(* collecting all knowledge for Root

   created by: 

         date: 

   changed by: rlang

   last change by: rlang

             date: 02.10.24

*)

(* use"../knowledge/Root.ML";

   use"Knowledge/Root.ML";

   use"Root.ML";

   remove_thy"Root";

   use_thy"Knowledge/Isac";

   use"ROOT.ML";

   cd"knowledge";

 *)

"******* Root.ML begin *******";

theory' := overwritel (!theory', [("Root.thy",Root.thy)]);                      

(*-------------------------functions---------------------*)

(*evaluation square-root over the integers*)

fun eval_sqrt (thmid:string) (op_:string) (t as 

	       (Const(op0,t0) $ arg)) thy = 

    (case arg of 

	Free (n1,t1) =>

	(case int_of_str n1 of

	     SOME ni => 

	     if ni < 0 then NONE

	     else

		 let val fact = squfact ni;

		 in if fact*fact = ni 

		    then SOME ("#sqrt #"^(string_of_int ni)^" = #"

			       ^(string_of_int (if ni = 0 then 0

						else ni div fact)),

			       Trueprop $ mk_equality (t, term_of_num t1 fact))

		    else if fact = 1 then NONE

		    else SOME ("#sqrt #"^(string_of_int ni)^" = sqrt (#"

			       ^(string_of_int fact)^" * #"

			       ^(string_of_int fact)^" * #"

			       ^(string_of_int (ni div (fact*fact))^")"),

			       Trueprop $ 

					(mk_equality 

					     (t, 

					      (mk_factroot op0 t1 fact 

							   (ni div (fact*fact))))))

	     end

	   | NONE => NONE)

      | _ => NONE)

  | eval_sqrt _ _ _ _ = NONE;

(*val (thmid, op_, t as Const(op0,t0) $ arg) = ("","", str2term "sqrt 0");

> eval_sqrt thmid op_ t thy;

> val Free (n1,t1) = arg; 

> val SOME ni = int_of_str n1;

*)

calclist':= overwritel (!calclist', 

   [("SQRT"    ,("Root.sqrt"   ,eval_sqrt "#sqrt_"))

    (*different types for 'sqrt 4' --- 'Calculate sqrt_'*)

    ]);

local (* Vers. 7.10.99.A *)

open Term;  (* for type order = EQUAL | LESS | GREATER *)

fun pr_ord EQUAL = "EQUAL"

  | pr_ord LESS  = "LESS"

  | pr_ord GREATER = "GREATER";

fun dest_hd' (Const (a, T)) =                          (* ~ term.ML *)

  (case a of "Root.sqrt"  => ((("|||", 0), T), 0)      (*WN greatest *)

	   | _ => (((a, 0), T), 0))

  | dest_hd' (Free (a, T)) = (((a, 0), T), 1)

  | dest_hd' (Var v) = (v, 2)

  | dest_hd' (Bound i) = ((("", i), dummyT), 3)

  | dest_hd' (Abs (_, T, _)) = ((("", 0), T), 4);

fun size_of_term' (Const(str,_) $ t) =

    (case str of "Root.sqrt"  => (1000 + size_of_term' t)

               | _ => 1 + size_of_term' t)

  | size_of_term' (Abs (_,_,body)) = 1 + size_of_term' body

  | size_of_term' (f $ t) = size_of_term' f  +  size_of_term' t

  | size_of_term' _ = 1;

fun term_ord' pr thy (Abs (_, T, t), Abs(_, U, u)) =       (* ~ term.ML *)

      (case term_ord' pr thy (t, u) of EQUAL => typ_ord (T, U) | ord => ord)

  | term_ord' pr thy (t, u) =

      (if pr then 

	 let

	   val (f, ts) = strip_comb t and (g, us) = strip_comb u;

	   val _=writeln("t= f@ts= \""^

	      ((Syntax.string_of_term (thy2ctxt thy)) f)^"\" @ \"["^

	      (commas(map(Syntax.string_of_term (thy2ctxt thy)) ts))^"]\"");

	   val _=writeln("u= g@us= \""^

	      ((Syntax.string_of_term (thy2ctxt thy)) g)^"\" @ \"["^

	      (commas(map(Syntax.string_of_term (thy2ctxt thy)) us))^"]\"");

	   val _=writeln("size_of_term(t,u)= ("^

	      (string_of_int(size_of_term' t))^", "^

	      (string_of_int(size_of_term' u))^")");

	   val _=writeln("hd_ord(f,g)      = "^((pr_ord o hd_ord)(f,g)));

	   val _=writeln("terms_ord(ts,us) = "^

			   ((pr_ord o terms_ord str false)(ts,us)));

	   val _=writeln("-------");

	 in () end

       else ();

	 case int_ord (size_of_term' t, size_of_term' u) of

	   EQUAL =>

	     let val (f, ts) = strip_comb t and (g, us) = strip_comb u in

	       (case hd_ord (f, g) of EQUAL => (terms_ord str pr) (ts, us) 

	     | ord => ord)

	     end

	 | ord => ord)

and hd_ord (f, g) =                                        (* ~ term.ML *)

  prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd' f, dest_hd' g)

and terms_ord str pr (ts, us) = 

    list_ord (term_ord' pr (assoc_thy "Isac.thy"))(ts, us);

in

(* associates a+(b+c) => (a+b)+c = a+b+c ... avoiding parentheses 

  by (1) size_of_term: less(!) to right, size_of 'sqrt (...)' = 1 

     (2) hd_ord: greater to right, 'sqrt' < numerals < variables

     (3) terms_ord: recurs. on args, greater to right

*)

(*args

   pr: print trace, WN0509 'sqrt_right true' not used anymore

   thy:

   subst: no bound variables, only Root.sqrt

   tu: the terms to compare (t1, t2) ... *)

fun sqrt_right (pr:bool) thy (_:subst) tu = 

    (term_ord' pr thy(***) tu = LESS );

end;

rew_ord' := overwritel (!rew_ord',

[("termlessI", termlessI),

 ("sqrt_right", sqrt_right false (theory "Pure"))

 ]);

(*-------------------------rulse-------------------------*)

val Root_crls = 

      append_rls "Root_crls" Atools_erls 

       [Thm  ("real_unari_minus",num_str real_unari_minus),

        Calc ("Root.sqrt" ,eval_sqrt "#sqrt_"),

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

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

        Calc ("op +", eval_binop "#add_"), 

        Calc ("op -", eval_binop "#sub_"),

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

        Calc ("op =",eval_equal "#equal_") 

        ];

val Root_erls = 

      append_rls "Root_erls" Atools_erls 

       [Thm  ("real_unari_minus",num_str real_unari_minus),

        Calc ("Root.sqrt" ,eval_sqrt "#sqrt_"),

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

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

        Calc ("op +", eval_binop "#add_"), 

        Calc ("op -", eval_binop "#sub_"),

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

        Calc ("op =",eval_equal "#equal_") 

        ];

ruleset' := overwritelthy thy (!ruleset',

			[("Root_erls",Root_erls) (*FIXXXME:del with rls.rls'*) 

			 ]);

val make_rooteq = prep_rls(

  Rls{id = "make_rooteq", preconds = []:term list, 

      rew_ord = ("sqrt_right", sqrt_right false Root.thy),

      erls = Atools_erls, srls = Erls,

      calc = [],

      (*asm_thm = [],*)

      rules = [Thm ("real_diff_minus",num_str real_diff_minus),			

	       (*"a - b = a + (-1) * b"*)

	       Thm ("real_add_mult_distrib" ,num_str real_add_mult_distrib),	

	       (*"(z1.0 + z2.0) * w = z1.0 * w + z2.0 * w"*)

	       Thm ("real_add_mult_distrib2",num_str real_add_mult_distrib2),	

	       (*"w * (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)

	       Thm ("real_diff_mult_distrib" ,num_str real_diff_mult_distrib),	

	       (*"(z1.0 - z2.0) * w = z1.0 * w - z2.0 * w"*)

	       Thm ("real_diff_mult_distrib2",num_str real_diff_mult_distrib2),	

	       (*"w * (z1.0 - z2.0) = w * z1.0 - w * z2.0"*)

	       Thm ("real_mult_1",num_str real_mult_1),                         

	       (*"1 * z = z"*)

	       Thm ("real_mult_0",num_str real_mult_0),                         

	       (*"0 * z = 0"*)

	       Thm ("real_add_zero_left",num_str real_add_zero_left),		

	       (*"0 + z = z"*)

	       Thm ("real_mult_commute",num_str real_mult_commute),		(*AC-rewriting*)

	       Thm ("real_mult_left_commute",num_str real_mult_left_commute),	(**)

	       Thm ("real_mult_assoc",num_str real_mult_assoc),			(**)

	       Thm ("real_add_commute",num_str real_add_commute),		(**)

	       Thm ("real_add_left_commute",num_str real_add_left_commute),	(**)

	       Thm ("real_add_assoc",num_str real_add_assoc),	                (**)

	       Thm ("sym_realpow_twoI",num_str (realpow_twoI RS sym)),		

	       (*"r1 * r1 = r1 ^^^ 2"*)

	       Thm ("realpow_plus_1",num_str realpow_plus_1),			

	       (*"r * r ^^^ n = r ^^^ (n + 1)"*)

	       Thm ("sym_real_mult_2",num_str (real_mult_2 RS sym)),		

	       (*"z1 + z1 = 2 * z1"*)

	       Thm ("real_mult_2_assoc",num_str real_mult_2_assoc),		

	       (*"z1 + (z1 + k) = 2 * z1 + k"*)

	       Thm ("real_num_collect",num_str real_num_collect), 

	       (*"[| l is_const; m is_const |] ==> l * n + m * n = (l + m) * n"*)

	       Thm ("real_num_collect_assoc",num_str real_num_collect_assoc),	

	       (*"[| l is_const; m is_const |] ==>  l * n + (m * n + k) =  (l + m) * n + k"*)

	       Thm ("real_one_collect",num_str real_one_collect),		

	       (*"m is_const ==> n + m * n = (1 + m) * n"*)

	       Thm ("real_one_collect_assoc",num_str real_one_collect_assoc), 

	       (*"m is_const ==> k + (n + m * n) = k + (1 + m) * n"*)

	       Calc ("op +", eval_binop "#add_"), 

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

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

	       ],

      scr = Script ((term_of o the o (parse thy)) "empty_script")

      }:rls);      

ruleset' := overwritelthy thy (!ruleset',

			[("make_rooteq", make_rooteq)

			 ]);

val expand_rootbinoms = prep_rls(

  Rls{id = "expand_rootbinoms", preconds = [], 

      rew_ord = ("termlessI",termlessI),

      erls = Atools_erls, srls = Erls,

      calc = [],

      (*asm_thm = [],*)

      rules = [Thm ("real_plus_binom_pow2"  ,num_str real_plus_binom_pow2),     

	       (*"(a + b) ^^^ 2 = a ^^^ 2 + 2 * a * b + b ^^^ 2"*)

	       Thm ("real_plus_binom_times" ,num_str real_plus_binom_times),    

	       (*"(a + b)*(a + b) = ...*)

	       Thm ("real_minus_binom_pow2" ,num_str real_minus_binom_pow2),    

		(*"(a - b) ^^^ 2 = a ^^^ 2 - 2 * a * b + b ^^^ 2"*)

	       Thm ("real_minus_binom_times",num_str real_minus_binom_times),   

	       (*"(a - b)*(a - b) = ...*)

	       Thm ("real_plus_minus_binom1",num_str real_plus_minus_binom1),   

		(*"(a + b) * (a - b) = a ^^^ 2 - b ^^^ 2"*)

	       Thm ("real_plus_minus_binom2",num_str real_plus_minus_binom2),   

		(*"(a - b) * (a + b) = a ^^^ 2 - b ^^^ 2"*)

	       (*RL 020915*)

	       Thm ("real_pp_binom_times",num_str real_pp_binom_times), 

		(*(a + b)*(c + d) = a*c + a*d + b*c + b*d*)

               Thm ("real_pm_binom_times",num_str real_pm_binom_times), 

		(*(a + b)*(c - d) = a*c - a*d + b*c - b*d*)

               Thm ("real_mp_binom_times",num_str real_mp_binom_times), 

		(*(a - b)*(c p d) = a*c + a*d - b*c - b*d*)

               Thm ("real_mm_binom_times",num_str real_mm_binom_times), 

		(*(a - b)*(c p d) = a*c - a*d - b*c + b*d*)

	       Thm ("realpow_mul",num_str realpow_mul),                 

		(*(a*b)^^^n = a^^^n * b^^^n*)

	       Thm ("real_mult_1",num_str real_mult_1),               (*"1 * z = z"*)

	       Thm ("real_mult_0",num_str real_mult_0),               (*"0 * z = 0"*)

	       Thm ("real_add_zero_left",num_str real_add_zero_left), (*"0 + z = z"*)

	       Calc ("op +", eval_binop "#add_"), 

	       Calc ("op -", eval_binop "#sub_"), 

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

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

	       Calc ("Root.sqrt",eval_sqrt "#sqrt_"),

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

	       Thm ("sym_realpow_twoI",num_str (realpow_twoI RS sym)),		

	       (*"r1 * r1 = r1 ^^^ 2"*)

	       Thm ("realpow_plus_1",num_str realpow_plus_1),			

	       (*"r * r ^^^ n = r ^^^ (n + 1)"*)

	       Thm ("real_mult_2_assoc",num_str real_mult_2_assoc),		

	       (*"z1 + (z1 + k) = 2 * z1 + k"*)

	       Thm ("real_num_collect",num_str real_num_collect), 

	       (*"[| l is_const; m is_const |] ==> l * n + m * n = (l + m) * n"*)

	       Thm ("real_num_collect_assoc",num_str real_num_collect_assoc),	

	       (*"[| l is_const; m is_const |] ==>  l * n + (m * n + k) =  (l + m) * n + k"*)

	       Thm ("real_one_collect",num_str real_one_collect),		

	       (*"m is_const ==> n + m * n = (1 + m) * n"*)

	       Thm ("real_one_collect_assoc",num_str real_one_collect_assoc), 

	       (*"m is_const ==> k + (n + m * n) = k + (1 + m) * n"*)

	       Calc ("op +", eval_binop "#add_"), 

	       Calc ("op -", eval_binop "#sub_"), 

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

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

	       Calc ("Root.sqrt",eval_sqrt "#sqrt_"),

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

	       ],

      scr = Script ((term_of o the o (parse thy)) "empty_script")

       }:rls);      

ruleset' := overwritelthy thy (!ruleset',

			[("expand_rootbinoms", expand_rootbinoms)

			 ]);

"******* Root.ML end *******";