(*  Title:      src/Tools/isac/BridgeJEdit/Calculation.thy

     Author:     Walther Neuper, JKU Linz

 Outer syntax for Isabelle/Isac's Calculation interactive via Isabelle/PIDE.

 Second trial following Makarius' definition of "problem" already existing in this repository.

 *)

 theory Calculation

   imports

   (**)"$ISABELLE_ISAC/Knowledge/Build_Thydata"   (*remove after devel.of BridgeJEdit*)

   (**)"$ISABELLE_ISAC/MathEngine/MathEngine"

   (** )"SPARK_FDL"                             ( * remove after devel.of BridgeJEdit*)

 keywords "Example" :: thy_decl

 and "Problem" "Specification" "Model" "References" "Solution" 

 begin

 ML_file "parseC.sml"

 ML_file "preliminary.sml"

 section \<open>new code for Outer_Syntax Example  ...\<close>

 text \<open> 

   stepwise development starts at changeset

   https://hg.risc.uni-linz.ac.at/wneuper/isa/rev/9d98791b4080

   and can be inspected following the subsequent changesets..

 \<close>

 ML \<open>

 \<close> ML \<open>

 \<close> ML \<open>

 structure Data = Theory_Data

 (

   type T = Ctree.ctree option;

   val empty = NONE;

   val extend = I;

   fun merge _ = NONE;

 );

 val set_data = Data.put o SOME;

 fun the_data thy = 

   case Data.get thy of NONE => Ctree.EmptyPtree

   | SOME ctree => ctree;

 \<close> ML \<open>

 \<close> text \<open>

 A provisional Example collection.

 For notes from ISAC's discontinued Java front-end see

 https://isac.miraheze.org/wiki/Extend_ISAC_Knowledge#Add_an_example_in_XML_format

 \<close> ML \<open>

 type description = string

 type example = (description * Formalise.T)

 type example_id = string

 val example_store = Unsynchronized.ref ([]: (example_id * example) list)

 fun get_example example_id =

   case AList.lookup op= (!example_store) example_id of

     NONE => raise ERROR ("Examnple " ^ quote example_id ^ " not found")

   | SOME expl => expl

 \<close> ML \<open>

 get_example: example_id -> example;

 \<close> ML \<open>

 example_store := AList.update op= ("Diff_App/No.123 a", 

  ("The efficiency of an electrical coil depends on the mass of the kernel." ^

   "Given is a kernel with cross-sectional area determined by two rectangles" ^

   "of same shape as shown in the figure." ^

   "Given a radius r = 7, determine the length u and width v of the rectangles" ^

   "such that the cross-sectional area A (and thus the mass of the kernel) is a" ^

   "maximum. + Figure", 

    ([

    (*Problem model:*)

      "Constants [r = (7::real)]", "Maximum A", "AdditionalValues [u, v]",

      "Extremum (A = 2 * u * v - u \<up> 2)",

      "SideConditions [((u::real) / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2]",

      "SideConditions [((u::real) / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2]",

      "SideConditions [(u::real) / 2 = r * sin \<alpha>, 2 / v = r * cos \<alpha>]",

    (*MethodC model:*)

      "FunctionVariable a", "FunctionVariable b", "FunctionVariable \<alpha>",

      "Domain {0 <..< r}",

      "Domain {0 <..< r}",

      "Domain {0 <..< \<pi> / 2}",

      "ErrorBound (\<epsilon> = (0::real))"]: TermC.as_string list,

     ("Diff_App", ["univariate_calculus", "Optimisation"], 

       ["Optimisation", "by_univariate_calculus"]): References.T)): example) (!example_store)

 \<close> ML \<open>

 case get_example "Diff_App/No.123 a" of

   (_, ("Constants [r = (7::real)]" :: "Maximum A" :: "AdditionalValues [u, v]" :: _, 

     ("Diff_App", ["univariate_calculus", "Optimisation"] ,["Optimisation", "by_univariate_calculus"]))) 

     => ()

 | _ => error "intermed. example_store CHANGED";

 \<close> ML \<open>

 \<close> ML \<open>

 (*

   Implementation reasonable, as soo as

  * clarified, how "empty" items in Model are represented

  * parse_references_input works

  * switching \<Odot>\<Otimes> i_model for probl and meth works.

 *)

 fun check_input (*ctxt o-model ??*) (_: Problem.model_input) = []: I_Model.T (*TODO*)

 \<close> ML \<open>

 \<close> ML \<open>

 (* at the first encounter of an Example create the following data and transfer them to ctree:

     origin: eventually used by sub-problems, too

     O_Model: for check of missing items

     I_Model: for efficient check of user input

 *)

 \<close> ML \<open>

 fun init_ctree example_id =

     let

       (* TODO     vvvvvvvvvvvvvvv works only within Isac_Test_Base *)

       val thy = (*ThyC.get_theory thy_id*)@{theory Diff_App}

       val (_, (fmz as (model, refs as (_(*thy_id*), probl_id, _)))) = get_example example_id

       val ctxt = ContextC.initialise' thy model;

       val o_model = Problem.from_store probl_id |> #ppc |> O_Model.init thy model

     in

       Ctree.Nd (Ctree.PblObj {

         fmz = fmz, origin = (o_model, refs, TermC.empty (*TODO handle CAS_Cmd*)),

         spec = References.empty, probl = I_Model.empty, meth = I_Model.empty,

         ctxt = ctxt, loc = (NONE, NONE), 

         branch = Ctree.NoBranch, ostate = Ctree.Incomplete, result = (TermC.empty, [])}, [])

     end

 \<close> ML \<open>

 (* 

 At the first call 

 * initialise ctree with origin from example_id

 * add items already input ..TODO..TODO..TODO..TODO..TODO..TODO..TODO..TODO..TODO

 *)

 \<close> ML \<open>

 fun update_state (example_id, (model, refs)) Ctree.EmptyPtree = 

     init_ctree example_id |>  update_state (example_id, (model, refs))

   | update_state (_, (model, (thy_id, probl_id, meth_id)))

     (Ctree.Nd (Ctree.PblObj {fmz, origin, spec as (othy, opbl, omet), probl = _, meth, ctxt, loc, branch, ostate, result}, 

       children)) =

       let 

         val _ = if thy_id <> othy then "re-parse all i_model" else "do nothing"

         val _ = if probl_id <> opbl then "switch from meth? check_input of probl" else "do nothing"

         val _ = if meth_id <> omet then "switch from probl check_input of meth" else "do nothing"

       in

         Ctree.Nd (Ctree.PblObj {

           fmz = fmz, origin = origin, spec = References.select_input spec (thy_id, probl_id, meth_id), 

           probl = check_input model, meth = meth, (*TODO +switch Problem_Ref | Method_Ref*)

           ctxt = ctxt, loc = loc, 

           branch = branch, ostate = ostate, result = result}, children)

       end

   | update_state _ _ = raise ERROR "update_state: uncovered case in fun.def"

 \<close> ML \<open>

 \<close> ML \<open>

 \<close> ML \<open>

 update_state: example_id * (Problem.model_input * References.T) -> Ctree.ctree -> Ctree.ctree

 \<close> ML \<open>

 type references_input = (string * (string * string))

 \<close> ML \<open>

 val parse_references_input =

   Parse.!!! ( \<^keyword>\<open>Theory_Ref\<close> -- \<^keyword>\<open>Theory_Ref\<close> |-- Parse.name --

   Parse.!!! ( \<^keyword>\<open>Problem_Ref\<close> -- \<^keyword>\<open>Theory_Ref\<close> |-- Parse.name --

   Parse.!!! ( \<^keyword>\<open>Method_Ref\<close> -- \<^keyword>\<open>Theory_Ref\<close> |-- Parse.name)))

 \<close> ML \<open>

 parse_references_input: references_input parser (*TODO: dpes not yet work,

   thus in Outer_Syntax.command \<^command_keyword>\<open>Example\<close> replacced by Problem.parse_cas*)

 \<close> ML \<open>

 op --  : ('a -> 'b * 'c) * ('c -> 'd * 'e) -> 'a -> ('b * 'd) * 'e;

 op |-- : ('a -> 'b * 'c) * ('c -> 'd * 'e) -> 'a -> 'd * 'e

 \<close> ML \<open>

 \<close> ML \<open>

 \<close> ML \<open>

 fun is_empty str = 

   let

     val strl = Symbol.explode str |> rev

   in

     take (2, strl) = ["_", " "] orelse take (3, strl) = ["]", "_", "["]

   end

 \<close> ML \<open>

 val m2 = "0 < r";                val m2' = Symbol.explode m2 |> rev;

 val m3 = "Maximum _";            val m3' = Symbol.explode m3 |> rev;

 val m4 = "AdditionalValues [_]"; val m4' = Symbol.explode m4 |> rev;

 \<close> ML \<open>

 \<close> ML \<open>

 val _ =

   Outer_Syntax.command \<^command_keyword>\<open>Example\<close>

     "prepare ISAC problem type and register it to Knowledge Store"

     (Parse.name -- Parse.!!! ( \<^keyword>\<open>Specification\<close> -- \<^keyword>\<open>:\<close> --

          \<^keyword>\<open>Model\<close> -- \<^keyword>\<open>:\<close>  |-- Problem.parse_model_input --

          Parse.!!! ( \<^keyword>\<open>References\<close> -- \<^keyword>\<open>:\<close> |-- (*parse_references_input*) Problem.parse_cas)) >>

       (fn (example_id, (model_input, _(*references_input*))) =>

         Toplevel.theory (fn thy =>

           let

 (** )

 val _ = writeln ("#Example model_input: " ^ @{make_string} model_input)

 (*                #Example model_input:

     [("#Given", ["<markup>"]), ("#Where", ["<markup>"]), ("#Find", ["<markup>", "<markup>"]), ("#Relate", ["<markup>", "<markup>"])]*)

 val [("#Given", [m1]), ("#Where", [m2]), ("#Find", [m3, m4]), ("#Relate", [m5, m6])] = 

   model_input : Problem.model_input

 val _ = writeln ("#Example m.: " ^ m1 ^ " " ^ m2 ^ " " ^ m3 ^ " " ^ m4 ^ " " ^ m4 ^ " " ^ m5 ^ " " ^ m6)

 val m2' = Symbol.explode m2;

 val _ = writeln ("#Example Symbol.explode m2: " ^ @{make_string} m2')

 val _ = if (is_empty m2) then writeln "true" else writeln "false";

 val _ = if (is_empty m3) then writeln "true" else writeln "false";

 val _ = if (is_empty m4) then writeln "true" else writeln "false";

 (*                #Example m.: Constants [r = 7] 0 < r Maximum _ AdditionalValues [_] AdditionalValues [_] Extremum _ SideCondition [_]*)

 ( **)

             val (thy_id, (probl_id, meth_id)) = (*references_input*)("Diff_App", ("univariate_calculus/Optimisation", "Optimisation/by_univariate_calculus"))

             val input = update_state (example_id, (model_input, 

               (thy_id, References_Def.explode_id probl_id, References_Def.explode_id meth_id)))

                 Ctree.EmptyPtree;

           in set_data input thy end)));

 \<close> ML \<open>

 \<close> ML \<open>

 (*/----------------------------------------------------------------------------\*)

      Parse.name -- Parse.!!! (  \<^keyword>\<open>Problem\<close> |-- Parse.name -- 

        Parse.!!! ( \<^keyword>\<open>Specification\<close> -- \<^keyword>\<open>:\<close> --

          \<^keyword>\<open>Model\<close> -- \<^keyword>\<open>:\<close>  |-- Problem.parse_model_input --

          Parse.!!! ( \<^keyword>\<open>References\<close> -- \<^keyword>\<open>:\<close> |-- parse_references_input)))

 : (string * (string * (Problem.model_input * references_input))) parser

 (*\----------------------------------------------------------------------------/*) 

 : Token.T list ->

 (*/----------------------------------------------------------------------------\*)

     (string * (string * (Problem.model_input * references_input)))

 (*\----------------------------------------------------------------------------/*)

 * Token.T list

 (*/----------------------------------------------------------------------------\* )

    the type above is the type of the argument of \<open>(fn (_(*name*),..\<close> 

 ( *\----------------------------------------------------------------------------/*)

 \<close> ML \<open>

 \<close> ML \<open>

 \<close> text \<open>

   INVESTIGATE Problem.Outer_Syntax.command \ <^command_keyword>\<open>problem\<close>

   on Biegelinie.problem pbl_bieg : "Biegelinien"

   ML-source shows error-positions already perfectly: what types are involved?..

 \<close> ML \<open>

 Rule_Set.append_rules "empty" Rule_Set.empty [] (* ORIGINAL source = ARGUMENT IN fn *)

 (* (1a)

   Ouptut from Biegelinie.problem pbl_bieg : "Biegelinien":

   #problem source: Source {delimited = true, range = ({offset=38, end_offset=87, id=-1652}, {offset=87, id=-1652}), 

     text = "\127Rule_Set.append_rules \"empty\" Rule_Set.empty []\127"}

 *)

 \<close> ML \<open>

 val source = Input.empty;

 val ml = ML_Lex.read;

 \<close> ML \<open>

   (ml "Theory.setup (Problem.set_data (" @ ML_Lex.read_source source @ ml "))")

 (*= 

    [Text (Token (({}, {}), (Long_Ident, "Theory.setup"))), Text (Token (({}, {}), (Space, " "))), Text (Token (({}, {}), (Keyword, "("))), Text (Token (({}, {}), (Long_Ident, "Problem.set_data"))),

     Text (Token (({}, {}), (Space, " "))), Text (Token (({}, {}), (Keyword, "("))), Text (Token (({}, {}), (Space, " "))), Text (Token (({}, {}), (Keyword, ")"))), Text (Token (({}, {}), (Keyword, ")"))),

     Text (Token (({}, {}), (Space, " ")))]

    : ML_Lex.token Antiquote.antiquote list

    ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ type of (1a)

 *)

 \<close> ML \<open>

 ML_Context.expression (Input.pos_of source)

   (ml "Theory.setup (Problem.set_data (" @ ML_Lex.read_source source @ ml "))")

   : Context.generic -> Context.generic

 \<close> ML \<open>

 ML_Context.expression (Input.pos_of source)

   (ml "Theory.setup (Problem.set_data (" @ ML_Lex.read_source source @ ml "))")

   |> Context.theory_map

   : theory -> theory

 \<close> ML \<open>

 Outer_Syntax.command: Outer_Syntax.command_keyword -> string -> 

   (Toplevel.transition -> Toplevel.transition) parser -> unit

 \<close> ML \<open>

 \<close> text \<open>

   ML-source shows error-positions already perfectly: types involved are above.

   Input at Given does NOT show error-position, 

     but ISAC msg \<open>ME_Isa: thy "Isac_Knowledge" not in system\<close>

   Thus compare ML-source/input with model_input ...

 \<close> ML \<open>

 Problem.parse_model_input:                 Problem.model_input parser;

 Problem.parse_model_input: Token.src ->    Problem.model_input * Token.src;

 Problem.parse_model_input: Token.T list -> Problem.model_input * (Token.T list)

 \<close> ML \<open>

 []: Position.range list;

 []: Position.T list;

 \<close> ML \<open>

 \<close> ML \<open>

 (* Given: "Traegerlaenge l_l" "Streckenlast q_q" *)

 (* (1b)

   Ouptut from Biegelinie.problem pbl_bieg : "Biegelinien":

   #problem model_input: [("#Given", ["<markup>", "<markup>"]), ("#Find", ["<markup>"]), ("#Relate", ["<markup>"])] 

                         : Problem.model_input

   type of  (1b) --------^^^^^^^^^^^^^^^^^^^^^^> contains ? Markup.T ?..

   #problem m1: Traegerlaenge l_l

   #problem m2: Streckenlast q_q 

   I this -----^^^______________^^^ Markup.T ?

 *)

 \<close> ML \<open> (** investigate parse_model_input **)

 \<close> ML \<open> (* how get a Token.T list without Outer_Syntax.command ? *)

 \<close> ML \<open>

 Parse.term:                 string parser;

 Parse.term: Token.T list -> string * Token.T list;

 \<close> ML \<open>

 \<close> ML \<open> (* relation Token.T -- Markup.T ??? *)

 \<close> ML \<open>

 val ctxt = Proof_Context.init_global @{theory};

 val given_1 = Syntax.read_term ctxt "Traegerlaenge l_l" (* as in parse_tagged_terms *)

 (*  ^^^^^^^ : term  -- why then evaluates parse_model_input to markup ? *)

 \<close> ML \<open>

 \<close> ML \<open>

 Markup.literal_fact "Traegerlaenge l_l" = ("literal_fact", [("name", "Traegerlaenge l_l")])

 \<close> ML \<open>

 \<close> ML \<open>

 \<close> ML \<open>

 \<close>

 end