]> matita.cs.unibo.it Git - helm.git/commitdiff
New session (the H-Bugs interactive session).
authorClaudio Sacerdoti Coen <claudio.sacerdoticoen@unibo.it>
Fri, 30 May 2003 15:08:25 +0000 (15:08 +0000)
committerClaudio Sacerdoti Coen <claudio.sacerdoticoen@unibo.it>
Fri, 30 May 2003 15:08:25 +0000 (15:08 +0000)
helm/papers/calculemus-2003/eps/step1.eps [new file with mode: 0644]
helm/papers/calculemus-2003/eps/step2.eps [new file with mode: 0644]
helm/papers/calculemus-2003/hbugs-calculemus-2003.tex

diff --git a/helm/papers/calculemus-2003/eps/step1.eps b/helm/papers/calculemus-2003/eps/step1.eps
new file mode 100644 (file)
index 0000000..4d55d66
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+rOi3]JY[jmJY_J)!+Po?!IFgO]`W!Ls5*I_")7i9hY+VbC&n:akbJ5geb5d=@Y+Q1s+14*rrZ^1
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+rPAT`?%J]#Tn/p%T`NSIrPASd!0I3\dcdA*?./G?!*t0UJcC<$h#@I^!<:pR^&VI:^'&9Qs3f?o
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+rOi6^>(NK#Uk,?+U]K"LrOi5Y!0I3\e``e0>1N>B!*XsRJcC<$h#@I[!<:pR]`;76]``'Ms4,Zu
+Ujr~>
+rOi6^@Y(>+Uk,?+U]K"TrOi5Y!0>[oU]FrTp7q[tJcC<$JcFO*"(D91hY+VcC&n:aebu:o~>
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+J,~>
+rPAWa?(q2sn"B^]JY@XgJY<+m?2_V@JH17pp7VLmde9@7?%N$,s+14*rrZO,s5*I`"Dn/=daJ)f
+J,~>
+rOi9_>,;)sn"]p`JY[jmJYW=s>5c,8HN8Vmp7q^meb5d=>(Q^)s+14*rrZF)s5*I_"DRr:e^aVo
+J,~>
+rOi<`@\a#'U]:DaU]:CGUk,=mU]K"TrOi5Y!.gs>U]FrTp7q[tJcC<$JcFO*"(D91V"JI)!<:U"
+rM4r~>
+rPAZb?(h8tT`>)^T`>(DTn/ngT`NSIrPASd!.gj;T`JHIp7VIlJcC<$JcFO*"'kp,V=e[-!<:Kq
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+rOi<`>,2/tU]:DaU]:CGUk,=mU]K"LrOi5Y!.gs>U]FZLp7q[lJcC<$JcFO*"'P^)V"JI)!<:U"
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+rOi<`@\a#'U]:DaU]:CGUk,=mU]K"TrOi5Y!.gs>U]FrTp7q[tJcC<$JcFO*!b)/*o)Jjle^aVo
+J,~>
+rPAZb?(h8tT`>)^T`>(DTn/ngT`NSIrPASd!.gj;T`JHIp7VIlJcC<$JcFO*!aPf&o)JjldaJ)f
+J,~>
+rOi<`>,2/tU]:DaU]:CGUk,=mU]K"LrOi5Y!.gs>U]FZLp7q[lJcC<$JcFO*!a5T"o)Jjle^aVo
+J,~>
+rOi<`@\a#'U]LOlV#CAnV#CAnV#LDsU]@1jrhKMoJY[jmLSOt$@f<t@HN8Vmp7q^ueb5d=@Y+Q1
+s+14*s8QQus8UXJUjr~>
+rPAZb?(h8tT`P4fU&G&kU&G&kU&P)pT`Cbdrh0;lJY@XgLS4as?2_V@JH17pp7VLmde9@7?%N$,
+s+14*s8QBps8UOGTn!~>
+rOi<`>,2/tU]LOlV#CAnV#CAnV#LDsU]@1jrhKMoJY[jmLSOt$>5c,8HN8Vmp7q^meb5d=>(Q^)
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+rOi9_@\ir&s.fVprhKMor1jSuU]@3d!!&eprhKMoJY[jmLSOt$@f<t@HN8Vmp7q^ueb5d=@Y+Q1
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+rPAWa?(q2ss.KDmrh0;lr1OArT`Cd[!!&\mrh0;lJY@XgLS4as?2_V@JH17pp7VLmde9@7?%N$,
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+rOi9_>,;)ss.fVprhKMor1jSuU]@3d!!&eprhKMoJY[jmLSOt$>5c,8HN8Vmp7q^meb5d=>(Q^)
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+rPA`d?(h7l!</\i!<8bk!!/bnrh0JqTqMI[!.ghpTn]6AdTugg!J(6%?1hJ'de9@7R=We;dXfif
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+rPAlh?(h7lT`Cd[!;rMj!</Yn!20DlT`kFiT`CbdJY@XgL7nXr?2_V@JH18Lo[8;aJY@Xg\=nE~>
+rOiNf>,2.oU]@3d!;rVm!</bq!2KVoU]gaoU]@1jJY[jmL84k#>5c,8HN8WIo[SMgJY[jm\>4W~>
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+rOi2qJQdV.JQh2>rOi5Y!.gqsUk,=mUoU;A~>
+J\?WJJ\BmQ!IFftUk,=mUk,>BUjr~>
+J\luTJ\p6[!J(6%Tn/ngTn/o<Tn!~>
+J\?WJJ\BmQ!IFftUk,=mUk,>BUjr~>
+J\?WJJ\BmQ!IFft@Y&!>@Y&!h@Xn~>
+J\luTJ\p6[!J(6%?%H:4?%H:^?%;~>
+J\?WJJ\BmQ!IFft>(Kk.>(KkX>(?~>
+o)A]kJ^o>%J^o>%J^o>%J^pXJ!1`TZJ,~>
+o)A]mJ^T+tJ^T+tJ^T+tJ^UFD!1EBWJ,~>
+o)A]kJ^o>%J^o>%J^o>%J^pXJ!0m$RJ,~>
+%%EndData
+showpage
+%%Trailer
+end
+%%EOF
index b91c1ef523bb3bcca1ea3212f6e1663cd053a5e2..22036320c318cc0a0117ca56dc0db0936f8c8ca2 100644 (file)
@@ -15,8 +15,8 @@
    \end{figure}
 }
 
-\usepackage[show]{ed}
-\usepackage{draftstamp}
+%\usepackage[show]{ed}
+%\usepackage{draftstamp}
 
 \newcommand{\musing}{\texttt{musing}}
 \newcommand{\musings}{\texttt{musings}}
     new status are sent to the broker as soon as the proof change (e.g. when the
     user applies a tactic or when a new proof is started) and hints are shown to
     the user be the means of some effect in the user interface (e.g. popping a
-    dialog box or enlightening a tactic button).\ednote{CSC: questo \'e un
-    possibile posto dove mettere una reference a una mini-sessione interattiva.
-    \'E l'appendice un posto dove metterla?}
-
-    \myincludegraphics{interfaces}{t!}{10cm}{\hbugs{} \wss{} interfaces}
-     {\hbugs{} \wss{} interfaces}
+    dialog box or enlightening a tactic button).
 
     \hbugs{} clients act as MONET clients and ask brokers to provide access to a
     set of services (the tutors). \hbugs{} has no actors corresponding to
     Getter.
 
   \paragraph{Brokers}
+    \myincludegraphics{interfaces}{t!}{10cm}{\hbugs{} \wss{} interfaces}
+     {\hbugs{} \wss{} interfaces}
+
     Brokers are the key actors of the \hbugs{} architecture since they
     act as intermediaries between clients and tutors. They behave as \wss{}
     providers and requesters for \emph{both} clients and tutors, see Fig.
     \hbugs{} tutors act as MONET services.
 
 \section{An \hbugs{} Session Example}
+In this section we describe a typical \hbugs{} session. The aim of the
+session is to solve the following easy exercise:
+\begin{exercise}
+Let $x$ be a generic real numbers. Using the \helm{} proof-engine,
+prove that
+\begin{displaymath}
+x = \frac{(x+1)*(x+1) - 1 - x*x}{2}
+\end{displaymath}
+\end{exercise}
+
+\myincludegraphics{step1}{t}{12cm}{Example session, snapshot 1.}
+  {Example session, snapshot 1.}
+%\myincludegraphics{step2}{t}{4cm}{Example session, snapshot 2.}
+% {Example session, snapshot 2.}
+
+Let us suppose that the \hbugs{} broker is already running and that several
+tutors already registered themselves to the broker.
+When the user starts \texttt{gTopLevel}, the system registers itself to
+the broker, that sends back the list of available tutors. By default,
+\texttt{gTopLevel} notifies the broker its intention of subscribing to every
+tutor available. The user can always open a configuration window where she
+is presented the list of available tutors and she can independently subscribe
+and unsubscribe each tutor.
+
+The user can now insert into the system the statement of the theorem and start
+proving it. Let us suppose that the first step of the user is proving
+that the denominator 2 is different from 0. Once that this technical result
+is proven, the user must prove the goal shown in the upper left corner
+of the window in background in Fig. \ref{step1}.
+
+While the user is wondering how to proceed in the proof, the tutors are
+trying to progress in the proof. After a while, the tutors' suggestions
+start to appear in the lower part of the \hbugs{} interface window
+(the topmost window in Fig. \ref{prima}). In this case, the tutors are able
+to produce 23 hints. The first and not very useful hint suggests to proceed in
+the proof by exchanging the two sides of the equality.
+The second hint suggests to reduce both sides of the equality to their normal
+form by using only reductions which are justified by the ring structure of the
+real numbers. The two normal forms, though, are so different that the proof is
+not really simplified.
+All the residual 21 hints suggest to apply one lemma from the distributed
+library of \helm{}.
+
+The user can look at the list of suggestions and realize that a good one is
+that of applying the lemma \texttt{r\_Rmult\_mult} which
+allow\footnote{The user can always look at
+the statement of a theorem by clicking on its URI.} to multiply both equality
+members by the same scalar\footnote{Even if she does not receive the hint, the
+user probably already knows that this is the right way to proceed. The
+difficult part where the hint helps is guessing what is the name of the lemma
+to apply.}.
+Double-clicking on the hint automatically applies
+the lemma, reducing the proof to closing three new goals. The first one asks
+the user the scalar to use as an argument of the previous lemma; the second
+one states that the scalar is different from 0; the third lemma (the main
+one) asks to prove the equality between the products of the two old members
+with the scalar.
+% is shown in Fig. \ref{step2} where $?_3[H;x]$ stands for
+% the still unkown scalar argument, which can have only $H$ and $x$ as
+% free variables.
+
+The user proceeds by istantiating the scalar with the number 2. The
+\texttt{Assumption} tutor now suggests to close the second goal by applying
+the hypothesis $H$. No useful suggestions, instead, are generated for the
+main goal $2x = 2*\frac{((x+1)*(x+1)-1-x*x)}{2}$.
+To proceed in the proof, indeed, the user needs to symplify the
+expression using the lemma $Rinv\_r\_simpl\_m$ that states that
+$\forall x,y.\;y = x * y * x^{-1}$. Since we do not provide yet any tutor
+suggesting symplifications, the user must find out this symplication by
+himself. Once she founds it, the goal is reduced to proving that
+$2x = (x+1)*(x+1) - 1 - x*x$. This equality is easily solved by the
+\texttt{Ring} tutor, that suggests\footnote{The \texttt{Ring} suggestion is
+just one of the 22 hints that the user receives. It is the only hint that
+does not open new goals.} to the user how to directly finish the proof.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%    Comandi da dare a gTopLevel    %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% New proof:
+%  !x.(not (eqT ? (Rplus R1 R1) R0)) -> (eqT ? x (Rdiv (Rminus (Rminus (Rmult (Rplus x R1) (Rplus x R1)) R1) (Rmult x x)) (Rplus R1 R1)))
+% Intros x H
+% Apply  r_Rmult_mult
+% 3: Apply H
+% Simpl   (per fare unfold di Rdiv)
+% Rewrite <-
+%  (Rmult_assoc (Rplus R1 R1) (Rplus (Rplus (Rmult (Rplus x R1) (Rplus x R1)) (Ropp R1)) (Ropp (Rmult x x))) (Rinv (Rplus R1 R1)))
+% Rewrite ->
+%  (Rinv_r_simpl_m (Rplus R1 R1) (Rplus (Rplus (Rmult (Rplus x R1) (Rplus x R1)) (Ropp R1)) (Ropp (Rmult x x))) H)
+% *** Ring
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \section{Implementation's Highlights}
 \label{implementation}
@@ -254,12 +342,13 @@ the \hbugs{} architecture.
     exchange status in WSDL using the XML Schema type system, we have chosen an
     XML format as the target format for the serialization.
 
-    A schematic representation of the gTopLevel internal status is depicted in
-    Fig. \ref{status}. Each proof is represented by a tuple of four elements:
+%    A schematic representation of the gTopLevel internal status is depicted in
+%    Fig. \ref{status}.
+    Each proof is represented by a tuple of four elements:
     \emph{uri}, \emph{metasenv}, \emph{proof}, \emph{thesis}.
 
-    \myincludegraphics{status}{t}{8cm}{gTopLevel proof status}{gTopLevel proof
-    status}
+%    \myincludegraphics{status}{t}{8cm}{gTopLevel proof status}{gTopLevel proof
+%    status}
 
     \begin{description}
       \item[uri]: an URI chosen by the user at the beginning of the proof
@@ -334,8 +423,6 @@ the \hbugs{} architecture.
     the proof found: the client applies the hint reconstructing (and checking
     the correctness of) the proof from the witness, without having to
     re-discover the proof itself.
-    \ednote{Zack: che ne dici di un "reinvent the whell" qui sopra? fa sempre
-    effetto ...}
 
     An alternative implementation where the tutors are trusted would simply
     send back to the client a new proof-status. Upon receiving the
@@ -374,18 +461,17 @@ the \hbugs{} architecture.
     \ws{}.
     Additionally tutors are required to send an human readable description of
     their capabilities; this information could be used by client's user to
-    decide which tutors he needs to subscribe to. Like clients\ednote{Zack: mi
-    pare che questo sia un caso in cui si debba usare "as" e non like, ma non ne
-    sono certo}, tutors can
+    decide which tutors he needs to subscribe to. As the clients, tutors can
     unregister from brokers using \texttt{Unregister\_broker} method.
 
     Each time the client status change, it get sent sent to the
     broker using its \texttt{Status} method. Using both clients registry (to
     lookup client's subscription) and tutors registry (to check if some tutors
     has unsubscribed), the broker is able to decide to which tutors the
-    new status have to be forwarded.\ednote{CSC: qui o nei lavori futuri parlare
-    della possibilit\'a di avere un vero brocker che multiplexi le richieste
-    dei client localizzando i servizi, etc.}
+    new status have to be forwarded.
+%   \ednote{CSC: qui o nei lavori futuri parlare
+%    della possibilit\'a di avere un vero brocker che multiplexi le richieste
+%    dei client localizzando i servizi, etc.}
 
     The forwarding operation is performed using the \texttt{Start\_musing}
     method of the tutors, that is a request to start a new computation
@@ -515,14 +601,13 @@ we have investigated three classes of tutors:
        or more constructors when the goal thesis is an inductive type or a
        proposition inductively defined according to the declarative
        style\footnote{An example of a proposition that can be given in
-       declarative style is the $\le$ relation: $\le$ is the smallest relation
+       declarative style is the $\le$ relation over natural numbers:
+       $\le$ is the smallest relation
        such that $n \le n$ for every $n$ and $n \le m$ for every $n,m$ such
        that $n \le p$ where $p$ is the predecessor of $m$. Thus, a proof
        of $n \le n$ is simply the application of the first constructor to
        $n$ and a proof of $n \le m$ is the application of the second
        constructor to $n,m$ and a proof of $n \le m$.}.
-       \ednote{Zack: non e' necessario specificare che stai parlando di numeri
-       naturali nella footnote?}
        Since disjunction, conjunction, existential quantification and
        Leibniz equality are particular cases of inductive propositions,
        all the other tutors of this class are instantiations of the