(* Title: tests for ProgLang/rewrite.sml

   TODO.WN0509 collect typical tests from systest here !!!!!

   Author: Walther Neuper 050908

   (c) copyright due to lincense terms.

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*)

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

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

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

"----------- assemble rewrite ---------------------------";

"----------- test rewriting without Isac's thys ---------";

"----------- conditional rewriting without Isac's thys --";

"----------- step through 'and rew_sub': ----------------";

"----------- step through 'fun rewrite_terms_'  ---------";

"----------- rewrite_inst_ bdvs -------------------------";

"----------- check diff 2002--2009-3 --------------------";

"----------- fun app_rev, Rrls, prepat ------------------";

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

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

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

(*-.-.-.-.-.-isolate response.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.

"----------- assemble rewrite ---------------------------";

"----------- assemble rewrite ---------------------------";

"----------- assemble rewrite ---------------------------";

"===== rewriting by thm with 'a";

show_types := true;

val thy = @{theory Complex_Main};

val ctxt = @{context};

val thm = @{thm add_commute};

val t = (term_of o the) (parse thy "((r + u) + t) + s");

"----- from old: fun rewrite__";

val bdv = [];

val r = (((inst_bdv bdv) o norm o #prop o rep_thm) thm);

"----- from old: and rew_sub";

val (lhs,rhs) = (dest_equals' o strip_trueprop 

   	      o Logic.strip_imp_concl) r;

(* old

val insts = Pattern.match thy (lhs,t) (Vartab.empty, Vartab.empty);*)

"----- fun match_rew in Pure/pattern.ML";

val rtm = the_default rhs (Term.rename_abs lhs t rhs);

writeln(Syntax.string_of_term ctxt rtm);

writeln(Syntax.string_of_term ctxt lhs);

writeln(Syntax.string_of_term ctxt t);

(Pattern.match thy (lhs, t) (Vartab.empty, Vartab.empty));

val (rew, rhs) = (Envir.subst_term 

  (Pattern.match thy (lhs, t) (Vartab.empty, Vartab.empty)) rtm, rtm);

(*lookup in isabelle?trace?response...*)

writeln(Syntax.string_of_term ctxt rew);

writeln(Syntax.string_of_term ctxt rhs);

"===== rewriting: prep insertion into rew_sub";

val thy = @{theory Complex_Main};

val ctxt = @{context};

val thm =  @{thm nonzero_mult_divide_cancel_right};

val r = Thm.prop_of thm;

val tm = @{term "x*2 / 2::real"};

"----- and rew_sub";

val (lhs, rhs) = (HOLogic.dest_eq o HOLogic.dest_Trueprop

                  o Logic.strip_imp_concl) r;

val r' = Envir.subst_term (Pattern.match thy (lhs, tm) 

                                (Vartab.empty, Vartab.empty)) r;

val p' = (fst o Logic.strip_prems) (Logic.count_prems r', [], r');

val t' = (snd o HOLogic.dest_eq o HOLogic.dest_Trueprop 

            o Logic.strip_imp_concl) r';

(*is displayed on top of <response> buffer...*)

Pretty.writeln (ProofContext.pretty_term_abbrev @{context} r');

Pretty.writeln (ProofContext.pretty_term_abbrev @{context} t');

(*}*)

"----------- test rewriting without Isac's thys ---------";

"----------- test rewriting without Isac's thys ---------";

"----------- test rewriting without Isac's thys ---------";

"===== rewriting with Isabelle2009-1 only, i.e without isac-hacks";

val thy = @{theory Complex_Main};

val ctxt = @{context};

val thm =  @{thm add_commute};

val tm = @{term "x + y*z::real"};

val SOME (r,_) = (rewrite_ thy dummy_ord e_rls false thm tm)

  handle _ => error "rewrite.sml diff.behav. in rewriting";

(*is displayed on _TOP_ of <response> buffer...*)

Pretty.writeln (ProofContext.pretty_term_abbrev @{context} r);

if r = @{term "y*z + x::real"}

then () else error "rewrite.sml diff.result in rewriting";

"----- rewriting a subterm";

val tm = @{term "w*(x + y*z)::real"};

val SOME (r,_) = (rewrite_ thy dummy_ord e_rls false thm tm)

  handle _ => error "rewrite.sml diff.behav. in rew_sub";

"----- ordered rewriting";

fun tord (_:subst) pp = Term_Ord.termless pp;

if tord [] (@{term "x + y*z::real"}, @{term "y*z + x::real"}) then ()

else error "rewrite.sml diff.behav. in ord.rewr.";

val NONE = (rewrite_ thy tord e_rls false thm tm)

  handle _ => error "rewrite.sml diff.behav. in rewriting";

(*is displayed on _TOP_ of <response> buffer...*)

Pretty.writeln (ProofContext.pretty_term_abbrev @{context} r);

val tm = @{term "x*y + z::real"};

val SOME (r,_) = (rewrite_ thy tord e_rls false thm tm)

  handle _ => error "rewrite.sml diff.behav. in rewriting";

"----------- conditional rewriting without Isac's thys --";

"----------- conditional rewriting without Isac's thys --";

"----------- conditional rewriting without Isac's thys --";

(*ML {*)

"===== prepr cond.rew. with Pattern.match";

val thy = @{theory Complex_Main};

val ctxt = @{context};

val thm =  @{thm nonzero_mult_divide_cancel_right};

val rule = Thm.prop_of thm;

val tm = @{term "x*2 / 2::real"};

val prem = Logic.strip_imp_prems rule;

val nps = Logic.count_prems rule;

val prems = Logic.strip_prems (nps, [], rule);

val eq = Logic.strip_imp_concl rule;

val (lhs, rhs) = (HOLogic.dest_eq o HOLogic.dest_Trueprop) eq;

val mtcs = Pattern.match thy (lhs, tm) (Vartab.empty, Vartab.empty);

val rule' = Envir.subst_term mtcs rule;

val prems' = (fst o Logic.strip_prems) 

              (Logic.count_prems rule', [], rule');

val rhs' = (snd o HOLogic.dest_eq o HOLogic.dest_Trueprop 

            o Logic.strip_imp_concl) rule';

"----- conditional rewriting creating an assumption";

"----- conditional rewriting creating an assumption";

val tm = @{term "x*y / y::real"};

val SOME (rew, asm) = (rewrite_ thy dummy_ord e_rls false thm tm)

  handle _ => error "rewrite.sml diff.behav. in cond.rew.";

if rew = @{term "x::real"} then () (* the rewrite is _NO_ Trueprop *)

else error "rewrite.sml diff.result in cond.rew.";

if hd asm = @{term "~ y = (0::real)"} (* dropped Trueprop $ ...*)

then () else error "rewrite.sml diff.asm in cond.rew.";

"----- conditional rewriting immediately: can only be done with ";

"------Isabelle numerals, because erls cannot handle them yet.";

"----------- step through 'and rew_sub': ----------------";

"----------- step through 'and rew_sub': ----------------";

"----------- step through 'and rew_sub': ----------------";

(*and make asms without Trueprop, beginning with the result:*)

val tm = @{term "x*y / y::real"};

val (t', asm, _, _) = rew_sub thy 0 [] dummy_ord e_rls true [] (prop_of thm) tm;

show_types := false;

"----- evaluate arguments";

val (thy, i, bdv, tless, rls, put_asm, lrd, r, t) = 

    (thy, 0, [], dummy_ord, e_rls, true, [], (prop_of thm), tm);

"----- step 1: lhs, rhs of rule";

     val (lhs, rhs) = (HOLogic.dest_eq o HOLogic.dest_Trueprop

                       o Logic.strip_imp_concl) r;

term2str r = "?b ~= (0::?'a) ==> ?a * ?b / ?b = ?a";

term2str lhs = "?a * ?b / ?b"; term2str rhs = "?a";

"----- step 2: the rule instantiated";

     val r' = Envir.subst_term 

                  (Pattern.match thy (lhs, t) (Vartab.empty, Vartab.empty)) r;

term2str r' = "y ~= 0 ==> x * y / y = x";

"----- step 3: get the (instantiated) assumption(s)";

     val p' = (fst o Logic.strip_prems) (Logic.count_prems r', [], r');

term2str (hd p') = "y ~= 0";

"=====vvv make asms without Trueprop ---vvv";

     val p' = map HOLogic.dest_Trueprop ((fst o Logic.strip_prems) 

                                             (Logic.count_prems r', [], r'));

case p' of

    [Const ("Not", _) $ (Const ("op =", _) $ Free ("y", _) $

                               Const ("Groups.zero_class.zero", _))] => ()

  | _ => error "rewrite.sml assumption changed";

"=====^^^ make asms without Trueprop ---^^^";

"----- step 4: get the (instantiated) rhs";

     val t' = (snd o HOLogic.dest_eq o HOLogic.dest_Trueprop 

               o Logic.strip_imp_concl) r';

term2str t' = "x";

"----------- step through 'fun rewrite_terms_'  ---------";

"----------- step through 'fun rewrite_terms_'  ---------";

"----------- step through 'fun rewrite_terms_'  ---------";

"----- step 0: args for rewrite_terms_, local fun";

val (thy, ord, erls, equs, t) =

    (theory "Biegelinie", dummy_ord, Erls, [str2term "x = 0"],

     str2term "M_b x = -1 * q_0 * x ^^^ 2 / 2 + x * c + c_2");

"----- step 1: args for rew_";

val ((t', asm'), (rules as r::rs), t) = ((e_term, []), equs, t);

"----- step 2: rew_sub";

rew_sub thy 1 [] ord erls false [] (Trueprop $ r) t;

"----- step 3: step through rew_sub -- inefficient: goes into subterms";

val SOME (t', _) = rewrite_terms_ thy dummy_ord Erls equs t;

writeln "----------- rewrite_terms_  1---------------------------";

if term2str t' = "M_b 0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2" then ()

else error "rewrite.sml rewrite_terms_ [x = 0]";

val equs = [str2term "M_b 0 = 0"];

val t = str2term "M_b 0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2";

val SOME (t', _) = rewrite_terms_ thy dummy_ord Erls equs t;

writeln "----------- rewrite_terms_  2---------------------------";

if term2str t' = "0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2" then ()

else error "rewrite.sml rewrite_terms_ [M_b 0 = 0]";

val equs = [str2term "x = 0", str2term"M_b 0 = 0"];

val t = str2term "M_b x = -1 * q_0 * x ^^^ 2 / 2 + x * c + c_2";

val SOME (t', _) = rewrite_terms_ thy dummy_ord Erls equs t;

writeln "----------- rewrite_terms_  3---------------------------";

if term2str t' = "0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2" then ()

else error "rewrite.sml rewrite_terms_ [x = 0, M_b 0 = 0]";

"----------- rewrite_inst_ bdvs -------------------------";

"----------- rewrite_inst_ bdvs -------------------------";

"----------- rewrite_inst_ bdvs -------------------------";

(*see smltest/Scripts/term_G.sml: inst_bdv 2*)

val t = str2term"-1 * (q_0 * L ^^^ 2) / 2 + (L * c_3 + c_4) = 0";

val bdvs = [(str2term"bdv_1",str2term"c"),

	    (str2term"bdv_2",str2term"c_2"),

	    (str2term"bdv_3",str2term"c_3"),

	    (str2term"bdv_4",str2term"c_4")];

(*------------ outcommented WN071210, after inclusion into ROOT.ML 

val SOME (t,_) = 

    rewrite_inst_ thy e_rew_ord 

		  (append_rls "erls_isolate_bdvs" e_rls 

			      [(Calc ("EqSystem.occur'_exactly'_in", 

				      eval_occur_exactly_in 

					  "#eval_occur_exactly_in_"))

			       ]) 

		  false bdvs (num_str @{separate_bdvs_add) t;

(writeln o term2str) t;

if term2str t = "L * c_3 + c_4 = 0 + -1 * (-1 * (q_0 * L ^^^ 2) / 2)"

then () else error "rewrite.sml rewrite_inst_ bdvs";

trace_rewrite:=true;

trace_rewrite:=false;--------------------------------------------*)

"----------- check diff 2002--2009-3 --------------------";

"----------- check diff 2002--2009-3 --------------------";

"----------- check diff 2002--2009-3 --------------------";

(*----- 2002 -------------------------------------------------------------------

#  rls: norm_Rational_noadd_fractions on: 1 / EI * (L * q_0 * x / 2 + -1 *

q_0 * x ^^^ 2 / 2)

##  rls: discard_minus_ on: 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2

/ 2)

###  try thm: real_diff_minus

###  try thm: sym_real_mult_minus1

##  rls: rat_mult_poly on: 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2

/ 2)

###  try thm: rat_mult_poly_l

###  try thm: rat_mult_poly_r

####  eval asms: L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2 is_polyexp

==> 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2) =

    1 * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2) / EI

#####  rls: e_rls-is_polyexp on: L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2

is_polyexp

######  try calc: Poly.is'_polyexp'

======  calc. to: False

######  try calc: Poly.is'_polyexp'

######  try calc: Poly.is'_polyexp'

####  asms false: ["L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2 is_polyexp"]

----- 2002 NONE rewrite --------------------------------------------------------

----- 2009 should maintain this behaviour, but: --------------------------------

#  rls: norm_Rational_noadd_fractions on: 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2)

##  rls: discard_minus on: 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2)

###  try thm: real_diff_minus

###  try thm: sym_real_mult_minus1

##  rls: rat_mult_poly on: 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2)

###  try thm: rat_mult_poly_l

###  try thm: rat_mult_poly_r

####  eval asms: L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2 is_polyexp

==> 1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2) =

    1 * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2) / EI

#####  rls: e_rls-is_polyexp on: L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2 is_polyexp

######  try calc: Poly.is'_polyexp'

======  calc. to: False

######  try calc: Poly.is'_polyexp'

######  try calc: Poly.is'_polyexp'

####  asms accepted: ["L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2 is_polyexp"]   stored: ["False"]

===  rewrites to: 1 * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2) / EI

----- 2009 -------------------------------------------------------------------*)

(*the situation as was before repair (asm without Trueprop) is outcommented*)

val thy = theory "Isac";

"===== example which raised the problem =================";

val t = @{term "1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2)"};

"----- rewrite_set_inst_ norm_Rational_noadd_fractions--";

val subs = [(str2term "bdv", str2term "x")];

val rls = norm_Rational_noadd_fractions;

val NONE (*SOME (t', _)*) = rewrite_set_inst_ thy true subs rls t;

"----- rewrite_ rat_mult_poly_r--------------------------";

val thm = @{thm rat_mult_poly_r};

         "?c::real is_polyexp ==> (?a::real) / (?b::real) * ?c = ?a * ?c / ?b";

val erls = append_rls "e_rls-is_polyexp" e_rls 

                      [Calc ("Poly.is'_polyexp", eval_is_polyexp "")];

val NONE (*SOME (t'', _)*) = rewrite_ thy dummy_ord erls true thm t;

(*t' = t''; (*false because of further rewrites in t'*)*)

"----- rew_sub  --------------------------------";

val (t''', _, _, _) = rew_sub thy 0 [] dummy_ord erls true [] (prop_of thm) t;

(*t'' = t'''; (*true*)*)

"----- rewrite_set_ erls --------------------------------";

val cond = @{term "(L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2)"};

val NONE = rewrite_set_ thy true erls cond; 

(* ^^^^^ goes with '======  calc. to: False' above from beginning*)

writeln "===== maximally simplified example =====================";

val t = @{term "a / b * (x / x ^^^ 2)"};

         "?c::real is_polyexp ==> (?a::real) / (?b::real) * ?c = ?a * ?c / ?b";

writeln "----- rewrite_set_inst_ norm_Rational_noadd_fractions--";

val (*NONE*) SOME (t', asm) = rewrite_set_inst_ thy true subs rls t;

term2str t' = "a * x / (b * x ^^^ 2)"; (*rew. by thm outside test case*)

(*checked visually: trace_rewrite looks like above for 2009*)

trace_rewrite := false; (*<<<<<<<<<<<<<<<<<<<<<###############################*)

show_types := false;

writeln "----- rewrite_ rat_mult_poly_r--------------------------";

val NONE (*SOME (t'', _)*) = rewrite_ thy dummy_ord erls true thm t;

(*t' = t''; (*false because of further rewrites in t'*)*)

writeln "----- rew_sub  --------------------------------";

val (t''', _, _, _) = rew_sub thy 0 [] dummy_ord erls true [] (prop_of thm) t;

(*t'' = t'''; (*true*)*)

writeln "----- rewrite_set_ erls --------------------------------";

val cond = @{term "(x / x ^^^ 2)"};

val NONE = rewrite_set_ thy true erls cond; 

(* ^^^^^ goes with '======  calc. to: False' above from beginning*)

trace_rewrite := false; (*<<<<<<<<<<<<<<<<<<<<<###############################*)

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

-.-.-.-.-.-.-isolate response.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.*)

"----------- fun app_rev, Rrls, prepat ------------------";

"----------- fun app_rev, Rrls, prepat ------------------";

"----------- fun app_rev, Rrls, prepat ------------------";

(* Christian Urban, 101001 

theory Test

imports Main Complex

begin

ML {*

let

  val parser = Args.context -- Scan.lift Args.name_source

  fun term_pat (ctxt, str) = str |> ProofContext.read_term_pattern ctxt

  |> ML_Syntax.print_term |> ML_Syntax.atomic

in

  ML_Antiquote.inline "term_pat" (parser >> term_pat)

end

*}

ML {*

  val t = @{term "a + b * x = (0 ::real)"};

  val pat = @{term_pat "?l = (?r ::real)"};

  val precond = @{term_pat "is_polynomial (?l::real)"};

  val inst = Pattern.match @{theory} (pat, t) (Vartab.empty, Vartab.empty);

*}

ML {*

  Envir.subst_term inst precond

  |> Syntax.string_of_term @{context}

  |> writeln

*}

end *)

val t = @{term "a + b * x = (0 ::real)"};

val pat = parse_patt thy "?l = (?r ::real)";

val precond = parse_patt thy "is_polynomial (?l::real)";(*no infix def*)

val precond = parse_patt thy " (?l::real) is_expanded"; 

val inst = Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty);

val preinst = Envir.subst_term inst precond;

term2str preinst;

"===== Rational.thy: cancel ===";

(* pat matched with the current term gives an environment 

   (or not: hen the Rrls not applied);

   if pre1 and pre2 evaluate to HOLogic.true_const in this environment,

   then the Rrls is applied. *)

val t = str2term "(a + b) / c ::real";

val pat = parse_patt thy "?r / ?s ::real";

val pres = [parse_patt thy "?r is_expanded", parse_patt thy "?s is_expanded"];

val prepat = [(pres, pat)];

val erls = rational_erls;

(* erls got from Rrls {erls, prepat, scr = Rfuns {normal_form, ...}, ...} *)

val subst = Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty);

val asms = map (Envir.subst_term subst) pres;

if terms2str asms = "[\"a + b is_expanded\",\"c is_expanded\"]"

then () else error "rewrite.sml: prepat cancel subst";

if ([], true) = eval__true thy 0 asms [] erls

then () else error "rewrite.sml: prepat cancel eval__true";

"===== Rational.thy: common_nominator_p ===";

(* if each pat* matches with the current term, the Rrls is applied

   (there are no preconditions to be checked, they are HOLogic.true_const) *)

val t = str2term "a / b + 1 / 2";

val pat = parse_patt thy "?r / ?s + ?u / ?v";

val pres = [HOLogic.true_const];

val prepat = [(pres, pat)];

val erls = rational_erls;

(* erls got from Rrls {erls, prepat, scr = Rfuns {normal_form, ...}, ...} *)

val subst = Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty);

if ([], true) = eval__true thy 0 (map (Envir.subst_term subst) pres) [] erls

then () else error "rewrite.sml: prepat common_nominator_p";

"===== Poly.thy: order_mult_ ===";

          (* ?p matched with the current term gives an environment,

             which evaluates (the instantiated) "p is_multUnordered" to true*)

val t = str2term "x^^^2 * x";

val pat = parse_patt thy "?p :: real"

val pres = [parse_patt thy "?p is_multUnordered"];

val prepat = [(pres, pat)];

val erls = append_rls "e_rls-is_multUnordered" e_rls

		      [Calc ("Poly.is'_multUnordered", 

                             eval_is_multUnordered "")];

val subst = Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty);

val asms = map (Envir.subst_term subst) pres;

if terms2str asms = "[\"x ^^^ 2 * x is_multUnordered\"]"

then () else error "rewrite.sml: prepat order_mult_ subst";

if ([], true) = eval__true thy 0 asms [] erls

then () else error "rewrite.sml: prepat order_mult_ eval__true";

(*========== inhibit exn =======================================================

============ inhibit exn =====================================================*)

(*-.-.-.-.-.-isolate response.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.

-.-.-.-.-.-.-isolate response.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.*)