(* Handle user-input during the specify- and the solve-phase. 

   author: Walther Neuper

   0603

   (c) due to copyright terms

use"ME/inform.sml";

use"inform.sml";

*)

signature INFORM =

  sig 

    type castab

    type icalhd

   (* type iitem *)

    datatype

      iitem =

          Find of cterm' list

        | Given of cterm' list

        | Relate of cterm' list

    type imodel

    val imodel2fstr : iitem list -> (string * cterm') list

    val Isac : 'a -> Theory.theory

    val appl_add' :

       theory' ->

       SpecifyTools.ori list ->

       SpecifyTools.itm list ->

       ('a * (Term.term * Term.term)) list ->

       string * cterm' -> SpecifyTools.itm

  (*  val appl_adds :

       theory' ->

       SpecifyTools.ori list ->

       SpecifyTools.itm list ->

       (string * (Term.term * Term.term)) list ->

       (string * string) list -> SpecifyTools.itm list *)

   (* val cas_input : string -> ptree * ocalhd *)

   (* val cas_input_ :

       spec ->

       (Term.term * Term.term list) list ->

       pblID * SpecifyTools.itm list * metID * SpecifyTools.itm list *

       (bool * Term.term) list  *)

    val castab : castab ref

    val compare_step :

       calcstate' -> Term.term -> string * calcstate'

   (* val concat_deriv :

       'a * ((Term.term * Term.term) list -> Term.term * Term.term -> bool)

       ->

       rls ->

       rule list ->

       Term.term ->

       Term.term ->

       bool * (Term.term * rule * (Term.term * Term.term list)) list *)

    val dropwhile' :   (* systest/auto-inform.sml *)

       ('a -> 'b -> bool) -> 'a list -> 'b list -> 'a list * 'b list

   (* val dtss2itm_ :

       pbt_ list ->

       Term.term * Term.term list ->

       int list * bool * string * SpecifyTools.itm_ *)

   (* val e_icalhd : icalhd *)

    val eq7 : ''a * ''b -> ''a * (''b * 'c) -> bool

    val equal : ''a -> ''a -> bool

   (* val filter_dsc :

       SpecifyTools.ori list -> SpecifyTools.itm -> SpecifyTools.ori list *)

   (* val filter_sep : ('a -> bool) -> 'a list -> 'a list * 'a list *)

   (* val flattup2 : 'a * ('b * 'c * 'd * 'e) -> 'a * 'b * 'c * 'd * 'e *)

   (* val fstr2itm_ :

       Theory.theory ->

       (''a * (Term.term * Term.term)) list ->

       ''a * string -> int list * bool * ''a * SpecifyTools.itm_ *)

    val inform :

       calcstate' -> cterm' -> string * calcstate'   

    val input_icalhd : ptree -> icalhd -> ptree * ocalhd

   (* val is_Par : SpecifyTools.itm -> bool *)

   (* val is_casinput : cterm' -> fmz -> bool *)

   (* val is_e_ts : Term.term list -> bool *)

   (* val itms2fstr : SpecifyTools.itm -> string * string *)

   (* val mk_tacis :

       rew_ord' * 'a ->

       rls ->

       Term.term * rule * (Term.term * Term.term list) ->

       tac * tac_ * (pos' * istate)      *)

    val oris2itms :

       'a -> int -> SpecifyTools.ori list -> SpecifyTools.itm list

   (* val par2fstr : SpecifyTools.itm -> string * cterm' *)

   (* val parsitm : Theory.theory -> SpecifyTools.itm -> SpecifyTools.itm *)

    val rev_deriv' : 'a * rule * ('b * 'c) -> 'b * rule * ('a * 'c)

   (* val unknown_expl :

       theory' ->

       (string * (Term.term * Term.term)) list ->

       (string * string) list -> SpecifyTools.itm list *)

  end

(***. handle an input calc-head .***)

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

structure inform :INFORM =

struct

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

datatype iitem = 

  Given of cterm' list

(*Where is never input*) 

| Find  of cterm' list

| Relate  of cterm' list;

type imodel = iitem list;

(*calc-head as input*)

type icalhd =

     pos' *     (*the position of the calc-head in the calc-tree

		 pos' as (p,p_) where p_ is neglected due to pos_ below*) 

     cterm' *   (*the headline*)

     imodel *   (*the model (without Find) of the calc-head*)

     pos_ *     (*model belongs to Pbl or Met*)

     spec;      (*specification: domID, pblID, metID*)

val e_icalhd = (e_pos', "", [Given [""]], Pbl, e_spec): icalhd;

fun is_casinput (hdf: cterm') ((fmz_, spec): fmz) =

    hdf <> "" andalso fmz_ = [] andalso spec = e_spec;

(*.handle an input as into an algebra system.*)

fun dtss2itm_ ppc (d, ts) =

    let val (f, (d, id)) = the (find_first ((curry op= d) o 

					    (#1: (term * term) -> term) o

					    (#2: pbt_ -> (term * term))) ppc)

    in ([1], true, f, Cor ((d, ts), (id, ts))) end;

fun flattup2 (a,(b,c,d,e)) = (a,b,c,d,e);

(*.association list with cas-commands, for generating a complete calc-head.*)

type castab = 

     (term *         (*cas-command, eg. 'solve'*)

      (spec * 	     (*theory, problem, method*)

       		     (*the function generating a kind of formalization*)

       (term list -> (*the arguments of the cas-command, eg. (x+1=2, x)*)

	(term *      (*description of an element*)

	 term list)  (*value of the element (always put into a list)*)

	    list)))  (*of elements in the formalization*)

	 list;       (*of cas-entries in the association list*)

val castab = ref ([]: castab);

(*..*)

(* val (dI,pI,mI) = spec;

   *)

(*fun cas_input_ ((dI,pI,mI): spec) dtss =

    let val thy = assoc_thy dI

	val {ppc,...} = get_pbt pI

	val its_ = map (dtss2itm_ ppc) dtss (*([1],true,"#Given",Cor (...))*)

	val its = add_id its_

	val pits = map flattup2 its

	val (pI, mI) = if mI <> ["no_met"] then (pI, mI)

		   else let val Some (pI,_) = refine_pbl thy pI pits

			in (pI, (hd o #met o get_pbt) pI) end

	val {ppc,pre,prls,...} = get_met mI

	val its_ = map (dtss2itm_ ppc) dtss (*([1],true,"#Given",Cor (...))*)

	val its = add_id its_

	val mits = map flattup2 its

	val pre = check_preconds thy prls pre mits

in (pI, pits: itm list, mI, mits: itm list, pre) end;*)

(* val (dI,pI,mI) = spec;

   *)

fun cas_input_ ((dI,pI,mI): spec) dtss =

    let val thy = assoc_thy dI

	val {ppc,...} = get_pbt pI

	val its_ = map (dtss2itm_ ppc) dtss (*([1],true,"#Given",Cor (...))*)

	val its = add_id its_

	val pits = map flattup2 its

	val (pI, mI) = if mI <> ["no_met"] then (pI, mI)

		   else case refine_pbl thy pI pits of

			    Some (pI,_) => (pI, (hd o #met o get_pbt) pI)

			  | None => (pI, (hd o #met o get_pbt) pI)

	val {ppc,pre,prls,...} = get_met mI

	val its_ = map (dtss2itm_ ppc) dtss (*([1],true,"#Given",Cor (...))*)

	val its = add_id its_

	val mits = map flattup2 its

	val pre = check_preconds thy prls pre mits

in (pI, pits: itm list, mI, mits: itm list, pre) end;

(*.check if the input term is a CAScmd and return a ptree with 

   a _complete_ calchead.*)

(* val hdt = ifo;

   *)

fun cas_input hdt =

    let val (h,argl) = strip_comb hdt

    in case assoc (!castab, h) of

	   None => None

	 (*let val (pt,_) = 

		   cappend_problem e_ptree [] e_istate 

				   ([], e_spec) ([], e_spec, e_term)

	   in (pt, (false, Pbl, e_term(*FIXXME031:'not found'*),

		    [], [], e_spec)) end*)

	 | Some (spec as (dI,_,_), argl2dtss) =>

	   (* val Some (spec as (dI,_,_), argl2dtss ) = assoc (!castab, h);

	    *)

	   let val dtss = argl2dtss argl

	       val (pI, pits, mI, mits, pre) = cas_input_ spec dtss

	       val spec = (dI, pI, mI)

	       val (pt,_) = 

		   cappend_problem e_ptree [] e_istate ([], e_spec) 

				   ([], e_spec, hdt)

	       val pt = update_spec pt [] spec

	       val pt = update_pbl pt [] pits

	       val pt = update_met pt [] mits

	   in Some (pt, (true, Met, hdt, mits, pre, spec):ocalhd) end

    end;

(*lazy evaluation for Isac.thy*)

fun Isac _  = assoc_thy "Isac.thy";

(*re-parse itms with a new thy and prepare for checking with ori list*)

fun parsitm dI (itm as (i,v,b,f, Cor ((d,ts),_)):itm) =

(* val itm as (i,v,b,f, Cor ((d,ts),_)) = hd probl;

   *)

    (let val t = (term_of o comp_dts (Isac "delay")) (d,ts);

	 val s = Sign.string_of_term (sign_of dI) t;

     (*this    ^ should raise the exn on unability of re-parsing dts*)

     in itm end handle _ => ((i,v,false,f, Syn (term2str t)):itm))

  | parsitm dI (itm as (i,v,b,f, Syn str)) =

    (let val t = (term_of o the o (parse dI)) str

     in (i,v,b,f, Par str) end handle _ => (i,v,b,f, Syn str))

  | parsitm dI (itm as (i,v,b,f, Typ str)) =

    (let val t = (term_of o the o (parse dI)) str

     in (i,v,b,f, Par str) end handle _ => (i,v,b,f, Syn str))

  | parsitm dI (itm as (i,v,_,f, Inc ((d,ts),_))) =

    (let val t = (term_of o comp_dts (Isac "delay")) (d,ts);

	 val s = Sign.string_of_term (sign_of dI) t;

     (*this    ^ should raise the exn on unability of re-parsing dts*)

     in itm end handle _ => ((i,v,false,f, Syn (term2str t)):itm))

  | parsitm dI (itm as (i,v,_,f, Sup (d,ts))) =

    (let val t = (term_of o comp_dts (Isac"delay" )) (d,ts);

	 val s = Sign.string_of_term (sign_of dI) t;

     (*this    ^ should raise the exn on unability of re-parsing dts*)

     in itm end handle _ => ((i,v,false,f, Syn (term2str t)):itm))

  | parsitm dI (itm as (i,v,_,f, Mis (d,t'))) =

    (let val t = d $ t';

	 val s = Sign.string_of_term (sign_of dI) t;

     (*this    ^ should raise the exn on unability of re-parsing dts*)

     in itm end handle _ => ((i,v,false,f, Syn (term2str t)):itm))

  | parsitm dI (itm as (i,v,_,f, Par _)) = 

    raise error ("parsitm ("^itm2str_ dI itm^

		 "): Par should be internal");

(*separate a list to a pair of elements that do NOT satisfy the predicate,

 and of elements that satisfy the predicate, i.e. (false, true)*)

fun filter_sep pred xs =

  let fun filt ab [] = ab

        | filt (a,b) (x :: xs) = if pred x 

				 then filt (a,b@[x]) xs 

				 else filt (a@[x],b) xs

  in filt ([],[]) xs end;

fun is_Par ((_,_,_,_,Par _):itm) = true

  | is_Par _ = false;

fun is_e_ts [] = true

  | is_e_ts [Const ("List.list.Nil", _)] = true

  | is_e_ts _ = false;

(*WN.9.11.03 copied from fun appl_add (in modspec.sml)*)

(* val (sel,ct) = selct;

   val (dI, oris, ppc, pbt, (sel, ct))=

       (#1 (some_spec ospec spec), oris, []:itm list,

	((#ppc o get_pbt) (#2 (some_spec ospec spec))),

	hd (imodel2fstr imodel));

   *)

fun appl_add' dI oris ppc pbt (sel, ct) = 

    let 

	val thy = assoc_thy dI;

    in case parse thy ct of

	   None => (0,[],false,sel, Syn ct):itm

	 | Some ct => (* val Some ct = parse thy ct;

		          *)

    (case is_known thy sel oris (term_of ct) of

	 (* val ("",ori'(*ts='ct'*), all) = is_known thy sel oris (term_of ct);

	     *)

	 ("",ori'(*ts='ct'*), all) => 

	 (case is_notyet_input thy ppc all ori' pbt of

	      (* val ("",itm) = is_notyet_input thy ppc all ori' pbt;

	          *)

	      ("",itm)  => itm

	 (* val (msg,xx) = is_notyet_input thy ppc all ori' pbt;

	    *)

	    | (msg,_) => raise error ("appl_add': "^msg))

	 (* val (msg,(_,_,_,d,ts),all) = is_known thy sel oris (term_of ct);

	    *)

       | (msg,(i,v,_,d,ts),_) => 

	 if is_e_ts ts then (i,v,false, sel, Inc ((d,ts),(e_term,[])))

	 else (i,v,false,sel, Sup (d,ts)))

    end;

(*.generate preliminary itm_ from a strin (with field "#Given" etc.).*)

(* val (f, str) = hd selcts;

   *)

fun eq7 (f, d) (f', (d', _)) = f=f' andalso d=d';

fun fstr2itm_ thy pbt (f, str) =

    let val topt = parse thy str

    in case topt of

	   None => ([], false, f, Syn str)

	 | Some ct => 

(* val Some ct = parse thy str;

   *)

	   let val (d,ts) = ((split_dts thy) o term_of) ct

	       val popt = find_first (eq7 (f,d)) pbt

	   in case popt of

		  None => ([1](*??*), true(*??*), f, Sup (d,ts))

		| Some (f, (d, id)) => ([1], true, f, Cor ((d,ts), (id, ts))) 

	   end

    end; 

(*.input into empty PblObj, i.e. empty fmz+origin (unknown example).*)

fun unknown_expl dI pbt selcts =

  let

    val thy = assoc_thy dI

    val its_ = map (fstr2itm_ thy pbt) selcts (*([1],true,"#Given",Cor (...))*)

    val its = add_id its_ 

in (map flattup2 its): itm list end;

(*WN.11.03 for input_icalhd, ~ specify_additem for Add_Given/_Find/_Relation

 appl_add': generate 1 item 

 appl_add' . is_known: parse, get data from oris (vats, all (elems if list)..)

 appl_add' . is_notyet_input: compare with items in model already input

 insert_ppc': insert this 1 item*)

(* val (dI,oris,ppc,pbt,selcts) =((#1 (some_spec ospec spec)),oris,[(*!!*)],

			       ((#ppc o get_pbt) (#2 (some_spec ospec spec))),

			       (imodel2fstr imodel));

   *)

fun appl_adds dI [] _ pbt selcts = unknown_expl dI pbt selcts

  (*already present itms in model are being overwritten*)

  | appl_adds dI oris ppc pbt [] = ppc

  | appl_adds dI oris ppc pbt (selct::ss) =

    (* val selct = (sel, string_of_cterm ct);

       *)

    let val itm = appl_add' dI oris ppc pbt selct;

    in appl_adds dI oris (insert_ppc' itm ppc) pbt ss end;

(* val (dI, oris, ppc, pbt, selct::ss) = 

       (dI, pors, probl, ppc, map itms2fstr probl);

   ...vvv

   *)

(* val (dI, oris, ppc, pbt, (selct::ss))=

       (#1 (some_spec ospec spec), oris, []:itm list,

	((#ppc o get_pbt) (#2 (some_spec ospec spec))),(imodel2fstr imodel));

   val iii = appl_adds dI oris ppc pbt (selct::ss); 

   writeln(itms2str_ thy iii);

 val itm = appl_add' dI oris ppc pbt selct;

 val ppc = insert_ppc' itm ppc;

 val _::selct::ss = (selct::ss);

 val itm = appl_add' dI oris ppc pbt selct;

 val ppc = insert_ppc' itm ppc;

 val _::selct::ss = (selct::ss);

 val itm = appl_add' dI oris ppc pbt selct;

 val ppc = insert_ppc' itm ppc;

 writeln(itms2str_ thy ppc);

 val _::selct::ss = (selct::ss);

 val itm = appl_add' dI oris ppc pbt selct;

 val ppc = insert_ppc' itm ppc;

   *)

fun oris2itms _ _ ([]:ori list) = ([]:itm list)

  | oris2itms pbt vat ((i,v,f,d,ts)::(os: ori list)) =

    if vat mem v 

    then (i,v,true,f,Cor ((d,ts),(e_term,[])))::(oris2itms pbt vat os)

    else oris2itms pbt vat os;

fun filter_dsc oris itm = 

    filter_out ((curry op= ((d_in o #5) (itm:itm))) o 

		(#4:ori -> term)) oris;

fun par2fstr ((_,_,_,f, Par s):itm) = (f, s)

  | par2fstr itm = raise error ("par2fstr: called with "^

			      itm2str_ (assoc_thy "Isac.thy") itm);

fun itms2fstr ((_,_,_,f, Cor ((d,ts),_)):itm) = (f, comp_dts'' (d,ts))

  | itms2fstr (_,_,_,f, Syn str) = (f, str)

  | itms2fstr (_,_,_,f, Typ str) = (f, str)

  | itms2fstr (_,_,_,f, Inc ((d,ts),_)) = (f, comp_dts'' (d,ts))

  | itms2fstr (_,_,_,f, Sup (d,ts)) = (f, comp_dts'' (d,ts))

  | itms2fstr (_,_,_,f, Mis (d,t)) = (f, term2str (d $ t))

  | itms2fstr (itm as (_,_,_,f, Par _)) = 

    raise error ("parsitm ("^itm2str_ (assoc_thy "Isac.thy") itm^

		 "): Par should be internal");

fun imodel2fstr iitems = 

    let fun xxx is [] = is

	  | xxx is ((Given strs)::iis) = 

	    xxx (is @ (map (pair "#Given") strs)) iis

	  | xxx is ((Find strs)::iis) = 

	    xxx (is @ (map (pair "#Find") strs)) iis

	  | xxx is ((Relate strs)::iis) = 

	    xxx (is @ (map (pair "#Relate") strs)) iis

    in xxx [] iitems end;

(*.input a CAS-command via a whole calchead;

   dWN0602 ropped due to change of design in the front-end.*)

(*since previous calc-head _only_ has changed:

  EITHER _1_ part of the specification OR some items in the model;

  the hdform is left as is except in cas_input .*)

(*FIXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX___Met___XXXXXXXXXXXME.TODO.WN:11.03*)

(*   val ((p,_), hdf, imodel, Pbl, spec as (dI,pI,mI)) = 

       (p, "xxx", empty_model, Pbl, e_spec);

   val ((p,_), hdf, imodel, Pbl, spec as (dI,pI,mI)) = 

       (p,"", [Given ["fixedValues [r=Arbfix]"],

	       Find ["maximum A", "valuesFor [a,b]"],

	       Relate ["relations [A=a*b, a/2=r*sin alpha, \

		       \b/2=r*cos alpha]"]], Pbl, e_spec);   

   val ((p,_), hdf, imodel, Pbl, spec as (dI,pI,mI)) = 

       (([],Pbl), "not used here",

	[Given ["fixedValues [r=Arbfix]"],

	 Find ["maximum A", "valuesFor [a,b]"(*new input*)], 

	 Relate ["relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]"]], Pbl, 

        ("DiffApp.thy", ["e_pblID"], ["e_metID"]));

   val ((p,_), hdf, imodel, Pbl, spec as (dI,pI,mI)) = ichd;

   *)

fun input_icalhd pt (((p,_), hdf, imodel, Pbl, spec as (dI,pI,mI)):icalhd) =

    let val PblObj {fmz = fmz as (fmz_,_), origin = (oris, ospec, hdf'), 

		    spec = sspec as (sdI,spI,smI), probl, meth,...} = 

	    get_obj I pt p;

    in if is_casinput hdf fmz then the (cas_input (str2term hdf)) 

       else        (*hacked WN0602 ~~~            ~~~~~~~~~,   ..dropped !*)

       let val (pos_, pits, mits) = 

	       if dI <> sdI

	       then let val its = map (parsitm (assoc_thy dI)) probl;

			val (its, trms) = filter_sep is_Par its;

			val pbt = (#ppc o get_pbt) (#2(some_spec ospec sspec));

		    in (Pbl, appl_adds dI oris its pbt 

				       (map par2fstr trms), meth) end else

	       if pI <> spI 

	       then if pI = snd3 ospec then (Pbl, probl, meth) else

		    let val pbt = (#ppc o get_pbt) pI

			val dI' = #1 (some_spec ospec spec)

			val oris = if pI = #2 ospec then oris 

				   else prep_ori fmz_(assoc_thy"Isac.thy") pbt;

		    in (Pbl, appl_adds dI' oris probl pbt 

				       (map itms2fstr probl), meth) end else

	       if mI <> smI (*FIXME.WN0311: what if probl is incomplete?!*)

	       then let val met = (#ppc o get_met) mI

		        val mits = complete_metitms oris probl meth met

		    in if foldl and_ (true, map #3 mits)

		       then (Pbl, probl, mits) else (Met, probl, mits) 

		    end else

	       (Pbl, appl_adds (#1 (some_spec ospec spec)) oris [(*!!!*)]

			       ((#ppc o get_pbt) (#2 (some_spec ospec spec)))

			       (imodel2fstr imodel), meth);

	   val pt = update_spec pt p spec;

       in if pos_ = Pbl

	  then let val {prls,where_,...} = get_pbt (#2 (some_spec ospec spec))

		   val pre =check_preconds(assoc_thy"Isac.thy")prls where_ pits

	       in (update_pbl pt p pits,

		   (ocalhd_complete pits pre spec, 

		    Pbl, hdf', pits, pre, spec):ocalhd) end

	  else let val {prls,pre,...} = get_met (#3 (some_spec ospec spec))

		   val pre = check_preconds (assoc_thy"Isac.thy") prls pre mits

	       in (update_met pt p mits,

		   (ocalhd_complete mits pre spec, 

		    Met, hdf', mits, pre, spec):ocalhd) end

       end end

  | input_icalhd pt ((p,_), hdf, imodel, _(*Met*), spec as (dI,pI,mI)) =

    raise error "input_icalhd Met not impl.";

(***. handle an input formula .***)

(*

Untersuchung zur Formeleingabe (appendFormula, replaceFormla) zu einer Anregung von Alan Krempler:

Welche RICHTIGEN Formeln koennen NICHT abgeleitet werden, 

wenn Abteilungen nur auf gleichem Level gesucht werden ?

WN.040216 

Beispiele zum Equationsolver von Richard Lang aus /src/sml/kbtest/rlang.sml

------------------------------------------------------------------------------

"Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";

------------------------------------------------------------------------------

1. "5 * x / (x - 2) - x / (x + 2) = 4"

...

4. "12 * x + 4 * x ^^^ 2 = 4 * (-4 + x ^^^ 2)",Subproblem["normalize", "poly"..

...

4.3. "16 + 12 * x = 0", Subproblem["degree_1", "polynomial", "univariate"..

...

4.3.3. "[x = -4 / 3]")), Check_elementwise "Assumptions"

...

"[x = -4 / 3]"

------------------------------------------------------------------------------

(1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]

(4.1)..(4.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]

------------------------------------------------------------------------------

------------------------------------------------------------------------------

"Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";

------------------------------------------------------------------------------

1. "x / (x ^^^ 2 - 6 * x + 9) - 1 / (x ^^^ 2 - 3 * x) = 1 / x"

...

4. "(3 + (-1 * x + x ^^^ 2)) * x = 1 * (9 * x + (x ^^^ 3 + -6 * x ^^^ 2))"

                         Subproblem["normalize", "polynomial", "univariate"..

...

4.4. "-6 * x + 5 * x ^^^ 2 = 0", Subproblem["bdv_only", "degree_2", "poly"..

...

4.4.4. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"

4.4.5. "[x = 0, x = 6 / 5]"

...

5. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"

   "[x = 6 / 5]"

------------------------------------------------------------------------------

(1)..(4): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite schiebt [Ableitung waere in 4.4.x]

(4.1)..(4.4.5): keine 'richtige' Eingabe kann abgeleitet werden, die dem Ergebnis "[x = 6 / 5]" aequivalent ist [Ableitung waere in 5.]

------------------------------------------------------------------------------

------------------------------------------------------------------------------

"Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";

------------------------------------------------------------------------------

1. "sqrt (x + 1) + sqrt (4 * x + 4) = sqrt (9 * x + 9)"

...

6. "13 + 13 * x + -2 * sqrt ((4 + 4 * x) * (9 + 9 * x)) = 1 + x"

                             Subproblem["sq", "root", "univariate", "equation"]

...

6.6. "144 + 288 * x + 144 * x ^^^ 2 = 144 + x ^^^ 2 + 288 * x + 143 * x ^^^ 2"

                Subproblem["normalize", "polynomial", "univariate", "equation"]

...

6.6.3 "0 = 0"    Subproblem["degree_0", "polynomial", "univariate", "equation"]

...                                       Or_to_List

6.6.3.2 "UniversalList"

------------------------------------------------------------------------------

(1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die eine der Wurzeln auf die andere Seite verschieb [Ableitung ware in 6.6.n]

(6.1)..(6.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 6.6.n]

------------------------------------------------------------------------------

*)

(*sh. comments auf 498*)

fun equal a b = a=b;

(*the lists contain eq-al elem-pairs at the beginning;

  return first list reverted (again) - ie. in order as required subsequently*)

fun dropwhile' equal (f1::f2::fs) (i1::i2::is) =

    if equal f1 i1 then

	 if equal f2 i2 then dropwhile' equal (f2::fs) (i2::is)

	 else (rev (f1::f2::fs), i1::i2::is)

    else raise error "dropwhile': did not start with equal elements"

  | dropwhile' equal (f::fs) [i] =

    if equal f i then (rev (f::fs), [i])

    else raise error "dropwhile': did not start with equal elements"

  | dropwhile' equal [f] (i::is) =

    if equal f i then ([f], i::is)

    else raise error "dropwhile': did not start with equal elements";

(*

 fun equal a b = a=b;

 val foder = [0,1,2,3,4,5]; val ifoder = [11,12,3,4,5];

 val r_foder = rev foder;  val r_ifoder = rev ifoder;

 dropwhile' equal r_foder r_ifoder;

> vval it = ([0, 1, 2, 3], [3, 12, 11]) : int list * int list

 val foder = [3,4,5]; val ifoder = [11,12,3,4,5];

 val r_foder = rev foder;  val r_ifoder = rev ifoder;

 dropwhile' equal r_foder r_ifoder;

> val it = ([3], [3, 12, 11]) : int list * int list

 val foder = [5]; val ifoder = [11,12,3,4,5];

 val r_foder = rev foder;  val r_ifoder = rev ifoder;

 dropwhile' equal r_foder r_ifoder;

> val it = ([5], [5, 4, 3, 12, 11]) : int list * int list

 val foder = [10,11,12,13,14,15]; val ifoder = [11,12,3,4,5];

 val r_foder = rev foder;  val r_ifoder = rev ifoder;

 dropwhile' equal r_foder r_ifoder;

> *** dropwhile': did not start with equal elements*)

(*040214: version for concat_deriv*)

fun rev_deriv' (t, r, (t', a)) = (t', sym_Thm r, (t, a));

fun mk_tacis ro erls (t, r as Thm _, (t', a)) = 

    (Rewrite (rule2thm' r), 

     Rewrite' ("Isac.thy", fst ro, erls, false, 

	       rule2thm' r, t, (t', a)),

     (e_pos'(*to be updated before generate tacis!!!*), Uistate))

  | mk_tacis ro erls (t, r as Rls_ rls, (t', a)) = 

    (Rewrite_Set (rule2rls' r), 

     Rewrite_Set' ("Isac.thy", false, rls, t, (t', a)),

     (e_pos'(*to be updated before generate tacis!!!*), Uistate));

(*fo = ifo excluded already in inform*)

fun concat_deriv rew_ord erls rules fo ifo =

    let fun derivat ([]:(term * rule * (term * term list)) list) = e_term

	  | derivat dt = (#1 o #3 o last_elem) dt

        fun equal (_,_,(t1, _)) (_,_,(t2, _)) = t1=t2

	val  fod = make_deriv (Isac"") erls rules (snd rew_ord) None  fo

	val ifod = make_deriv (Isac"") erls rules (snd rew_ord) None ifo

    in case (fod, ifod) of

	   ([], []) => if fo = ifo then (true, [])

		       else (false, [])

	 | (fod, []) => if derivat fod = ifo 

			then (true, fod) (*ifo is normal form*)

			else (false, [])

	 | ([], ifod) => if fo = derivat ifod 

			 then (true, ((map rev_deriv') o rev) ifod)

			 else (false, [])

	 | (fod, ifod) =>

	   if derivat fod = derivat ifod (*common normal form found*)

	   then let val (fod', rifod') = 

			dropwhile' equal (rev fod) (rev ifod)

		in (true, fod' @ (map rev_deriv' rifod')) end

	   else (false, [])

    end;

(*

 val ({rew_ord, erls, rules,...}, fo, ifo) = 

     (rep_rls Test_simplify, str2term "x+1+ -1*2=0", str2term "-2*1+(x+1)=0");

 (writeln o trtas2str) fod';

> ["

(x + 1 + -1 * 2 = 0, Thm ("radd_commute","?m + ?n = ?n + ?m"), (-1 * 2 + (x + 1) = 0, []))","

(-1 * 2 + (x + 1) = 0, Thm ("radd_commute","?m + ?n = ?n + ?m"), (-1 * 2 + (1 + x) = 0, []))","

(-1 * 2 + (1 + x) = 0, Thm ("radd_left_commute","?x + (?y + ?z) = ?y + (?x + ?z)"), (1 + (-1 * 2 + x) = 0, []))","

(1 + (-1 * 2 + x) = 0, Thm ("#mult_Float ((~1,0), (0,0)) __ ((2,0), (0,0))","-1 * 2 = -2"), (1 + (-2 + x) = 0, []))"]

val it = () : unit

 (writeln o trtas2str) (map rev_deriv' rifod');

> ["

(1 + (-2 + x) = 0, Thm ("sym_#mult_Float ((~2,0), (0,0)) __ ((1,0), (0,0))","-2 = -2 * 1"), (1 + (-2 * 1 + x) = 0, []))","

(1 + (-2 * 1 + x) = 0, Thm ("sym_radd_left_commute","?y + (?x + ?z) = ?x + (?y + ?z)"), (-2 * 1 + (1 + x) = 0, []))","

(-2 * 1 + (1 + x) = 0, Thm ("sym_radd_commute","?n + ?m = ?m + ?n"), (-2 * 1 + (x + 1) = 0, []))"]

val it = () : unit

*)

(*.compare inform with ctree.form at current pos by nrls;

   if found, embed the derivation generated during comparison

   if not, let the mat-engine compute the next ctree.form.*)

(*structure copied from complete_solve

  CAUTION: tacis in returned calcstate' do NOT construct resulting ptp --

           all_modspec etc. has to be inserted at Subproblem'*)

(* val (tacis, c, ptp as (pt, pos as (p,p_))) = (tacis, ptp);

   val (tacis, c, ptp as (pt, pos as (p,p_))) = cs';

   val (tacis, c, ptp as (pt, pos as (p,p_))) = ([],[],(pt, lev_back pos));

   -----rec.call:

   val (tacis, c, ptp as (pt, pos as (p,p_))) = cs';

   *)

fun compare_step ((tacis, c, ptp as (pt, pos as (p,p_))): calcstate') ifo =

    let val fo = case p_ of Frm => get_obj g_form pt p

			  | Res => (fst o (get_obj g_result pt)) p

			  | _ => e_term (*on PblObj is fo <> ifo*);

	val {nrls,...} = get_met (get_obj g_metID pt (par_pblobj pt p))

	val {rew_ord, erls, rules,...} = rep_rls nrls

	val (found, der) = concat_deriv rew_ord erls rules fo ifo;

    in if found

       then let val tacis' = map (mk_tacis rew_ord erls) der;

		val (c', ptp) = embed_deriv tacis' ptp;

	    in ("ok", (tacis (*@ tacis'?WN050408*), c @ c', ptp)) end

       else 

	   if pos = ([], Res) 

	   then ("no derivation found", (tacis, c, ptp): calcstate') 

	   else let val cs' as (tacis, c', ptp) = nxt_solve_ ptp;

		    val cs' as (tacis, c'', ptp) = 

			case tacis of

			    ((Subproblem _, _, _)::_) => 

			    let val ptp as (pt, (p,_)) = all_modspec ptp

				val mI = get_obj g_metID pt p

			    in nxt_solv (Apply_Method' (mI, None, e_istate)) 

					e_istate ptp end

			  | _ => cs';

		in compare_step (tacis, c @ c' @ c'', ptp) ifo end

    end;

(* writeln (trtas2str der);

   *)

(*.handle a user-input formula, which may be a CAS-command, too.

CAS-command:

   create a calchead, and do 1 step

   TOOODO.WN0602 works only for the root-problem !!!

formula, which is no CAS-command:

   compare iform with calc-tree.form at pos by equ_nrls and all subsequent pos;

   collect all the tacs applied by the way.*)

(*structure copied from autocalc*)

(* val (cs as (_,  _, (pt, pos as (p, p_))): calcstate') = cs';

   val ifo = str2term ifo;

   val ((cs as (_, _, ptp as (pt, pos as (p, p_))): calcstate'), istr) =

       (cs', encode ifo);

   val ((cs as (_, _, ptp as (pt, pos as (p, p_)))), istr)=(cs', (encode ifo));

   val ((cs as (_, _, ptp as (pt, pos as (p, p_))): calcstate'), istr) =

       (([],[],(pt,p)), (encode ifo));

   *)

fun inform (cs as (_, _, ptp as (pt, pos as (p, p_))): calcstate') istr =

    case parse (assoc_thy "Isac.thy") istr of

(* val Some ifo = parse (assoc_thy "Isac.thy") istr;

   *)

	Some ifo =>

	let val ifo = term_of ifo

	    val fo = case p_ of Frm => get_obj g_form pt p

			      | Res => (fst o (get_obj g_result pt)) p

			      | _ => #3 (get_obj g_origin pt p)

	in if fo = ifo

	   then ("same-formula", cs)

	   (*thus ctree not cut with replaceFormula!*)

	   else case cas_input ifo of

(* val Some (pt, _) = cas_input ifo;

   *)

		    Some (pt, _) => ("ok",([],[],(pt, (p, Met))))

		  | None =>

		    compare_step ([],[],(pt,

				     (*last step re-calc in compare_step TODO*)

					 lev_back pos)) ifo

	end

      | None => ("syntax error in '"^istr^"'", e_calcstate');

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

end

open inform; 

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