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<!DOCTYPE html>
<HTML>
<!-- Mirrored from lamport.azurewebsites.net/tla/tla2.html by HTTrack Website Copier/3.x [XR&CO'2014], Thu, 26 Mar 2020 22:38:05 GMT -->
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<title>TLA+ Version 2</title>
<table id="main">
<tr>
<td id="main_leftcolumn" >
</td>
<td id="main_contentcolumn">
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<td style="vertical-alight:top">
<div id = "showleftcol"> </div>
<H1>TLA+ Version 2</H1>
<p style="margin-top:-8px; margin-bottom:-18px">
Leslie Lamport<p>
<font size=-1><I> Last modified on 21 September 2018</I></font>
</td>
<td style="vertical-alight:top;width:auto">
</td>
</tr>
</table>
<HR style="margin-bottom:-5px;margin-top:-11px">
<P style="margin-top:0px"> </P>
<DIV class="hidden-div" style="color:red;margin-bottom:-22px"><b>
You'll miss a lot on this web site unless you enable Javascript
in your browser. </b></DIV>
<DIV>
<H2 id="h2intro" class="show-hide" onclick="showHide('hide-intro','intro')">
What is TLA+ Version 2?
<font id="hide-intro" > [show]</font>
</H2>
<DIV id="intro" class = "hidden-div">
TLA+ Version 2, here called TLA+2
for short, is the current version of TLA+.
TLA+ now means TLA+2. The previous version is
referred to here as TLA+1. This page contains a brief description
of how TLA+2 differs from TLA+1, which is the language described in
the book <em><a href = "book.html">Specifying Systems</a></em>.
<!-- Available documentation on the language is listed <A
HREF="#documentation"
onclick="show('hide-documentation','documentation')">below</A>.
-->
</DIV>
<H2 id="h2features" class="show-hide"
onclick="showHide('hide-features','features')">
Features for Writing Specifications
<font id="hide-features" > [show]</font>
</H2>
<DIV id="features" class = "hidden-div">
<!-- The following new features have been added to the language. -->
<H4 style="margin-top:0px;margin-bottom:3px">Recursive Operator Definitions</H4>
A <TT>RECURSIVE</TT> statement allows you to define operators
recursively, including the use of mutual recursion. For example,
here's a silly way to define both <TT>fact1(n)</TT> and
<TT>fact2(n)</TT> to equal <TT>n</TT> factorial, for any natural number
<TT>n</TT>:
<PRE> RECURSIVE fact1(_), fact2(_)
fact1(n) == IF n = 0 THEN 1
ELSE n*fact2(n-1)
fact2(n) == IF n = 0 THEN 1
ELSE n*fact1(n-1)
</PRE>
<H4 style="margin-top:15px;margin-bottom:3px">LAMBDA Expressions </H4>
TLA+ allows you to define a higher-order operator that takes an
operator as an argument. In TLA+1, you could use
only the name of an operator that has already been defined or declared
as such an argument. TLA+2 allows the use of a <TT>LAMBDA</TT>
expression as the argument. For example, if <tt>F</tt> is an
operator that takes as its argument an operator with two arguments,
then you can write the expression
<PRE style="margin-bottom:-10px"> LET Id(a, b) == a + 2*b
IN F(Id)
</PRE>
In TLA+2, you can write this as
<PRE> F(LAMBDA a, b : a + 2*b)
</PRE>
You can also use a <TT>LAMBDA</TT> expression to substitute for an
operator in the <TT>WITH</TT> clause of an <TT>INSTANCE</TT>
statement.
</DIV>
<H2 id="h2proofs" class="show-hide" onclick="showHide('hide-proofs','proofs')">Writing Proofs
<font id="hide-proofs" > [show]</font>
</H2>
<DIV id="proofs" class = "hidden-div">
The major new feature of TLA+2 is the introduction of constructs for
writing proofs. A checker for these proofs is
being built as part of a
<A HREF="https://tla.msr-inria.inria.fr/tlaps/content/Home.html">project</A>
at the
<A HREF="https://www.inria.fr/en/institute/partnerships/industrial-partnerships2/microsoft-research">Microsoft Research–Inria Joint Centre</A>.
It does not yet handle temporal-logic reasoning, but it can
check most other parts of a proof.
<p>
The language supports hierarchically structured
proofs. The paper
<A HREF="http://lamport.azurewebsites.net/pubs/pubs.html#lamport-how-to-write"><I>How to
Write a Proof</I></A>
describes the basic hierarchical proof style and explains why it is
much better than the way mathematicians and computer scientists now
write proofs.
The TLA+2 documentation describes the language
features for writing structured proofs.
The TLAPS project page
contains a <A
HREF="https://tla.msr-inria.inria.fr/tlaps/content/Documentation/Tutorial/The_example.html"
>brief tutorial</A> on writing TLA+ proofs.
<P>
<!-- One feature introduced for writing proofs is the naming of
subexpressions of a definition, which can be assisted by adding
labels.
You can use subexpression names in a specification, but you
shouldn't.
However, they can be useful for writing tests when model checking a
specification.
Moreover, labels could be useful in referring to parts of a
specification in documentation.
-->
</DIV>
<H2 id="h2other" class="show-hide" onclick="showHide('hide-other','other')">
<A name="other">Other Changes</A>
<font id="hide-other" > [show]</font>
</H2>
<DIV id="other" class = "hidden-div">
Other than introducing a few new keywords that can no longer be used
as identifiers, there are two changes in TLA+2 that may make a TLA+
specification no longer legal. The first is the handling of
instantiated infix operators. In TLA+1, if you wrote
<PRE> Foo(x) == INSTANCE M </PRE>
and module <TT>M</TT> defines the infix operator <TT>++</TT>, then you
had to write a weird expression like
<PRE> a Foo(42)!++ b</PRE>
to use the instantiated operator.
In TLA+2, this is written <TT>Foo(42)!++(a,b)</TT>.
<P>
The second change is that certain operators can no longer be used to
instantiate operator parameters in a constant module. You're unlikely
to encounter it. However, if you get an error message of the form
<PRE>
Error in instantiating module '...':
A non-Leibniz operator substituted for '...'.
</PRE>
then you should read Section 5.2 in the TLA+2
<A HREF ="tla2-guide.pdf">Preliminary Guide</A>
for an explanation.
</DIV>
<H2 id="h2documentation" class="show-hide" onclick="showHide('hide-documentation','documentation')">
<A name="documentation">Documentation</A>
<font id="hide-documentation" > [show]</font>
</H2>
<DIV id="documentation" class = "hidden-div">
All current documentation written since 2008 describes
TLA+2. That include
the <a href="http://lamport.azurewebsites.net/video/videos.html">TLA+ Video Course</a>
and the <a href="hyperbook235d.html?back-link=tla2.html#documentation">TLA+ Hyperbook</a>.
Here is some more detailed documentation:
<DL>
<DT><B><A HREF ="tla2-guide.pdf">TLA Version 2: A Preliminary Guide</A></B>
<DD> This is a fairly complete 30-page description of the features
added to the language. However, it is not easy reading, being written
more as a guide for tool implementers than as a user manual.<BR>
<P>
<DT><B><A HREF ="TLAPlus2Grammar.tla">A TLA+ Specification of the
Grammar</A></B>
<DD> This is a version of the <I>TLAPlusGrammar</I> module from
Section 15.1 (page 276) of <I>Specifying Systems</I> (the TLA+ book),
without comments, that has been updated for TLA+2.
There is also a pretty-printed
<A HREF ="TLAPlus2Grammar.pdf">PDF version</A>.
</DL>
</DIV>
</DIV>
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