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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>
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- <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>
+ <div class="spacer">
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<tbody>
<tr>
- <td style="vertical-align: top; background-color: rgb(223, 223, 223); text-align: center;">Version<br>
+ <td class="snss component sky">
+ <a href="http://lambdadelta.info/index.html">foreword</a>
</td>
- <td style="vertical-align: top; background-color: rgb(223, 223, 223); text-align: center;">Name<br>
+ <td class="snss component 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;">Started<br>
+ <td class="snss component 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;">Released<br>
- </td>
- <td style="vertical-align: top; background-color: rgb(223, 223, 223); text-align: center;">Dismissed<br>
+ <td class="ssss component green">
+ <a href="http://lambdadelta.info/implementation.html">implementation</a>
</td>
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+
+ <a xmlns:ld="http://lambdadelta.info/" name="foreword" />
+ <div xmlns:ld="http://lambdadelta.info/" class="head2dx">Foreword <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b9.png" />
+ </div>
+ <div xmlns:ld="http://lambdadelta.info/" class="text">
+ 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).
+ </div>
+ <div xmlns:ld="http://lambdadelta.info/" class="text">
+ 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>
+ <div xmlns:ld="http://lambdadelta.info/" class="text">
+ λδ comes in several versions listed in the following table,
+ which includes the major milestones:
+ </div>
+ <div xmlns:ld="http://lambdadelta.info/" class="text">
+ <table cellpadding="4" cellspacing="0">
+ <tbody>
<tr>
- <td style="vertical-align: top; background-color: rgb(255, 223, 191);">2<br>
- </td>
- <td style="vertical-align: top; background-color: rgb(255, 223, 191);">basic_2<br>
- </td>
- <td style="vertical-align: top; background-color: rgb(255, 223, 191);">April
-2011<br>
- </td>
- <td style="vertical-align: top; background-color: rgb(255, 223, 191);">planned
-in
-2014<br>
- </td>
- <td style="vertical-align: top; background-color: rgb(255, 223, 191);">not
-planned yet<br>
- </td>
+ <td class="snns component gray">version</td>
+ <td class="snnn component gray">name</td>
+ <td class="snnn component gray">developed with</td>
+ <td class="snnn component gray">started</td>
+ <td class="snnn component gray">announced</td>
+ <td class="snnn component gray">released</td>
+ <td class="ssnn component gray">dismissed</td>
</tr>
<tr>
- <td style="vertical-align: top; background-color: rgb(255, 191, 191);">1<br>
- </td>
- <td style="vertical-align: top; background-color: rgb(255, 191, 191);">basic_1<br>
- </td>
- <td style="vertical-align: top; background-color: rgb(255, 191, 191);">May
-2004<br>
+ <td class="snns orange">2</td>
+ <td class="snnn orange">basic_2</td>
+ <td class="snnn orange">
+ <a href="http://matita.cs.unibo.it/">Matita 0.99.2</a>
</td>
- <td style="vertical-align: top; background-color: rgb(255, 191, 191);">November
-2006<br>
- </td>
- <td style="vertical-align: top; background-color: rgb(255, 191, 191);">May
-2008<br>
+ <td class="snnn orange">April 2011</td>
+ <td class="snnn orange">July 2014</td>
+ <td class="snnn orange">Planned in 2014</td>
+ <td class="ssnn orange">Not planned yet</td>
+ </tr>
+ <tr>
+ <td class="snss red">1</td>
+ <td class="snsn red">basic_1</td>
+ <td class="snsn red">
+ <a href="http://coq.inria.fr/">Coq 7.3.1</a>
</td>
+ <td class="snsn red">May 2004</td>
+ <td class="snsn red">January 2006</td>
+ <td class="snsn red">November 2006</td>
+ <td class="sssn red">May 2008</td>
</tr>
</tbody>
</table>
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projects / helm.git / blobdiff