1.1 --- a/src/Tools/isac/Doc/Lucas_Interpreter/document/root.tex Sat Dec 30 17:52:03 2023 +0100
1.2 +++ b/src/Tools/isac/Doc/Lucas_Interpreter/document/root.tex Sun Dec 31 09:42:27 2023 +0100
1.3 @@ -1,4 +1,4 @@
1.4 -% into "root.tex" as created by "isabelle mkdir"
1.5 +% into "root.tex" as created by "isabelle mkdir"
1.6 % code from "llncs/samplepaper.tex" is inserted -- llncs NOT COMPATIBLE WITH package isabelle
1.7
1.8 \documentclass{article}
1.9 @@ -63,8 +63,7 @@
1.10 % optional bibliography
1.11 \bibliographystyle{plain}
1.12 % \bibliographystyle{splncs04}
1.13 -% splncs04 CAUSES ERROR
1.14 -% SEE ~/material/templates/llncs/README
1.15 +% .. causes ERROR, SEE isabisac/src/Doc/Demo_EPTCS
1.16 \bibliography{root}
1.17
1.18 \end{document}
2.1 --- a/src/Tools/isac/Doc/ROOT Sat Dec 30 17:52:03 2023 +0100
2.2 +++ b/src/Tools/isac/Doc/ROOT Sun Dec 31 09:42:27 2023 +0100
2.3 @@ -23,6 +23,7 @@
2.4 "Specify_Phase"
2.5 document_files
2.6 "coil-kernel-uv.png"
2.7 + "equat-ws-pbl.eps"
2.8 "Screenshot-problemdef-running-expl.png"
2.9 "specification-complete.png"
2.10 "specification-method.png"
3.1 --- a/src/Tools/isac/Doc/Specify_Phase/Specify_Phase.thy Sat Dec 30 17:52:03 2023 +0100
3.2 +++ b/src/Tools/isac/Doc/Specify_Phase/Specify_Phase.thy Sun Dec 31 09:42:27 2023 +0100
3.3 @@ -729,8 +729,456 @@
3.4 \texttt{Model\_Pattern.T} are clear, and only the hierarchy of problem types
3.5 would have to be searched for the appropriate type.
3.6
3.7 +\sisac's old Java front-end had a so-called CAS-command for that situation,
3.8 +where one had minimal input, for instance $\it{solve\;(12 - 6\cdot x = 0, \;x)}$. Then
3.9 +\sisac{} checked the most general precondition (an ``$=$'' in the input) and
3.10 +then started a breadth-first search in the tree of equations at the root
3.11 +``univariate'', checking in sequence the type of the input term,
3.12 +\texttt{linear}, \texttt{root}, \texttt{polynomial}, rational, complex or transcendental.
3.13 +Fig.\ref{fig:tre-of-equations} %on p.\pageref{fig:tre-of-equations}
3.14 +shows the currently available equations presented by the old Java fron-end.
3.15 +\begin{figure} [htb]
3.16 + \centering
3.17 + \includegraphics[width=0.75\textwidth]{equat-ws-pbl.eps}
3.18 + \caption{The tree of equations (middle panel).}
3.19 + \label{fig:tre-of-equations}
3.20 +\end{figure}
3.21 +All these panels shall be redone by Isabelle/PIDE via Isabelle/VSCode.
3.22
3.23 +The more interesting question is, whether this coarse refinement via
3.24 +preconditions can be generalised to a kind of matching, which involves also
3.25 +the postcondition (see p.\pageref{postcondition}); theoretical background
3.26 +would most likely be the refinement calculus \cite{Back1998}.
3.27
3.28 +
3.29 +\subsection{Transition to the Solve-Phase} \label{ssec:solve-phase}
3.30 +%------------------------------------------------------------------------------
3.31 +The solve-phase tackles the construction of a \texttt{Solution} for a given problem,
3.32 +where ``next-step-guidance'' is provided by Lucas-Interpretation \cite{wn:lucin-thedu20}.
3.33 +For that purpose Lucas-Interpretation uses a program, and for such a program
3.34 +the values specified by a \texttt{Model} instantiate the formal arguments
3.35 +of the program to actual arguments. So items move from \texttt{Relate} to
3.36 +\texttt{Given} and new items need to be added to the program's guard
3.37 +in order to provide the program
3.38 +with all data required for automatically construct a \texttt{Solution}. Thus the
3.39 +\texttt{Model} for the guard of the \texttt{demo\_example} might look as shown in
3.40 +Fig.\ref{fig:specification-method} below.
3.41 +%on p.\pageref{fig:specification-method}.
3.42 +\begin{figure} [htb]
3.43 + \centering
3.44 + \includegraphics[width=0.75\textwidth]{specification-method.png}
3.45 + \caption{The \texttt{Model} for the \texttt{Method\_Ref}.}
3.46 + \label{fig:specification-method}
3.47 +\end{figure}
3.48 +
3.49 +The reader might notice that the toggle $\odot\otimes$ has changed,
3.50 +indicating that the \texttt{Model} belongs to the \texttt{Method\_Ref}
3.51 +(The toggle is not implemented presently and just reminded of by a comment).
3.52 +
3.53 +\medskip
3.54 +So the \texttt{References} come into play, they raise lots of open design
3.55 +decisions: We encounter insightful \emph{references} into huge data collections;
3.56 +their representation will heavily depend on specific features of VSCode
3.57 +(while the structure of theories, DAGs, has not even an interactive representation
3.58 +presently). Should they be collapsed by settings, if they would distract
3.59 +a certain class from problem solving? Should students be forced to input
3.60 +\texttt{References}, and when?
3.61 +
3.62 +A reasonable intermediate step in development might be that a \texttt{Model}
3.63 +could be accepted as complete (e.g. Fig.\ref{fig:specification-complete}) by the
3.64 +system even with empty \texttt{References} (e.g.
3.65 +Fig.\ref{fig:specification-template}) and a \texttt{Solution} could be started.
3.66 +
3.67 +\medskip
3.68 +Toggling the \texttt{Model} between \texttt{Model\_Ref} and \texttt{Method\_Ref}
3.69 +(the former shown in Fig.\ref{fig:specification-complete} on p.\pageref{fig:specification-complete},
3.70 +the latter in Fig.\ref{fig:specification-method})
3.71 +will be a challenge for implementation in Isabelle/VSCode.
3.72 +
3.73 +
3.74 +\section{Implementation in Isabelle/Isar} \label{sect:implementation}
3.75 +%==============================================================================
3.76 +This paper also intends to demonstrate that it is waste of resources to start
3.77 +development of educational math software from scratch -- nowadays users
3.78 +expectations on software are high such that an isolated development cannot
3.79 +keep pace with the still rapidly evolving state of the art. This is
3.80 +particularly true for front-end technology. \sisac's long lasting experience with formula editors clearly
3.81 +demonstrates that unpleasant fact, which enforced \sisac{} to drop ten years of
3.82 +front-end development.
3.83 +
3.84 +This section is going to demonstrate simplicity of implementing a specific
3.85 +input language as introduced in \S\ref{sect:design} above in one of the
3.86 +advanced proof assistants, in this case Isabelle. Isar \cite{wenzel:isar} is
3.87 +the proof language of Isabelle and remarkably, this is defined in a generic
3.88 +manner such that almost arbitrary formal languages can be defined; for a
3.89 +particularly interesting example see \cite{Isabelle/Naproce}.
3.90 +
3.91 +\subsection{Isabelle's Outer and Inner Syntax} \label{ssec:outer-syntax}
3.92 +%------------------------------------------------------------------------------
3.93 +Isabelle separates two kinds of syntax, an inner syntax for mathematical terms
3.94 +and an outer syntax for Isabelle/Isar's language elements. The latter is generic
3.95 +such that it allows for definition of various language layers. And it is a
3.96 +pleasure to show how easily an \sisac{} \texttt{Specification} is defined such
3.97 +that all inner syntax errors are indicated at the right location on screen,
3.98 +i.e. how easily all what is shown in the screen-shots on the previous pages
3.99 +are implemented such that syntax errors are shown appropriately:
3.100 +\begin{small}
3.101 +\begin{verbatim}
3.102 + 01 keywords "Example" :: thy_decl
3.103 + 02 and "Specification" "Model" "References" "Solution"
3.104 +\end{verbatim}
3.105 +\end{small}
3.106 +The above two lines prepare Isar to re-use available parsers
3.107 +\footnote{In spite of Isabelle's convenient latex extensions we still use verbatim,
3.108 +which displays ``keyword$<$Specification$>$'' as clumsily as
3.109 +``keyword{\textbackslash}$<$open$>$Specification{\textbackslash}$<$close$>$''}:
3.110 +
3.111 +\begin{small}
3.112 +\begin{verbatim}
3.113 + 01 Outer_Syntax.command command_keyword\<open>Example_TEST\<close>
3.114 + 02 "prepare ISAC problem type and register it to Knowledge Store"
3.115 + 03 (Parse.name -- Parse.!!! (keyword\<open>Specification\<close> --keyword<:> --
3.116 + 04 keyword<Model> -- keyword<:> |-- Problem.parse_pos_model_input --
3.117 + 05 (keyword<References> -- keyword<:> |-- Parse.!!! References.parse_input_pos
3.118 + 06 )) >>
3.119 + 07 (fn (example_id, (model_input,
3.120 + 08 ((thy_id, thy_pos), ((probl_id, probl_pos), (meth_id, meth_pos))))) =>
3.121 + 09 Toplevel.theory (fn thy =>
3.122 + 10 let
3.123 + 11 val state = update_step example_id model_input
3.124 + 12 ((thy_id, thy_pos), ((probl_id, probl_pos), (meth_id, meth_pos)))
3.125 + 13 in set_data state thy end)));
3.126 +\end{verbatim}
3.127 +\end{small}
3.128 +
3.129 +With these two definitions done, one has in \texttt{update\_step} only to
3.130 +provide appropriate calls of this function:
3.131 +\begin{small}
3.132 +\begin{verbatim}
3.133 + 01 fun term_position ctxt (str, pos) =
3.134 + 02 Syntax.read_term ctxt str
3.135 + 03 handle ERROR msg => error (msg ^ Position.here pos)
3.136 + 04 (*this exception is caught by PIDE to show "msg" at the proper location*)
3.137 +\end{verbatim}
3.138 +\end{small}
3.139 +The exception \texttt{ERROR} is caught by Isabelle/PIDE and, for instance,
3.140 +syntax errors detected by \texttt{Syntax.read\_term} are displayed at the
3.141 +proper locations on screen together with \texttt{msg}.
3.142 +\emph{That is all what Isar requires to check syntax of input as
3.143 +shown in the screen shots in the previous section and to indicate errors
3.144 +at the proper location on screen.}
3.145 +
3.146 +\medskip
3.147 +The handling of \emph{semantic} errors is accomplished with Isabelle/ML,
3.148 +Standard ML \cite{pl:milner97} enriched with an abundant collection of tools for
3.149 +formal logic as well as for connection to the front-end via
3.150 +Isabelle/PIDE \cite{EPTCS79.9}.
3.151 +This will be shown in the sequel.
3.152 +
3.153 +
3.154 +\subsection{Interaction and Feedback} \label{ssec:interaction}
3.155 +%------------------------------------------------------------------------------
3.156 +Checking semantic appropriateness of user input to a Specification as
3.157 +described in \S\ref{sect:design} above, comprises a lot of
3.158 +questions: Does an item input to a \texttt{Model} belong to this particular
3.159 +example or is it just \texttt{Superfluous}? If there a list is
3.160 +to be input, are all the elements present or are some missing (items are
3.161 +\texttt{Incomplete})? Is a
3.162 +\texttt{Model} complete with respect to a specified \texttt{Problem\_Ref}?
3.163 +If \texttt{Theory\_Ref} is input, are all the items of a \texttt{Model} still
3.164 +parsed correctly (or can, for instance, $"\it{Re}\, a + \it{Im}\, b")$ not be
3.165 +parsed correctly, because the specified theory does not know the type
3.166 +``complex'')? Etc.
3.167 +
3.168 +The central device for handling feedback to the above questions is the so-called\\
3.169 +\texttt{INTERACTION\_MODEL} with the type \texttt{I\_Model.T}
3.170 +\footnote{In \sisac's code this definition is shifted into a separate
3.171 +\texttt{structure Model\_Def} \emph{before} the definition of the store of a
3.172 +calculation, \texttt{Ctree}, which still lacks type polymorphism}
3.173 +(where \texttt{variants} is a list of integers and \texttt{m\_field} has been
3.174 +introduced by \texttt{type Model\_Pattern.T} on p.\pageref{src:model-pattern}).
3.175 +\texttt{Position.T} establishes the reference to the location on screen:
3.176 +\begin{small}
3.177 +\begin{verbatim}
3.178 + 01 type I_Model.single =
3.179 + 02 variants * (* pointers to variants given in Formalise.model *)
3.180 + 03 m_field * (* #Given | #Find | #Relate *)
3.181 + 04 (feedback * (* state of feedback for variables and values *)
3.182 + 05 Position.T); (* for pushing feedback back to PIDE *)
3.183 +
3.184 + 06 type I_Model.T = I_Model.single list;
3.185 +\end{verbatim}
3.186 +\end{small}
3.187 +\texttt{feedback} implements \UR\ref{UR:feedback} and resembles the
3.188 +structure of \texttt{datatype feedback} in the presentation layer as shown on
3.189 +p.\pageref{src:feedback} in \S\ref{ssec:interactivity}.
3.190 +The first three characters suffice for internal naming:
3.191 +\begin{small}
3.192 +\begin{verbatim}
3.193 + 01 datatype I_Model.feedback =
3.194 + 02 Cor of (descriptor * (* a term identifying an item *)
3.195 + 03 (values)) (* of a particular example *)
3.196 + 04 | Inc of (descriptor * values) (* incomplete lists/sets,
3.197 + if empty then output according to UR*)
3.198 + 05 | Sup of (descriptor * values) (* input not found Model *)
3.199 + 06 | Syn of TermC.as_string (* kept for P_Model.switch_pbl_met *)
3.200 +\end{verbatim}\label{src:i-model}
3.201 +\end{small}
3.202 +
3.203 +
3.204 +\subsection{Step-wise Construction of Specifications} \label{ssec:stepwise}
3.205 +%------------------------------------------------------------------------------
3.206 +Step-wise construction is one of the axioms for \sisac's design as captured on
3.207 +p.\pageref{axiom:stepwise-inter}. While step-wise construction appears
3.208 +self-evident for the solve-phase, where Lucas-Interpretation suggests or checks
3.209 +one input formula after the other, this appears artificial for the
3.210 +specify-phase: one can input any item to a \texttt{Specification} in any
3.211 +sequence, items of a \texttt{Model} as well as \texttt{References}.
3.212 +But there is also \UR\ref{UR:next-step}, which calls for the system's ability
3.213 +to propose a next step -- and here we are:
3.214 +\begin{small}
3.215 +\begin{verbatim}
3.216 + 01 datatype Tactic.input =
3.217 + 02 (* for specify-phase *)
3.218 + 04 Add_Find of TermC.as_string (*add to the model*)
3.219 + 05 | Add_Given of TermC.as_string | Add_Relation of TermC.as_string
3.220 + 06 | Model_Problem (*internal*)
3.221 + 07 | Refine_Problem of Problem.id (*refine a Model_Pattern.T*)
3.222 + 08 | Refine_Tacitly of Problem.id (*internal*)
3.223 + 09 | Specify_Method of MethodC.id (*specify References*)
3.224 + 10 | Specify_Problem of Problem.id | Specify_Theory of ThyC.id
3.225 + 11 (* for solve-phase *)
3.226 + 12 | ...
3.227 +\end{verbatim}
3.228 +\end{small}
3.229 +The above \texttt{Tactic}s are shown to the user, while some are used only
3.230 +internally; \texttt{Refine\_*} will be introduced in \S\ref{ssec:refine} below.
3.231 +A variant stuffed with lots of data serve internal construction of a next step;
3.232 +the lists below shows only some examples:
3.233 +\begin{small}
3.234 +\begin{verbatim}
3.235 + 01 datatype T =
3.236 + 02 Add_Find' of TermC.as_string * I_Model.T | Add_Given' of TermC.as_string * I_Model.T
3.237 + 04 | Add_Relation' of TermC.as_string * I_Model.T
3.238 + 05 | Model_Problem' of (*starts the specify-phase *)
3.239 + 06 Problem.id * (*key to a Problem.T Store.node*)
3.240 + 07 I_Model.T * (*model for the Problem *)
3.241 + 08 I_Model.T (*model for the MethoC *)
3.242 + 09 | Refine_Problem' ...
3.243 +\end{verbatim}
3.244 +\end{small}
3.245 +
3.246 +
3.247 +\subsection{Refinement of Problems} \label{ssec:refine}
3.248 +%------------------------------------------------------------------------------
3.249 +\UR\ref{UR:refine} calls for refinement, a respective motivation was given
3.250 +in \S\ref{ssec:auto-spec}. Here implementation details are presented, because
3.251 +the subsequent section will address efficiency consideration raised by
3.252 +refinement
3.253 +\footnote{By the way, Lucas-Interpretation \cite{wn:lucin-thedu20} is straightened
3.254 +considerably when equation solving in sub-problems automatically refines to
3.255 +the appropriate type of equation}.
3.256 +
3.257 +A \texttt{Problem.T} is defined in an Isabelle theory; here the definition of
3.258 +the model-pattern of the running example is shown.
3.259 +\begin{figure} [htb]
3.260 + \centering
3.261 + \includegraphics[width=0.8\textwidth]{Screenshot-problemdef-running-expl.png}
3.262 + \caption{The problem-pattern for the running example.}
3.263 + \label{fig:pbl-max-expl}
3.264 +\end{figure}
3.265 +This model-pattern covers almost all examples of a well-known text book, the items
3.266 +are identified by the \texttt{descriptor}s; variables like \texttt{fixes}
3.267 +are to be instantiated from a \texttt{Formalise.model} as explained on
3.268 +p.\pageref{env-subst}.
3.269 +The convenient representation in Fig.\ref{fig:pbl-max-expl}
3.270 +is stuffed with data required to solve a problem
3.271 +(see, for instance, the \texttt{$<$eval\_rls$>$}) and expanded to the type
3.272 +\texttt{Problem.T}:
3.273 +\begin{small}
3.274 +\begin{verbatim}
3.275 + 01 type Problem.T =
3.276 + 02 {guh : Check_Unique.id, (* unique within Isac_Knowledge *)
3.277 + 03 mathauthors : string list, (* copyright etc *)
3.278 + 04 start_refine : References_Def.id, (* to start refinement with *)
3.279 + 05 thy : theory, (* allows to compile model, where_*)
3.280 + 06 cas : term option, (* CAS_Cmd *)
3.281 + 07 solve_mets : References_Def.id list,(* methods solving the T *)
3.282 + 08 where_rls : Rule_Set.T, (* for evaluation of preconditions*)
3.283 + 09 where_ : Pre_Conds.unchecked, (* preconditions as terms *)
3.284 + 10 model : Model_Pattern.T (* "#Given", "#Find", "#Relate" *)
3.285 + 11 }
3.286 +\end{verbatim}\label{src:Problem-T}
3.287 +\end{small}
3.288 +By this type problems are stored in a tree borrowed from Isabelle;
3.289 +the key \texttt{["univariate\_calculus", Optimisation""]}
3.290 +into this tree is created from the string
3.291 +\texttt{"univariate\_calculus/Optimisation"} in Fig.\ref{fig:pbl-max-expl}:
3.292 +\begin{small}
3.293 +\begin{verbatim}
3.294 + 01 type store = (T Store.node) list
3.295 +\end{verbatim}
3.296 +\end{small}
3.297 +
3.298 +
3.299 +\subsection{Efficiency Considerations with Parsing} \label{ssec:efficiency}
3.300 +%------------------------------------------------------------------------------
3.301 +Two decades ago, at the time when \sisac{} started with development, parsing
3.302 +required substantial resources. Thus a specific component, \texttt{O\_Model.T}
3.303 +was shifted in-between \texttt{Formalise.model} (p.\pageref{src:demo-expl})
3.304 +and the interaction model \texttt{I\_Model.T} (p.\pageref{src:i-model}).
3.305 +\begin{small}
3.306 +\begin{verbatim}
3.307 + 01 type O_Model.single =
3.308 + 02 variants * (* pointers to variants given in Formalise.T *)
3.309 + 03 m_field * (* #Given | #Find | #Relate *)
3.310 + 04 descriptor * (* see Input_Descript.thy *)
3.311 + 05 values (* HOLlist_to_MLlist t | [t] *)
3.312 + 06 );
3.313 + 07 type O_Model.T = O_Model.single list;
3.314 +\end{verbatim}
3.315 +\end{small}
3.316 +This structure is created at the beginning of the specify-phase
3.317 +(by \texttt{Tactic.Model\_Problem}). The terms are already parsed,
3.318 +\texttt{descriptor} and \texttt{values} conveniently separated;
3.319 +also the variants are ready for convenient handling. At the occasion of parsing
3.320 +also an Isabelle \texttt{Proof\_Context} is fed with the types of all variables
3.321 +in \texttt{Formalise.model}. This discharges the student of the necessity
3.322 +to explicitly input types.
3.323 +
3.324 +\paragraph{Refinement of types of equations} as introduced by \UR\ref{UR:refine}
3.325 +is particularly resources consuming: Fig.\ref{fig:tre-of-equations} on
3.326 +p.\pageref{fig:tre-of-equations} shows that already the old prototype
3.327 +implemented quite a lot of types of equations. Refinement starts at the root
3.328 +\texttt{["univariate", "equation"]} of the branch, an environment with respect
3.329 +to the given equation has to be created from the \texttt{I\_Model.T} and
3.330 +the current \texttt{Model\_Pattern.T},
3.331 +with this environment for each node in the tree the respective \texttt{"\#Given"}
3.332 +and \texttt{"\#Where"} needs to be instantiated, and last not least the latter
3.333 +requires evaluation by rewriting (see \S\ref{ssec:preconds} below).
3.334 +
3.335 +All that tasks act on terms, i.e. require parsing. If this is done during interactive
3.336 +problem solving, response time will get to high even with modern hardware.
3.337 +Thus not only \texttt{Problem.T} (see definition on p.\pageref{problem})
3.338 +contains terms alreay parsed, but also \texttt{Model\_Pattern.T} and other
3.339 +structures.
3.340 +These structures (\texttt{Model\_Pattern.T}, \texttt{Problem.T},
3.341 +\texttt{MethodC.T} and \texttt{Error\_Pattern.T}) hold terms, where the exact
3.342 +type is not known at compile time, and where the type needs to be adapted to
3.343 +the current \texttt{Problem.T}. Thus all these structures have a function
3.344 +\begin{small}
3.345 +\begin{verbatim}
3.346 + 01 val adapt_to_type Proof.context -> T -> T
3.347 +\end{verbatim}
3.348 +\end{small}
3.349 +and these functions in turn call
3.350 +\begin{small}
3.351 +\begin{verbatim}
3.352 + 01 val adapt_term_to_type: Proof.context -> term -> term
3.353 +\end{verbatim}
3.354 +\end{small}
3.355 +which is defined in structure \texttt{ParseC}.
3.356 +
3.357 +
3.358 +\subsection{Pre-Conditions in Problems and Methods} \label{ssec:preconds}
3.359 +%------------------------------------------------------------------------------
3.360 +Pre-conditions are an essential part of a formal specification
3.361 +(definition in \S\ref{ssec:urs-specify} Pt.\ref{UR:form-spec} on
3.362 +p.\pageref{UR:form-spec}). We compare the definition to \sisac's representation
3.363 +of a \texttt{Model} (e.g. on p.\pageref{fig:specification-template},
3.364 +p.\pageref{fig:specification-complete} or p.\pageref{fig:specification-method}):
3.365 +\begin{center}
3.366 + \begin{tabular}{ l | l}
3.367 + formal specification & \sisac's \texttt{Model} \\ \hline\hline
3.368 + $\it{in}$ & \texttt{Given} \\ \hline
3.369 + $\it{Pre}\;(\it{in})$ & \texttt{Where} \\ \hline
3.370 + $\it{out}$ & \texttt{Find} \\ \hline
3.371 + $\it{Post}\;(\it{in},\,\it{out})$ & \texttt{Relate} \\
3.372 + \hline
3.373 + \end{tabular}
3.374 +\end{center}
3.375 +However, \texttt{type Model\_Pattern.T} (defintion on p.\pageref{src:model-pattern})
3.376 +does \emph{not} contain a precondition ($\it{Pre}\;(\it{in})$, \texttt{Where})
3.377 +and so does the actual \texttt{Model} of a \texttt{Problem.T} (defintion on
3.378 +p.\pageref{src:Problem-T}; for specifics of \texttt{Relate} see
3.379 +p.\pageref{post-cond}).
3.380 +The reason is that the role of items in a \texttt{Model} is to
3.381 +conform with a particular \texttt{Formalise.model} (made ready by parsing
3.382 +in \texttt{I\_Model.T}) and whether it is present or not --
3.383 +whereas a precondition must evaluate to true in order to make a \texttt{Model}
3.384 +complete; this involves rewriting. The implementation details are as follows.
3.385 +\begin{small}
3.386 +\begin{verbatim}
3.387 + 01 type Pre_Conds.T = (bool * term) list;
3.388 + 02 type Pre_Conds.unchecked_pos = (term * Position.T) list
3.389 + 03 type Pre_Conds.checked_pos = bool * ((bool * (term * Position.T)) list)
3.390 +\end{verbatim}
3.391 +\end{small}
3.392 +The role of preconditions is different from \texttt{Model}-items such that
3.393 +preconditions are stored only in a \texttt{Problem.T}
3.394 +(accompanied by a \texttt{Model}) and evaluated by use of environments,
3.395 +which are generated on the fly according to \texttt{I\_Model} actually
3.396 +input:
3.397 +\begin{small}
3.398 +\begin{verbatim}
3.399 + 01 val make_environments: Model_Pattern.T -> I_Model.T ->
3.400 + 02 Env.T * (env_subst * env_eval)
3.401 + 03 val check_pos: Proof.context -> Rule_Set.T -> unchecked_pos ->
3.402 + 04 Model_Pattern.T * I_Model.T -> checked_pos
3.403 +\end{verbatim}
3.404 +\end{small}
3.405 +
3.406 +
3.407 +\section{Summary and Conclusions} \label{sect:conclusion}
3.408 +%==============================================================================
3.409 +This is the first concise description of how the \sisac{} prototype
3.410 +models the specify-phase. The specify-phase concerns the transition from a
3.411 +problem statement given in the form prose text and/or illustrations to a
3.412 +formal specification.
3.413 +
3.414 +The description starts with user requirements in \S\ref{sect:user-requirements}
3.415 +and thus presents the perspective of students solving exercises in engineering
3.416 +studies (similar learning scenarios can be found in secondary schools).
3.417 +Here is also the definition of the notion ``formal specification'' as given
3.418 +by input and output as well as precondition and postcondition.
3.419 +\S\ref{sect:design} describes the design of the specify-phase with regard to
3.420 +the user requirements and identifies open design issues.
3.421 +The description of the implementation in \S\ref{sect:implementation} emphasises
3.422 +the generic tools of Isabelle/Isar and the powerful helper functions of
3.423 +Isabelle/ML to motivate readers to use existing proof assistants as a basis
3.424 +for the development of for the development of learning systems rather than
3.425 +starting from scratch again and again.
3.426 +
3.427 +Another motivation for this description is to inform
3.428 +future collaborators of the Isac project about implementation details and
3.429 +its background.
3.430 +
3.431 +\paragraph{Conclusions} Over the decades, Isac's design of the specify-phase
3.432 +and the solve-phase was discussed long and wide and has proven useful in
3.433 +field tests;
3.434 +the time is ripe to move into development for widespread use.
3.435 +It seems helpful that the old Java-based front end has been abandoned and
3.436 +that the originally very ambitious specifications \cite{isac:all} are
3.437 +significantly reduced:
3.438 +\sisac{} will change from a multi-user system to a single-user system
3.439 +in line with the (current) architecture of Isabelle/PIDE;
3.440 +and in the next step of development the scope of application will be limited
3.441 +to inclusive learning situations (visually impaired students integrated)
3.442 +in secondary educational institutions
3.443 +to take advantage of the structural relationship between Isabelle's terms
3.444 +and the Braille display.
3.445 +
3.446 +The sudden penetration of AI will pose the following new research tasks.
3.447 +Starting from a differentiation of problem solving through
3.448 +\begin{compactenum}
3.449 +\item intuitively and associatively thinking humans who bear
3.450 + responsibility for their actions
3.451 +\item AI with deep learning
3.452 +\item formal mathematics
3.453 +\end{compactenum}
3.454 +the interaction of (3) and (2) will be analysed.
3.455 +Design and implementation of a user guide and a user model (from the
3.456 +interaction of (3) and (1)) is already planned in the next development step.
3.457 \<close>
3.458
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4.666 +%%Trailer
4.667 +%%Pages: 1
4.668 +%%DocumentFonts:
4.669 +%%EOF
5.1 --- a/src/Tools/isac/Doc/Specify_Phase/document/root.tex Sat Dec 30 17:52:03 2023 +0100
5.2 +++ b/src/Tools/isac/Doc/Specify_Phase/document/root.tex Sun Dec 31 09:42:27 2023 +0100
5.3 @@ -14,9 +14,11 @@
5.4
5.5 \def\isac{${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}
5.6 \def\sisac{{\footnotesize${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}}
5.7 -\def\see{$\rightarrow$}
5.8 -\newtheorem{UR}{UR}[section]
5.9 -\newtheorem{Expl}{Expl}[section]
5.10 +%WN231231 where did these 3 come from ?
5.11 +%\def\see{$\rightarrow$}
5.12 +%\newtheorem{UR}{UR}[section]
5.13 +%\newtheorem{Expl}{Expl}[section]
5.14 +\def\UR{\textbf{UR.}}
5.15
5.16 \begin{document}
5.17
5.18 @@ -24,6 +26,7 @@
5.19 \author{Walther Neuper}
5.20 %\institute{Johannes Kepler University, Linz, Austria}
5.21 \maketitle
5.22 +\vspace{2cm}
5.23 \tableofcontents
5.24 \newpage
5.25
5.26 @@ -38,8 +41,7 @@
5.27 % optional bibliography
5.28 \bibliographystyle{plain}
5.29 % \bibliographystyle{splncs04}
5.30 -% splncs04 CAUSES ERROR
5.31 -% SEE ~/material/templates/llncs/README
5.32 +% .. causes ERROR, SEE isabisac/src/Doc/Demo_EPTCS
5.33 \bibliography{root}
5.34
5.35 \end{document}