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

     Author:     Walther Neuper, JKU Linz

     (c) due to copyright terms

 Runnig example for developing Isabelle/Isac via Isabelle/PIDE in BridgeJEdit.

 File will go to test/Tools/isac/BridgeJEdit/VSCode_Example.thy

 compare         test/Tools/isac/BridgeJEdit/vscode-example.sml

 *)

 theory VSCode_Example 

   imports Calculation

 begin

 section \<open>Boilerplate, the example for Isabelle Workshop 2022\<close>

 subsection \<open>Specification Phase\<close>

 text \<open>Goal for Isabelle Workshop 2022: this part of the example should be ready for demonstration:

   1. The keyword \<open>Example\<close> inserts the template underneath

   2. The template is filled from a (hidden) formalisation with the following items in the

     2.1. \<open>Model\<close>:

         * Constants _  ("_" indicates some kind of place holder for input)

         * the complete Where-field (the pre-condition), items marked as True | False

         * Maximum _, AdditionalValues _

         * Extremum _, SideCondition _

     2.2 \<open>References\<close>:

         * place holders "_" for input

         * The toggle switch before \<open>Problem_Ref\<close> | \<open>Method_Ref\<close> is set to \<open>Problem_Ref\<close>

           This might be postponed after the Isabelle Workshop.

   3. Input to 2.1 is 

     * type checked and marked as Type-Error

     * marked as Correct | Superfluous | Incomplete | Unknown (compare Specify/p-model.sml)

   4. Input to 2.2 by selection from a list / tree

   5. On update of \<open>Problem_Ref\<close> (in the root problem) also \<open>Problem\<close> is updated;

      The argument of \<open>Problem\<close> comes with the template and is read-only.

 The specific representation of the Demo_Example demonstrate different situations

 in educational settings.

 \<close>

 subsubsection \<open>Complete Specification\<close>

 text \<open>

 * This is one correct result of interactive Specification.

 * Or this might be presented to the student in one go in order to start Solution immediately

   (and nevertheless make the Specification explicit)

 Note that \<open>Problem "univariate_calculus/Optimisation"\<close> and 

 \<open>Problem_Ref: "univariate_calculus/Optimisation"\<close> are redundant; the latter is for input,

 the former is given initially and needs to be updated in accordance to \<open>Problem_Ref\<close>.

 \<close>

 text \<open> (*.. remove as soon as this works as Isabelle/Isar commands ..*)

 Example "Diff_App/No.123 a"

   Problem "univariate_calculus/Optimisation"

     Specification:

       Model:

         Given: \<open>Constants r = 7\<close>

         Where: \<open>0 < r\<close>

         Find:  \<open>Maximum A\<close> \<open>AdditionalValues u, v\<close>

         Relate: \<open>Extremum A = 2 \<sqdot> u \<sqdot> v − u \<up> 2\<close> \<open>SideCondition (u / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2\<close>

       References:

          Theory_Ref: "Diff_App"

       \<Otimes> Problem_Ref: "univariate_calculus/Optimisation"

       \<Odot> Method_Ref: "Optimisation/by_univariate_calculus"

     Solution:

        (* remove as soon as this ^^^ works as Isabelle/Isar commands ..*) \<close>

 subsubsection \<open>Empty Specification\<close>

 text \<open>

   This is presented to the student in one go in order to start interactive Specification.

 \<close>

 text \<open> (*.. remove as soon as this works as Isabelle/Isar commands ..*)

 Example "Diff_App/No.123 a"

   Problem "_/_"

     Specification:

       Model:

         Given: \<open>Constants _\<close>

         Where: \<open>0 < r\<close>

         Find:  \<open>Maximum _\<close> \<open>AdditionalValues _\<close>

         Relate: \<open>Extremum _\<close> \<open>SideCondition _\<close>

       References:

          Theory_Ref: "_"

       \<Otimes> Problem_Ref: "_/_"

       \<Odot> Method_Ref: "_/_"

     Solution:

        (* remove as soon as this ^^^ works as Isabelle/Isar commands ..*) \<close>

 subsubsection \<open>Plain Example\<close>

 text \<open>

   This can occur in between text offering to start an interactive Calculation by using

   "Diff_App/No.123 a" as a link.

 \<close>

 text \<open> (*.. remove as soon as this works as Isabelle/Isar commands ..*)

 Example "Diff_App/No.123 a"

        (* remove as soon as this ^^^ works as Isabelle/Isar commands ..*) \<close>

 subsubsection \<open>Immediate Start of Interactive Solving\<close>

 text \<open>

   This is requested by teachers in case of CAS_Cmd, e.g. "solve (x+1=2, x)"

   where Specification usually is not interesting to students

   and thus done automatically by ISAC in the background.

 \<close>

 text \<open> (*.. remove as soon as this works as Isabelle/Isar commands ..*)

 Example "Diff_App/No.123 a"

   Problem "univariate_calculus/Optimisation"

     Specification:

     Solution:

        (* remove as soon as this ^^^ works as Isabelle/Isar commands ..*) \<close>

 subsubsection \<open>Show the Model associated to Method_Ref\<close>

 text \<open>

   The Model of a method usually comprises more items than the model of a Problem: all these

   are required to run the program such that it automatically generates a Solution. For instance,

   compare \<open>problem pbl_bieg\<close> and \<open>method met_biege_2\<close> in \<open>Biegelinie.thy\<close>

   (TODO: method/program for \<open>Problem "univariate_calculus/Optimisation"\<close>)

   The Model of a method is usually called a guard.

 \<close>

 text \<open> (*.. remove as soon as this works as Isabelle/Isar commands ..*)

 Example "Diff_App/No.123 a"

   Problem "univariate_calculus/Optimisation"

     Specification:

       Model:

         Given: \<open>Constants r = 7\<close>

         Where: \<open>0 < r\<close>

         Find:  \<open>Maximum A\<close> \<open>AdditionalValues u, v\<close>

         Relate: \<open>Extremum A = 2 \<sqdot> u \<sqdot> v − u \<up> 2\<close> \<open>SideCondition (u / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2\<close>

       References:

          Theory_Ref: "Diff_App"

       \<Odot> Problem_Ref: "univariate_calculus/Optimisation"

       \<Otimes> Method_Ref: "Optimisation/by_univariate_calculus"

     Solution:

        (* remove as soon as this ^^^ works as Isabelle/Isar commands ..*) \<close>

 section \<open>Stepwise Development\<close>

 subsection \<open>preparing VSCode_Example\<close>

 ML \<open>

 (**** preparing VSCode_Example ########################################################### ****)

 "----------- preparing VSCode_Example ----------------------------------------------------------";

 "----------- preparing VSCode_Example ----------------------------------------------------------";

 \<close> text \<open>

 --- maximum example with Step.specify_do_next --- from test/../step.sml

 val fmz = [

 (*Problem model:*)

   "fixedValues [r=Arbfix]", "maximum A",

   "valuesFor [a,b::real]",

   "relations [A=a*(b::real), (a/2) \<up> 2 + (b/2) \<up> 2 = (r::real) \<up> 2]",

   "relations [A=a*(b::real), (a/2) \<up> 2 + (b/2) \<up> 2 = (r::real) \<up> 2]",

   "relations [A=a*(b::real), a/2=r*sin alpha, b/2 = (r::real)*cos (alpha::real)]",

 (*MethodC model:*)

   "boundVariable a", "boundVariable b", "boundVariable alpha",

   "interval {x::real. 0 <= x & x <= 2*r}",

   "interval {x::real. 0 <= x & x <= 2*r}",

   "interval {x::real. 0 <= x & x <= pi}",

   "errorBound (eps=(0::real))"];

 val (dI',pI',mI') = 

 ("Diff_App", ["maximum_of", "function"], ["Diff_App", "max_by_calculus"]);

 \<close> text \<open>

 from paper "Towards Accessible Formal Mathematics with ISAC and Isabelle/VSCode"

 F_I \<equiv> [ [r = 7], [A, [u, v]], [A = 2 * u * v - u \<up> 2 , ( 2 / u ) \<up> 2 + ( 2 / v ) \<up> 2 = r \<up> 2], {0 <..< r} ]

 --- type conflict ^^ ----------^^

 F_II \<equiv> [ [r = 7], [A, \<alpha>], [A = 2 * u * v - u \<up> 2 , u / 2 = r * sin \<alpha>, 2 / v = r * cos \<alpha>], {0 <..< \<pi> / 2} ]

 \<close> ML \<open>

 val fmz = [

 (*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;

 val refs = 

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

 \<close> ML \<open>

 \<close>

 subsection \<open>Specification Phase\<close>

 text \<open> 

   Stepwise development of \<open>Outer_Syntax.command \<^command_keyword>\<open>Example\<close>\<close> begins with 

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

   in the repository.

   The intermediate steps below will be deleted as soon as all above representations 

   of Example "Diff_App/No.123 a" work out.

 \<close>

 subsubsection \<open>Complete Specification at once\<close>

 Example "Diff_App/No.123 a"

   Problem "univariate_calculus/Optimisation"

     Specification:

       Model:

         Given: \<open>Constants [r = 7]\<close>

         Where: \<open>0 < r\<close>

         Find:  \<open>Maximum A\<close> \<open>AdditionalValues [u, v]\<close>

         Relate: \<open>Extremum A = 2 * u * v - u \<up> 2\<close> 

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

       References:

 (**  )

          Theory_Ref: "Diff_App"

   (*\<Odot>*) Problem_Ref: "univariate_calculus/Optimisation"

   (*\<Otimes>*) Method_Ref: "Optimisation/by_univariate_calculus"

 (  **)

 ML \<open>

 val state = the_data @{theory}; (* state filled from the above Example by \<open>fun update_state\<close> *)

 \<close> ML \<open>

 val (o_model, refs, _) = Ctree.get_obj Ctree.g_origin state []

 val problem_model = Ctree.get_obj Ctree.g_pbl state []

 val method_model = Ctree.get_obj Ctree.g_met state []

 \<close> text \<open> (* this was with Specify.finish_phasePIDE in init_ctree, cf. 28da4f69d32d *)

 if length o_model = 12  andalso refs = 

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

   andalso length problem_model = 5 andalso length method_model = 8

 then () else error "initialised state CHANGED";

 \<close> ML \<open>

 if length o_model = 12  andalso refs = 

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

   andalso length problem_model = 0 andalso length method_model = 0

 then () else error "initialised state CHANGED";

 \<close> ML \<open>

 \<close>

 subsubsection \<open>Specification step by step\<close>

 end