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-<h1>The Formal System λδ (\lambda\delta)<br>
-</h1>
-<h2>Towards the unification of terms, types, environments and contexts</h2>
-<img style="width: 95%; height: 4px;" alt="[Separator]" title="Separator" src="images/rainbow.png"><br>
-<table style="text-align: left; width: 95%; margin-left: auto; margin-right: auto;" border="0" cellpadding="2" cellspacing="20">
- <tbody>
- <tr>
- <td style="vertical-align: top;">
- <ul>
- <li>Foreword</li>
- </ul>
- <ul>
- <li><a href="news.html">News</a></li>
- </ul>
- <ul>
- <li><a href="documentation.html">Papers</a></li>
- </ul>
- <ul>
- <li><a href="implementation.html">Resources</a><br>
- </li>
- </ul>
- </td>
- <td style="vertical-align: top; text-align: left;">
- <h3 style="text-align: right;">Foreword <img style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly" src="images/b9.png"></h3>
-The formal system λδ
-(\lambda\delta) is a typed lambda calculus that pursues the static and
-dynamic unification of terms, types, environments and contexts while
-enjoying a well-conceived theory, which includes the commonly
-desired properties.<br>
- <br>
-λδ takes some features from the calculi of the Automath family and
-some from the pure type systems, but it differs from both in that it
-does not include the Π construction while it provides for an
-abbreviation mechanism at the level of terms.<br>
- <br>
-λδ features explicit type annotations, which are borrowed from
-realistic type checker implementations and with which type checking is
-reduced to type inference.<br>
- <br>
-The reduction steps of λδ include β-contraction, δ-expansion,
-ζ-contraction and θ-swap. On the other hand,
-η-contraction is not included.<br>
- <br>
-The theory of λδ includes important properties such as the
-confluence of reduction, the correctness of types, the
-uniqueness of types up to conversion, the subject reduction of the type
-assignment, the strong normalization of the typed terms. The
-decidability of type inference and of type checking come as corollaries.<br>
- <br>
-λδ features uniformly dependent types and a predicative abstraction
-mechanism, so the calculus can serve as a formal specification language
-for the type theories that need a predicative foundation. λδ is
-expected to have the expressive power of λ→.<br>
- <br>
-λδ comes in several versions listed in the following table, which
-includes the major milestones:<br>
- <br>
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+ <div class="head1">The Formal System λδ (\lambda\delta)</div>
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<tbody>
<tr>
- <td style="vertical-align: top; background-color: rgb(223, 223, 223); text-align: center;">Version<br>
- </td>
- <td style="vertical-align: top; background-color: rgb(223, 223, 223); text-align: center;">Name<br>
+ <td class="snns capitalize italic sky">
+ <a href="http://lambdadelta.info/index.html">home</a>
</td>
- <td style="vertical-align: top; background-color: rgb(223, 223, 223); text-align: center;">Started<br>
+ <td class="snns capitalize italic magenta">
+ <a href="http://lambdadelta.info/news.html">news</a>
</td>
- <td style="vertical-align: top; background-color: rgb(223, 223, 223); text-align: center;">Released<br>
+ <td class="snns capitalize italic orange">
+ <a href="http://lambdadelta.info/documentation.html">documentation</a>
</td>
- <td style="vertical-align: top; background-color: rgb(223, 223, 223); text-align: center;">Dismissed<br>
+ <td class="snns capitalize italic green">
+ <a href="http://lambdadelta.info/implementation.html">implementation</a>
</td>
+ <td class="ssnn capitalize italic green">(<a href="http://lambdadelta.info/implementation.html#specifications">specifications</a> - <a href="http://lambdadelta.info/implementation.html#lddl">library</a> - <a href="http://lambdadelta.info/implementation.html#helena">Helena</a>)</td>
</tr>
<tr>
- <td style="vertical-align: top; background-color: rgb(255, 223, 191);">2<br>
+ <td class="snns sky">
+ <a href="http://lambdadelta.info/index.html#foreword">Foreword</a>
</td>
- <td style="vertical-align: top; background-color: rgb(255, 223, 191);">basic_2<br>
+ <td class="snns magenta">
+ <a href="http://lambdadelta.info/news.html#milestones">Milestones</a>
</td>
- <td style="vertical-align: top; background-color: rgb(255, 223, 191);">April
-2011<br>
+ <td class="snns orange">
+ <a href="http://lambdadelta.info/documentation.html#v2">Version 2</a>
</td>
- <td style="vertical-align: top; background-color: rgb(255, 223, 191);">planned
-in
-2013<br>
- </td>
- <td style="vertical-align: top; background-color: rgb(255, 223, 191);">not
-planned yet<br>
+ <td class="snns green">
+ <a href="http://lambdadelta.info/version_2.html">Version 2</a>
</td>
+ <td class="ssnn green">(<a href="http://lambdadelta.info/ground_2.html">Background</a> - <a href="http://lambdadelta.info/basic_2.html">Core</a> - <a href="http://lambdadelta.info/apps_2.html">Applications</a>)</td>
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<tr>
- <td style="vertical-align: top; background-color: rgb(255, 191, 191);">1<br>
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+ <a href="http://lambdadelta.info/index.html#notice">Notice</a>
</td>
- <td style="vertical-align: top; background-color: rgb(255, 191, 191);">basic_1<br>
+ <td class="snss magenta">
+ <a href="http://lambdadelta.info/news.html#visibility">Visibility</a>
</td>
- <td style="vertical-align: top; background-color: rgb(255, 191, 191);">May
-2004<br>
+ <td class="snss orange">
+ <a href="http://lambdadelta.info/documentation.html#v1">Version 1</a>
</td>
- <td style="vertical-align: top; background-color: rgb(255, 191, 191);">November
-2006<br>
+ <td class="snss green">
+ <a href="http://lambdadelta.info/version_1.html">Version 1</a>
</td>
- <td style="vertical-align: top; background-color: rgb(255, 191, 191);">May
-2008<br>
+ <td class="sssn green">
+ <br />
</td>
</tr>
</tbody>
</table>
- <br>
- <h3 style="text-align: right;">Notice
-for
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-Last update 2012-12-02 by <a href="http://www.cs.unibo.it/%7Efguidi/">Ferruccio
-Guidi</a><br>
-</div>
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+ The formal system λδ (\lambda\delta) is a typed λ-calculus aiming to support
+ the foundations of Mathematics that require an underlying specification language
+ (for example the <a href="http://www.math.unipd.it/~maietti/">Minimal Type Theory</a>
+ and its predecessors).
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+ λδ is developed in the context of the
+ <a href="http://helm.cs.unibo.it/">Hypertextual Electronic Library of Mathematics</a>
+ as a machine-checked digital specification
+ that is not the formal counterpart of some previously published informal material.
+ </div>
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+ This is the System logo: <a href="http://lambdadelta.info/images/crux_177.png">crux_177.png</a>
+ (revised <span class="date">2012-09</span>).
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