(* Title:  partial fraction decomposition

   Author: Jan Rocnik

   (c) due to copyright terms

*)

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

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

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

"----------- why helpless here ? ------------------------";

"----------- why not nxt = Model_Problem here ? ---------";

"----------- fun factors_from_solution ------------------";

"----------- Logic.unvarify_global ----------------------";

"----------- eval_drop_questionmarks --------------------";

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

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

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

"----------- why helpless here ? ------------------------";

"----------- why helpless here ? ------------------------";

"----------- why helpless here ? ------------------------";

val fmz = ["filterExpression (X z = 3 / (z - 1/4 + -1/8 * (1/(z::real))))", 

  "stepResponse (x[n::real]::bool)"];

val (dI,pI,mI) = ("Isac", ["inverse", "Z_Transform", "SignalProcessing"], 

  ["SignalProcessing","Z_Transform","inverse"]);

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

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

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

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

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

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

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

val (p,_,f,nxt,_,pt) = me nxt p [] pt; "nxt = Rewrite (ruleZY, Inverse_Z_Transform.ruleZY) --> X z = 3 / (z - 1 / 4 + -1 / 8 * (1 / z))";

val (p''',_,f,nxt''',_,pt''') = me nxt p [] pt; "nxt = Rewrite_Set norm_Rational --> X' z = 3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z)))";

"~~~~~ fun me, args:"; val ((_,tac), (p:pos'), _, (pt:ptree)) = (nxt, p, [], pt);

val ("ok", (_, _, ptp)) = locatetac tac (pt,p)

val (pt, p) = ptp;

"~~~~~ fun step, args:"; val (((ip as (_,p_)):pos'), ((ptp as (pt,p), tacis):calcstate)) = 

                           (p, ((pt, e_pos'),[]));

val pIopt = get_pblID (pt,ip);

ip = ([],Res); "false";

tacis; " = []";

pIopt; (* = SOME ["inverse", "Z_Transform", "SignalProcessing"]*)

member op = [Pbl,Met] p_ andalso is_none (get_obj g_env pt (fst p)); "false";

(*nxt_solve_ (pt,ip); "WAS isalist2list applied to NON-list 'no_meth'"

   THIS MEANS: replace no_meth by [no_meth] in Script.*)

(*WAS val ("helpless",_) = step p ((pt, e_pos'),[]) *)

(*WAS val (p,_,f,nxt,_,pt) = me nxt p [] pt; "Empty_Tac instead SubProblem";*)

"----------- why not nxt = Model_Problem here ? ---------";

"----------- why not nxt = Model_Problem here ? ---------";

"----------- why not nxt = Model_Problem here ? ---------";

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

"~~~~~ fun me, args:"; val (((_,tac):tac'_), (p:pos'), _, (pt:ptree)) = (nxt, p, c, pt);

val ("ok", (_, _, ptp)) = locatetac tac (pt,p);

val (pt, p) = ptp;

"~~~~~ fun step, args:"; val (((ip as (_,p_)):pos'), ((ptp as (pt,p), tacis):calcstate)) =

                           (p, ((pt, e_pos'),[]));

val pIopt = get_pblID (pt,ip);

ip = ([],Res); " = false";

tacis; " = []";                                         

pIopt (* = SOME ["inverse", "Z_Transform", "SignalProcessing"]*);

member op = [Pbl,Met] p_ andalso is_none (get_obj g_env pt (fst p)); " = false";

(*                               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ leads into

nxt_solve_, which is definitely WRONG (should be nxt_specify_ for FIND_ADD).

This ERROR seems to be introduced together with ctxt, concerns Apply_Method without init_form.

See TODO.txt

*)

"----------- fun factors_from_solution ------------------";

"----------- fun factors_from_solution ------------------";

"----------- fun factors_from_solution ------------------";

val ctxt = ProofContext.init_global @{theory Isac};

val SOME t = parseNEW ctxt "factors_from_solution [(z::real) = 1 / 2, z = -1 / 4]";

val SOME (_, t') = eval_factors_from_solution "" 0 t thy;

if term2str t' =

 "factors_from_solution [z = 1 / 2, z = -1 / 4] =\n(z + -1 * (1 / 2)) * (z + -1 * (-1 / 4))"

then () else error "factors_from_solution broken";

"----------- Logic.unvarify_global ----------------------";

"----------- Logic.unvarify_global ----------------------";

"----------- Logic.unvarify_global ----------------------";

val A_var = parseNEW ctxt "A::real" |> the |> Logic.varify_global

val B_var = parseNEW ctxt "B::real" |> the |> Logic.varify_global

val denom1 = parseNEW ctxt "(z + -1 * (1 / 2))::real" |> the;

val denom2 = parseNEW ctxt "(z + -1 * (-1 / 4))::real" |> the;

val test = HOLogic.mk_binop "Groups.plus_class.plus"

  (HOLogic.mk_binop "Rings.inverse_class.divide" (A_var, denom1),

   HOLogic.mk_binop "Rings.inverse_class.divide" (B_var, denom2));

if term2str test = "?A / (z + -1 * (1 / 2)) + ?B / (z + -1 * (-1 / 4))" then ()

  else error "HOLogic.mk_binop broken ?";

(* Logic.unvarify_global test

---> exception TERM raised (line 539 of "logic.ML"): Illegal fixed variable: "z"

thus we need another fun var2free in termC.sml*)

"----------- eval_drop_questionmarks --------------------";

"----------- eval_drop_questionmarks --------------------";

"----------- eval_drop_questionmarks --------------------";

if term2str test = "?A / (z + -1 * (1 / 2)) + ?B / (z + -1 * (-1 / 4))"

then () else error "test setup (ctxt!) probably changed";

val t = Const ("Partial_Fractions.drop_questionmarks", HOLogic.realT --> HOLogic.realT) $ test;

val SOME (_, t') = eval_drop_questionmarks "drop_questionmarks" 0 t @{theory Isac};

if term2str t' = "drop_questionmarks (?A / (z + -1 * (1 / 2)) + ?B / (z + -1 * (-1 / 4))) =" ^

  "\nA / (z + -1 * (1 / 2)) + B / (z + -1 * (-1 / 4))"

then () else error "eval_drop_questionmarks broken";