3 + (4 + a))  (subterm) changed";

val SOME (isa_str, eval_fn) = LibraryC.assoc (KEStore_Elems.get_calcs @{theory}, "DIVIDE");

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

val SOME (str, term) = get_pair thy isa_str eval_fn t;

if str =  "#divide_e-4_-2" andalso UnparseC.term term = "-4 / -2 = 2"

then () else error "get_pair  -4 / -2   changed";

val SOME (isa_str, eval_fn) = LibraryC.assoc (KEStore_Elems.get_calcs @{theory}, "POWER");

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

val SOME (str, term) = get_pair thy isa_str eval_fn t;

if str =  "#: 2 ^^^ 3 = 8" andalso UnparseC.term term = "2 ^^^ 3 = 8"

then () else error "get_pair  2 ^^^ 3   changed";

"----------- fun adhoc_thm: examples -----------------------------------------------------------";

"----------- fun adhoc_thm: examples -----------------------------------------------------------";

"----------- fun adhoc_thm: examples -----------------------------------------------------------";

(*--------------------------------------------------------------------vvvvvvvvvv*)

val SOME (isa_str, eval_fn) = LibraryC.assoc (KEStore_Elems.get_calcs @{theory}, "is_const");

val SOME t = parseNEW @{context} "9 is_const";

val SOME (str, thm) = adhoc_thm thy (isa_str, eval_fn) t;

if str = "#is_const_9_" andalso ThmC_Def.string_of_thm thm = "(9 is_const) = True"

then () else error "adhoc_thm  9 is_const  changed";

case assoc_calc thy "Orderings.ord_class.less" of

  "le" => () | _ => error "Orderings.ord_class.less <-> le changed";

(*--------------------------------------------------------------------vvvvvvvvvv*)

val SOME (isa_str, eval_fn) = LibraryC.assoc (KEStore_Elems.get_calcs @{theory}, "le");

val SOME t = parseNEW @{context} "4 < 4";

val SOME (str, thm) = adhoc_thm thy (isa_str, eval_fn) t;

if str = "#less_4_4" andalso ThmC_Def.string_of_thm thm = "(4 < 4) = False"

then () else error "adhoc_thm  4 < 4  changed";

val SOME t = parseNEW @{context} "a < 4";

case adhoc_thm thy (isa_str, eval_fn) t of

NONE => () | _ => error "adhoc_thm  a < 4  does NOT result in NONE";

(*--------------------------------------------------------------------vvvvvvvvvv*)

val SOME (isa_str, eval_fn) = LibraryC.assoc (KEStore_Elems.get_calcs @{theory}, "PLUS");

val SOME t = parseNEW @{context} "1 + 2";

val SOME (str, thm) = adhoc_thm thy (isa_str, eval_fn) t;

if str = "#: 1 + 2 = 3" andalso ThmC_Def.string_of_thm thm = "1 + 2 = 3"

then () else error "adhoc_thm  1 + 2  changed";

(*--------------------------------------------------------------------vvvvvvvvvv*)

val SOME (isa_str, eval_fn) = LibraryC.assoc (KEStore_Elems.get_calcs @{theory}, "DIVIDE");

val SOME t = parseNEW @{context} "6 / -8";

val SOME (str, thm) = adhoc_thm thy (isa_str, eval_fn) t;

if str = "#divide_e6_-8" andalso ThmC_Def.string_of_thm thm = "6 / -8 = -3 / 4"

then () else error "adhoc_thm  1 + 2  changed";

case assoc_calc thy "Prog_Expr.ident" of

  "ident" => () | _ => error "Prog_Expr.ident <-> ident  changed";

(*--------------------------------------------------------------------vvvvvvvvvv*)

val SOME (isa_str, eval_fn) = LibraryC.assoc (KEStore_Elems.get_calcs @{theory}, "ident");

val SOME t = parseNEW @{context} "3 =!= 3";

val SOME (str, thm) = adhoc_thm thy (isa_str, eval_fn) t;

if str = "#ident_(3)_(3)" andalso ThmC_Def.string_of_thm thm = "(3 =!= 3) = True"

then () else error "adhoc_thm  (3 =!= 3)  changed";

val SOME t = parseNEW @{context} "\<not> (4 + (4 * x + x ^ 2) =!= 0)";

val SOME (str, thm) = adhoc_thm thy (isa_str, eval_fn) t;

if str = "#ident_(4 + (4 * x + x ^ 2))_(0)" andalso ThmC_Def.string_of_thm thm = "(4 + (4 * x + x ^ 2) =!= 0) = False"

then () else error "adhoc_thm  (\<not> (4 + (4 * x + x ^ 2) =!= 0))  changed";

"----------- fun power -------------------------------------------------------------------------";

"----------- fun power -------------------------------------------------------------------------";

"----------- fun power -------------------------------------------------------------------------";

if power 2 3 = 8 then () else error "power 2 3 = 8";

if power ~2 3 = ~8 then () else error "power ~2 3 = ~8";

if power ~3 2 = 9 then () else error "power ~3 2 = 9";

(power 3 ~2; error "power 3 ~2: should raise an exn") handle _ => 000;

"----------- fun divisors ----------------------------------------------------------------------";

"----------- fun divisors ----------------------------------------------------------------------";

"----------- fun divisors ----------------------------------------------------------------------";

if divisors 30 = [5, 3, 2] then () else error "divisors 30 = [5, 3, 2]";

if divisors 32 = [2, 2, 2, 2, 2] then () else error "divisors 32 = [2, 2, 2, 2, 2]";

if divisors 60 = [5, 3, 2, 2] then () else error "divisors 60 = [5, 3, 2, 2]";

if divisors 11 = [11] then () else error "divisors 11 = [11]";

"----------- fun doubles, fun squfact ----------------------------------------------------------";

"----------- fun doubles, fun squfact ----------------------------------------------------------";

"----------- fun doubles, fun squfact ----------------------------------------------------------";

if doubles [2,3,4] = [] then () else error "doubles [2,3,4] changed";

if doubles [2,3,3,5,5,7] = [5, 3] then () else error "doubles [2,3,3,5,5,7] changed";

if squfact 30 = 1 then () else error "squfact  30  changed";

if squfact 32 = 4 then () else error "squfact  32  changed";

if squfact 60 = 2 then () else error "squfact  60  changed";

if squfact 11 = 1 then () else error "squfact  11  changed";