(* tests on PolyMinus

   author: Walther Neuper

   WN071207,

   (c) due to copyright terms

use"../smltest/IsacKnowledge/polyminus.sml";

use"polyminus.sml";

*)

val thy = PolyMinus.thy;

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

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

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

"----------- watch order_add_mult  -------------------------------";

"----------- build predicate for +- ordering ---------------------";

"----------- build fasse_zusammen --------------------------------";

"----------- build verschoenere ----------------------------------";

"----------- met simplification for_polynomials with_minus -------";

"----------- pbl polynom vereinfachen p.33 -----------------------";

"----------- met probe fuer_polynom ------------------------------";

"----------- pbl polynom probe -----------------------------------";

"----------- pbl klammer polynom vereinfachen p.34 ---------------";

"----------- try fun applyTactics --------------------------------";

"----------- pbl binom polynom vereinfachen p.39 -----------------";

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

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

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

"----------- watch order_add_mult  -------------------------------";

"----------- watch order_add_mult  -------------------------------";

"----------- watch order_add_mult  -------------------------------";

"----- with these simple variables it works...";

trace_rewrite:=true;

trace_rewrite:=false;

val t = str2term "((a + d) + c) + b";

val Some (t,_) = rewrite_set_ thy false order_add_mult t; term2str t;

if term2str t = "a + (b + (c + d))" then ()

else raise error "polyminus.sml 1 watch order_add_mult";

trace_rewrite:=false;

"----- the same stepwise...";

val od = ord_make_polynomial true Poly.thy;

val t = str2term "((a + d) + c) + b";

"((a + d) + c) + b"; 

val Some (t,_) = rewrite_ thy od e_rls true real_add_commute t; term2str t;

"b + ((a + d) + c)";

val Some (t,_) = rewrite_ thy od e_rls true real_add_commute t; term2str t;

"b + (c + (a + d))";

val Some (t,_) = rewrite_ thy od e_rls true real_add_left_commute t;term2str t;

"b + (a + (c + d))";

val Some (t,_) = rewrite_ thy od e_rls true real_add_left_commute t;term2str t;

"a + (b + (c + d))";

if term2str t = "a + (b + (c + d))" then ()

else raise error "polyminus.sml 2 watch order_add_mult";

"----- if parentheses are right, left_commute is (almost) sufficient...";

val t = str2term "a + (d + (c + b))";

"a + (d + (c + b))";

val Some (t,_) = rewrite_ thy od e_rls true real_add_left_commute t;term2str t;

"a + (c + (d + b))";

val Some (t,_) = rewrite_ thy od e_rls true real_add_commute t;term2str t;

"a + (c + (b + d))";

val Some (t,_) = rewrite_ thy od e_rls true real_add_left_commute t;term2str t;

"a + (b + (c + d))";

"----- but we do not want the parentheses at right; thus: cond.rew.";

"WN0712707 complicated monomials do not yet work ...";

val t = str2term "((5*a + 4*d) + 3*c) + 2*b";

val Some (t,_) = rewrite_set_ thy false order_add_mult t; term2str t;

if term2str t = "2 * b + (3 * c + (4 * d + 5 * a))" then ()

else raise error "polyminus.sml: order_add_mult changed";

"----- here we see rew_sub going into subterm with ord.rew....";

val od = ord_make_polynomial false Poly.thy;

val t = str2term "b + a + c + d";

val Some (t,_) = rewrite_ thy od e_rls false real_add_commute t; term2str t;

val Some (t,_) = rewrite_ thy od e_rls false real_add_commute t; term2str t;

(*@@@ rew_sub gosub: t = d + (b + a + c)

  @@@ rew_sub begin: t = b + a + c*)

"----------- build predicate for +- ordering ---------------------";

"----------- build predicate for +- ordering ---------------------";

"----------- build predicate for +- ordering ---------------------";

"a" < "b";

"ba" < "ab";

"123" < "a"; (*unused due to ---vvv*)

"12" < "3"; (*true !!!*)

" a kleiner b ==> (b + a) = (a + b)";

str2term "aaa";

str2term "222 * aaa";

case eval_kleiner 0 0 (str2term "12 kleiner 9") 0 of

    Some ("12 kleiner 9 = False", _) => ()

  | _ => raise error "polyminus.sml: 12 kleiner 9 = False";

case eval_kleiner 0 0 (str2term "a kleiner b") 0 of

    Some ("a kleiner b = True", _) => ()

  | _ => raise error "polyminus.sml: a kleiner b = True";

case eval_kleiner 0 0 (str2term "(10*g) kleiner f") 0 of

    Some ("10 * g kleiner f = False", _) => ()

  | _ => raise error "polyminus.sml: 10 * g kleiner f = False";

"----- compare tausche_plus with real_num_collect";

val od = dummy_ord;

val erls = erls_ordne_alphabetisch;

val t = str2term "b + a";

val Some (t,_) = rewrite_ thy od erls false tausche_plus t; term2str t;

if term2str t = "a + b" then ()

else raise error "polyminus.sml: ordne_alphabetisch1 b + a";

val erls = Atools_erls;

val t = str2term "2*a + 3*a";

val Some (t,_) = rewrite_ thy od erls false real_num_collect t; term2str t;

"----- test rewrite_, rewrite_set_";

trace_rewrite:=true;

val erls = erls_ordne_alphabetisch;

val t = str2term "b + a";

val Some (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;

if term2str t = "a + b" then ()

else raise error "polyminus.sml: ordne_alphabetisch a + b";

val t = str2term "2*b + a";

val Some (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;

if term2str t = "a + 2 * b" then ()

else raise error "polyminus.sml: ordne_alphabetisch a + 2 * b";

val t = str2term "a + c + b";

val Some (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;

if term2str t = "a + b + c" then ()

else raise error "polyminus.sml: ordne_alphabetisch a + b + c";

"----- rewrite goes into subterms";

val t = str2term "a + c + b + d";

val Some (t,_) = rewrite_ thy od erls false tausche_plus_plus t; term2str t;

if term2str t = "a + b + c + d" then ()

else raise error "polyminus.sml: ordne_alphabetisch1 a + b + c + d";

val t = str2term "a + c + d + b";

val Some (t,_) = rewrite_set_ thy false ordne_alphabetisch t; term2str t;

if term2str t = "a + b + c + d" then ()

else raise error "polyminus.sml: ordne_alphabetisch2 a + b + c + d";

"----- here we see rew_sub going into subterm with cond.rew....";

val t = str2term "b + a + c + d";

val Some (t,_) = rewrite_ thy od erls false tausche_plus t; term2str t;

if term2str t = "a + b + c + d" then ()

else raise error "polyminus.sml: ordne_alphabetisch3 a + b + c + d";

"----- compile rls for the most complicated terms";

val t = str2term "5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12";

"5 * e + 6 * f - 8 * g - 9 - 7 * e - 4 * f + 10 * g + 12";

val Some (t,_) = rewrite_set_ thy false ordne_alphabetisch t; 

if term2str t = "- 9 + 12 + 5 * e - 7 * e + 6 * f - 4 * f - 8 * g + 10 * g"

then () else raise error "polyminus.sml: ordne_alphabetisch finished";

"----------- build fasse_zusammen --------------------------------";

"----------- build fasse_zusammen --------------------------------";

"----------- build fasse_zusammen --------------------------------";

val t = str2term "- 9 + 12 + 5 * e - 7 * e + 6 * f - 4 * f - 8 * g + 10 * g";

val Some (t,_) = rewrite_set_ thy false fasse_zusammen t;

if term2str t = "3 + -2 * e + 2 * f + 2 * g" then ()

else raise error "polyminus.sml: fasse_zusammen finished";

"----------- build verschoenere ----------------------------------";

"----------- build verschoenere ----------------------------------";

"----------- build verschoenere ----------------------------------";

val t = str2term "3 + -2 * e + 2 * f + 2 * g";

val Some (t,_) = rewrite_set_ thy false verschoenere t;

if term2str t = "3 - 2 * e + 2 * f + 2 * g" then ()

else raise error "polyminus.sml: verschoenere 3 + -2 * e ...";

trace_rewrite:=true;

trace_rewrite:=false;

"----------- met simplification for_polynomials with_minus -------";

"----------- met simplification for_polynomials with_minus -------";

"----------- met simplification for_polynomials with_minus -------";

val str = 

"Script SimplifyScript (t_::real) =                \

\  (((Try (Rewrite_Set ordne_alphabetisch False)) @@     \

\    (Try (Rewrite_Set fasse_zusammen False)) @@     \

\    (Try (Rewrite_Set verschoenere False))) t_)"

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

atomty sc;

"----------- pbl polynom vereinfachen p.33 -----------------------";

"----------- pbl polynom vereinfachen p.33 -----------------------";

"----------- pbl polynom vereinfachen p.33 -----------------------";

"----------- 140 c ---";

states:=[];

CalcTree [(["term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",

	    "normalform N"],

	   ("PolyMinus.thy",["plus_minus","polynom","vereinfachen"],

	    ["simplification","for_polynomials","with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; show_pt pt;

if p = ([], Res) andalso 

   term2str (get_obj g_res pt (fst p)) = "3 - 2 * e + 2 * f + 2 * g"

then () else raise error "polyminus.sml: Vereinfache (3 - 2 * e + 2 * f...";

"----------- 140 d ---";

states:=[];

CalcTree [(["term (-r - 2*s - 3*t + 5 + 4*r + 8*s - 5*t - 2)",

	    "normalform N"],

	   ("PolyMinus.thy",["plus_minus","polynom","vereinfachen"],

	    ["simplification","for_polynomials","with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; show_pt pt;

if p = ([], Res) andalso 

   term2str (get_obj g_res pt (fst p)) = "3 + 3 * r + 6 * s - 8 * t"

then () else raise error "polyminus.sml: Vereinfache 140 d)";

"----------- 139 c ---";

states:=[];

CalcTree [(["term (3*e - 6*f - 8*e - 4*f + 5*e + 7*f)",

	    "normalform N"],

	   ("PolyMinus.thy",["plus_minus","polynom","vereinfachen"],

	    ["simplification","for_polynomials","with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; show_pt pt;

if p = ([], Res) andalso 

   term2str (get_obj g_res pt (fst p)) = "- (3 * f)"

then () else raise error "polyminus.sml: Vereinfache 139 c)";

"----------- 139 b ---";

states:=[];

CalcTree [(["term (8*u - 5*v - 5*u + 7*v - 6*u - 3*v)",

	    "normalform N"],

	   ("PolyMinus.thy",["plus_minus","polynom","vereinfachen"],

	    ["simplification","for_polynomials","with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; show_pt pt;

if p = ([], Res) andalso 

   term2str (get_obj g_res pt (fst p)) = "-3 * u - v"

then () else raise error "polyminus.sml: Vereinfache 139 b)";

"----------- 138 a ---";

states:=[];

CalcTree [(["term (2*u - 3*v - 6*u + 5*v)",

	    "normalform N"],

	   ("PolyMinus.thy",["plus_minus","polynom","vereinfachen"],

	    ["simplification","for_polynomials","with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; show_pt pt;

if p = ([], Res) andalso 

   term2str (get_obj g_res pt (fst p)) = "-4 * u + 2 * v"

then () else raise error "polyminus.sml: Vereinfache 138 a)";

"----------- met probe fuer_polynom ------------------------------";

"----------- met probe fuer_polynom ------------------------------";

"----------- met probe fuer_polynom ------------------------------";

val str = 

"Script ProbeScript (e_::bool) (ws_::bool list) =\

\ (let e_ = Take e_;                             \

\      e_ = Substitute ws_ e_                    \

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

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

\            (Try (Repeat (Calculate minus))))) e_)"

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

atomty sc;

"----------- pbl polynom probe -----------------------------------";

"----------- pbl polynom probe -----------------------------------";

"----------- pbl polynom probe -----------------------------------";

states:=[];

CalcTree [(["Pruefe (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12 =\

	    \3 - 2 * e + 2 * f + 2 * g)",

	    "mitWert [e = 1, f = 2, g = 3]",

	    "Geprueft b"],

	   ("PolyMinus.thy",["polynom","probe"],

	    ["probe","fuer_polynom"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1;

if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "11 = 11"

then () else raise error "polyminus.sml: Probe 11 = 11";

show_pt pt;

"----------- pbl klammer polynom vereinfachen p.34 ---------------";

"----------- pbl klammer polynom vereinfachen p.34 ---------------";

"----------- pbl klammer polynom vereinfachen p.34 ---------------";

states:=[];

CalcTree [(["term (2*u - 5 - (3 - 4*u) + (8*u + 9))",

	    "normalform N"],

	   ("PolyMinus.thy",["klammer","polynom","vereinfachen"],

	    ["simplification","for_polynomials","with_parentheses"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1;

if p = ([], Res) andalso 

   term2str (get_obj g_res pt (fst p)) = "1 + 14 * u"

then () else raise error "polyminus.sml: Vereinfache (2*u - 5 - (3 - ...";

show_pt pt;

"----- probe p.34 -----";

states:=[];

CalcTree [(["Pruefe (2*u - 5 - (3 - 4*u) + (8*u + 9) = 1 + 14 * u)",

	    "mitWert [u = 2]",

	    "Geprueft b"],

	   ("PolyMinus.thy",["polynom","probe"],

	    ["probe","fuer_polynom"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1;

if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "29 = 29"

then () else raise error "polyminus.sml: Probe 29 = 29";

show_pt pt;

"----------- try fun applyTactics --------------------------------";

"----------- try fun applyTactics --------------------------------";

"----------- try fun applyTactics --------------------------------";

states:=[];

CalcTree [(["term (5*e + 6*f - 8*g - 9 - 7*e - 4*f + 10*g + 12)",

	    "normalform N"],

	   ("PolyMinus.thy",["plus_minus","polynom","vereinfachen"],

	    ["simplification","for_polynomials","with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalcHead;

autoCalculate 1 (Step 1);

autoCalculate 1 (Step 1);

val ((pt,p),_) = get_calc 1; show_pt pt;

"----- 1 ^^^";

fetchApplicableTactics 1 0 p;

val appltacs = sel_appl_atomic_tacs pt p;

applyTactic 1 p (hd appltacs) (*addiere_x_plus_minus*);

val ((pt,p),_) = get_calc 1; show_pt pt;

"----- 2 ^^^";

trace_rewrite := true;

val erls = erls_ordne_alphabetisch;

val t = str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";

val Some (t',_) = 

    rewrite_ Isac.thy e_rew_ord erls false tausche_minus t;

term2str t';     "- 9 + 12 + 5 * e - 7 * e + (- 4 + 6) * f - 8 * g + 10 * g";

val t = str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";

val None = 

    rewrite_ Isac.thy e_rew_ord erls false tausche_minus_plus t;

val t = str2term "- 9 + 12 + 5 * e - 7 * e + (6 - 4) * f - 8 * g + 10 * g";

val Some (t',_) = 

    rewrite_set_ Isac.thy false ordne_alphabetisch t;

term2str t';     "- 9 + 12 + 5 * e - 7 * e - 8 * g + 10 * g + (- 4 + 6) * f";

trace_rewrite := false;

applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (*tausche_minus*);

val ((pt,p),_) = get_calc 1; show_pt pt;

"----- 3 ^^^";

applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);

val ((pt,p),_) = get_calc 1; show_pt pt;

"----- 4 ^^^";

applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);

val ((pt,p),_) = get_calc 1; show_pt pt;

"----- 5 ^^^";

applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);

val ((pt,p),_) = get_calc 1; show_pt pt;

"----- 6 ^^^";

(*<CALCMESSAGE> failure </CALCMESSAGE>

applyTactic 1 p (hd (sel_appl_atomic_tacs pt p)) (**);

val ((pt,p),_) = get_calc 1; show_pt pt;

"----- 7 ^^^";

*)

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; show_pt pt;

(*independent from failure above: met_simp_poly_minus not confluent:

(([9], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f)),

(([], Res), - (8 * g) + 10 * g + (3 - 2 * e + 2 * f))]

~~~~~~~~~~~###~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*)

states:=[];

CalcTree [(["term (- (8 * g) + 10 * g + h)",

	    "normalform N"],

	   ("PolyMinus.thy",["plus_minus","polynom","vereinfachen"],

	    ["simplification","for_polynomials","with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; show_pt pt;

if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "2 * g + h"

then () else raise error "polyminus.sml: addiere_vor_minus";

states:=[];

CalcTree [(["term (- (8 * g) + 10 * g + f)",

	    "normalform N"],

	   ("PolyMinus.thy",["plus_minus","polynom","vereinfachen"],

	    ["simplification","for_polynomials","with_minus"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; show_pt pt;

if p = ([], Res) andalso term2str (get_obj g_res pt (fst p)) = "f + 2 * g"

then () else raise error "polyminus.sml: tausche_vor_plus";

"----------- pbl binom polynom vereinfachen p.39 -----------------";

"----------- pbl binom polynom vereinfachen p.39 -----------------";

"----------- pbl binom polynom vereinfachen p.39 -----------------";

val rls = klammern_ausmultiplizieren;

val t = str2term "(3 * a + 2) * (4 * a - 1)";

val Some (t,_) = rewrite_set_ thy false rls t; term2str t;

"3 * a * (4 * a) - 3 * a * 1 + (2 * (4 * a) - 2 * 1)";

val rls = discard_parentheses;

val Some (t,_) = rewrite_set_ thy false rls t; term2str t;

"3 * a * 4 * a - 3 * a * 1 + (2 * 4 * a - 2 * 1)";

val rls = ordne_monome;

val Some (t,_) = rewrite_set_ thy false rls t; term2str t;

"3 * 4 * a * a - 1 * 3 * a + (2 * 4 * a - 1 * 2)";

(*

val t = str2term "3 * a * 4 * a";

val rls = ordne_monome;

val Some (t,_) = rewrite_set_ thy false rls t; term2str t;

*)

val rls = klammern_aufloesen;

val Some (t,_) = rewrite_set_ thy false rls t; term2str t;

"3 * 4 * a * a - 1 * 3 * a + 2 * 4 * a - 1 * 2";

val rls = ordne_alphabetisch;

(*TODO: make is_monom more general, a*a=a^2, ...*)

val Some (t,_) = rewrite_set_ thy false rls t; term2str t;

"3 * 4 * a * a - 1 * 2 - 1 * 3 * a + 2 * 4 * a";

(*GOON.WN080104

val rls = fasse_zusammen;

val Some (t,_) = rewrite_set_ thy false rls t; term2str t;

val rls = verschoenere;

val Some (t,_) = rewrite_set_ thy false rls t; term2str t;

*)

trace_rewrite := true;

trace_rewrite := false;

states:=[];

CalcTree [(["term ((3*a + 2) * (4*a - 1))",

	    "normalform N"],

	   ("PolyMinus.thy",["binom_klammer","polynom","vereinfachen"],

	    ["simplification","for_polynomials","with_parentheses_mult"]))];

moveActiveRoot 1;

autoCalculate 1 CompleteCalc;

val ((pt,p),_) = get_calc 1; show_pt pt;

(*

if p = ([], Res) andalso 

   term2str (get_obj g_res pt (fst p)) = "1 + 14 * u"

then () else raise error "polyminus.sml: Vereinfache (2*u - 5 - (3 - ...";

*)

(*

use"../smltest/IsacKnowledge/polyminus.sml";

use"polyminus.sml";

  *)