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Isabelle FAQ

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    <h2>General Questions</h2>
    <table class="question" width="100%">
        <tr>
          <td>What is Isabelle?</td>
        </tr>
    </table>

    <table class="answer" width="100%">
        <tr><td>Isabelle is a popular generic theorem proving
        environment developed at Cambridge University (<a
        href="http://www.cl.cam.ac.uk/users/lcp/">Larry Paulson</a>)
        and TU Munich (<a href="http://www.in.tum.de/~nipkow/">Tobias
        Nipkow</a>). See the <a
        href="http://isabelle.in.tum.de/">Isabelle homepage</a> for
        more information.</td></tr>
    </table>
    

    <table class="question" width="100%">
        <tr>
          <td>Where can I find documentation?</td>
        </tr>
    </table>    
    <table class="answer" width="100%">
        <tr><td><a href="http://isabelle.in.tum.de/docs.html">This
        way, please</a>. Also have a look at the <a
        href="http://isabelle.in.tum.de/library/">theory
        library</a>.</td></tr>
    </table>

    <table class="question" width="100%">
        <tr>
          <td>Is it available for download?</td>
        </tr>
    </table> <table class="answer" width="100%"> <tr><td>Yes, it is
    available from <a
    href="http://isabelle.in.tum.de/dist/">several mirror
    sites</a>. It should run on most recent Unix systems (Solaris,
    Linux, MacOS X, etc.).</td></tr>
    </table>


    <h2>Syntax</h2>
    <table class="question" width="100%">
        <tr>
          <td>There are lots of arrows in Isabelle. What's the
          difference between <tt>-&gt;</tt>, <tt>=&gt;</tt>, <tt>--&gt;</tt>,
          and <tt>==&gt;</tt> ?</td>
        </tr>
    </table>
    <table class="answer" width="100%">
        <tr><td>Isabelle uses the <tt>=&gt;</tt> arrow for the function
        type (contrary to most functional languages which use
        <tt>-&gt;</tt>). So <tt>a =&gt; b</tt> is the type of a function
        that takes an element of <tt>a</tt> as input and gives you an
        element of <tt>b</tt> as output. The long arrow <tt>--&gt;</tt>
        and <tt>==&gt;</tt> are object and meta level
        implication. Roughly speaking, the meta level implication
        should only be used when stating theorems where it separates
        the assumptions from the conclusion. Whenever you need an
        implication inside a HOL formula, use <code>--&gt;</code>.
        </td></tr>
    </table>

    <table class="question" width="100%"><tr><td>Where do I have to put those double quotes?</td></tr></table> 

    <table class="answer" width="100%"><tr><td>Isabelle distinguishes between <em>inner</em>
    and <em>outer</em> syntax. The outer syntax comes from the
    Isabelle framework, the inner syntax is the one in between
    quotation marks and comes from the object logic (in this case HOL).
    With time the distinction between the two becomes obvious, but in
    the beginning the following rules of thumb may work: types should
    be inside quotation marks, formulas and lemmas should be inside
    quotation marks, rules and equations (e.g. for definitions) should
    be inside quotation marks, commands like <tt>lemma</tt>,
    <tt>consts</tt>, <tt>primrec</tt>, <tt>constdefs</tt>,
    <tt>apply</tt>, <tt>done</tt> are without quotation marks, as are
    the names of constants in constant definitions (<tt>consts</tt>
    and <tt>constdefs</tt>)
    </td></tr></table>

    <table class="question" width="100%"><tr><td>What is <tt>"No such
    constant: _case_syntax"</tt> supposed to tell
    me?</td></tr></table>

    <table class="answer" width="100%"><tr><td>You get this message if
    you use a case construct on a datatype and have a typo in the
    names of the constructor patterns or if the order of the
    constructors in the case pattern is different from the order in
    which they where defined (in the datatype definition).
    </td></tr></table>
    
    <table class="question" width="100%"><tr><td>Why doesn't Isabelle understand my
    equation?</td></tr></table> 

    <table class="answer" width="100%"><tr><td>Isabelle's equality <tt>=</tt> binds
    relatively strongly, so an equation like <tt>a = b & c</tt> might
    not be what you intend. Isabelle parses it as <tt>(a = b) &
    c</tt>.  If you want it the other way around, you must set
    explicit parentheses as in <tt>a = (b & c)</tt>. This also applies
    to e.g. <tt>primrec</tt> definitions (see below).</td></tr></table>

    <table class="question" width="100%"><tr><td>What does it mean "not a proper
    equation"?</td></tr></table>
      
    <table class="answer" width="100%"><tr><td>Most commonly this is an instance of the
    question above. The <tt>primrec</tt> command (and others) expect
    equations as input, and since equality binds strongly in Isabelle,
    something like <tt>f x = b & c</tt> is not what you might expect
    it to be: Isabelle parses it as <tt>(f x = b) & c</tt> (which is
    indeed not a proper equation). To turn it into an equation you
    must set explicit parentheses: <tt>f x = (b & c)</tt>.</td></tr></table>

    <table class="question" width="100%"><tr><td>What does it mean
    "<tt>Not a meta-equality (==)</tt>"?</td></tr></table>
    
    <table class="answer" width="100%"><tr><td>This usually occurs if
    you use <tt>=</tt> for <tt>constdefs</tt>. The <tt>constdefs</tt>
    and <tt>defs</tt> commands expect not equations, but meta
    equivalences. Just use the <tt>\&lt;equiv&gt;</tt> or <tt>==</tt>
    signs instead of <tt>=</tt>.  </td></tr></table>


    <h2>Proving</h2>

    <table class="question" width="100%"><tr><td>What does "empty result sequence"
    mean?</td></tr></table> 

    <table class="answer" width="100%"><tr><td>It means that the applied proof method (or
    tactic) was unsuccessful. It did not transform the goal in any
    way, or simply just failed to do anything. You must try another
    tactic (or give the one you used more hints or lemmas to work
    with)</td></tr></table>


    <table class="question" width="100%"><tr><td>The Simplifier doesn't want to apply my
    rule, what's wrong?</td></tr></table>

    <table class="answer" width="100%"><tr><td>
    Most commonly this is a typing problem. The rule you want to apply
    may require a more special (or just plain different) type from
    what you have in the current goal. Use the ProofGeneral menu
    <tt>Isabelle/Isar -&gt; Settings -&gt; Show Types</tt> and the
    <tt>thm</tt> command on the rule you want to apply to find out if
    the types are what you expect them to be (also take a look at the
    types in your goal). <tt>Show Sorts</tt>, <tt>Show Constants</tt>,
    and <tt>Trace Simplifier</tt> in the same menu may also be
    helpful.
    </td></tr></table>


    <table class="question" width="100%"><tr><td>If I do <tt>auto</tt>, it leaves me a goal
    <tt>False</tt>. Is my theorem wrong?</td></tr></table>
    
    <table class="answer" width="100%"><tr><td>Not necessarily. It just means that
    <tt>auto</tt> transformed the goal into something that is not
    provable any more. That could be due to <tt>auto</tt> doing
    something stupid, or e.g. due to some earlier step in the proof
    that lost important information. It is of course also possible
    that the goal was never provable in the first place.</td></tr></table>


    <table class="question" width="100%"><tr><td>Why does <tt>lemma
    "1+1=2"</tt> fail?</td></tr></table> 

    <table class="answer" width="100%"><tr><td>Because it is not
    necessarily true.  Isabelle does not assume that 1 and 2 are
    natural numbers. Try <tt>"(1::nat)+1=2"</tt>
    instead.</td></tr></table>


    <table class="question" width="100%"><tr><td>Can Isabelle find
    counterexamples?</td></tr></table>
    
    <table class="answer" width="100%"><tr><td>
    <p>
    For arithmetic goals, <code>arith</code> finds counterexamples.
    For executable goals, <code>quickcheck</code> tries to find a
    counterexample.  For goals of a more logical nature (including
    quantifiers, sets and inductive definitions) <code>refute</code>
    searches for a countermodel.
    </p>
    <p>
    Otherwise, negate the proposition
    and instantiate (some) variables with concrete values. You may
    also need additional assumptions about these values.  For example,
    <tt>True & False ~= True | False</tt> is a counterexample of <tt>A
    & B = A | B</tt>, and <tt>A = ~B ==&gt; A & B ~= A | B</tt> is
    another one. Sometimes Isabelle can help you to find the
    counterexample: just negate the proposition and do <tt>auto</tt>
    or <tt>simp</tt>.  If lucky, you are left with the assumptions you
    need for the counterexample to work.
    </p>
    </td></tr></table>


    <h2>Interface</h2>

    <table class="question" width="100%"><tr><td>X-Symbol doesn't seem to work. What can I
    do?</td></tr></table>

    <table class="answer" width="100%"><tr><td>The most common reason why X-Symbol doesn't
    work is: it's not switched on yet. Assuming you are using
    ProofGeneral and have installed the X-Symbol package, you still
    need to turn X-Symbol on in ProofGeneral: select the menu items
    <tt>Proof-General -&gt; Options -&gt; X-Symbol</tt> and (if you want to
    save the setting for future sessions) select <tt>Options -&gt; Save
    Options</tt> in XEmacs.</td></tr></table>

    <table class="question" width="100%"><tr><td>How do I input those X-Symbols anyway?</td></tr></table>

    <table class="answer" width="100%"><tr><td>
    There are lots of ways to input x-symbols. The one that always
    works is writing it out in plain text (e.g. for the 'and' symbol
    type <tt>\&lt;and&gt;</tt>). For common symbols you can try to "paint
    them in ASCII" and if the xsymbol package recognizes them it will
    automatically convert them into their graphical
    representation. Examples: <tt>--&gt;</tt> is converted into the long
    single arrow, <tt>/\</tt> is converted into the 'and' symbol, the
    sequence <tt>=_</tt> into the equivalence sign, <tt>&lt;_</tt> into
    less-or-equal, <tt>[|</tt> into opening semantic brackets, and so
    on. For greek characters, the <code>rotate</code> command works well:
    to input &alpha; type <code>a</code> and then <code>C-.</code>
    (control and <code>.</code>).  You can also display the
    grid-of-characters in the x-symbol menu to get an overview of the
    available graphical representations (not all of them already have
    a meaning in Isabelle, though).
    </td></tr></table>

    <h2>System</h2>

    <table class="question" width="100%"><tr><td>I want to generate one of those flashy LaTeX
      documents. How?</td></tr></table>

    <table class="answer" width="100%"><tr><td>You will need to work with the
    <tt>isatool</tt> command for this (in a Unix shell). The easiest
    way to get to a document is the following: use <tt>isatool
    mkdir</tt> to set up a new directory. The command will also create
    a file called <tt>IsaMakefile</tt> in the current directory.  Put
    your theory file(s) into the new directory and edit the file
    <tt>ROOT.ML</tt> in there (following the comments) to tell
    Isabelle which of the theories to load (and in which order). Go
    back to the parent directory (where the <tt>IsaMakefile</tt> is)
    and type <tt>isatool make</tt>. Isabelle should then process your
    theories and tell you where to find the finished document. For
    more information on generating documents see the Isabelle Tutorial, Chapter 4.
    </td></tr></table>
      

    <table class="question" width="100%"><tr><td>I have a large formalization with many
      theories. Must I process all of them all of the time?</td></tr></table>

    <table class="answer" width="100%"><tr><td>No, you can tell Isabelle to build a so-called
    heap image. This heap image can contain your preloaded
    theories. To get one, set up a directory with a <tt>ROOT.ML</tt>
    file (as for generating a document) and use the command
    <tt>isatool usedir -b HOL MyImage</tt> in that directory to create
    an image <tt>MyImage</tt> using the parent logic <tt>HOL</tt>.
    You should then be able to invoke Isabelle with <tt>Isabelle -l
    MyImage</tt> and have everything that is loaded in ROOT.ML
    instantly available.</td></tr></table>
    
    <table class="question" width="100%"><tr><td>Does Isabelle run on Windows?</td></tr></table>

    <table class="answer" width="100%"><tr><td> After a fashion, yes,
    but Isabelle is not being developed for Windows. A friendly user
    (Norbert V&ouml;lker) has managed to get a minimal Isabelle environment
    to work on it.  See the description on <a
    href="http://cswww.essex.ac.uk/Research/FSS/projects/isawin/">his
    website</a>. Be warned, though: emphasis is on <em>minimal</em>,
    working with Windows is no fun at all. To enjoy Isabelle in its
    full beauty it is recommended to get a Linux distribution (they
    are inexpensive, any reasonably recent one should work, dualboot
    Windows/Linux should pose no problems).
    </td></tr></table>