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- <div class="head1">The Formal System λδ (\lambda\delta)</div>
+ <div class="head1">The Formal Systems of the λδ (\lambda\delta) Family</div>
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+ <a href="http://lambdadelta.info/specification.html">specification</a>
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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).
- </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 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>
+ <td class="ssnn capitalize italic green">
+ <br />
+ </td>
</tr>
<tr>
- <td class="snns orange">2</td>
- <td class="snnn orange">
- <a href="http://lambdadelta.info/version_2.html">basic_2</a>
+ <td class="snns capitalize sky">
+ <a href="http://lambdadelta.info/index.html#foreword">foreword</a>
+ </td>
+ <td class="snns capitalize magenta">
+ <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
+ </td>
+ <td class="snns capitalize white">
+ <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
+ </td>
+ <td class="snnn capitalize white">(<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>
+ <td class="snnn capitalize white">
+ <br />
</td>
- <td class="snnn orange">
- <a href="http://matita.cs.unibo.it/">Matita 0.99.2</a>
+ <td class="snns capitalize orange">
+ <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
</td>
- <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>
+ <td class="snns capitalize green">
+ <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
+ </td>
+ <td class="ssnn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
</tr>
<tr>
- <td class="snss red">1</td>
- <td class="snsn red">
- <a href="http://lambdadelta.info/version_1.html">basic_1</a>
+ <td class="snss capitalize sky">
+ <a href="http://lambdadelta.info/index.html#citations">citations</a>
+ </td>
+ <td class="snss capitalize magenta">
+ <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
+ </td>
+ <td class="snss capitalize white">
+ <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
</td>
- <td class="snsn red">
- <a href="http://coq.inria.fr/">Coq 7.3.1</a>
+ <td class="snsn capitalize white">(<a href="http://lambdadelta.info/ground_1.html">background</a> - <a href="http://lambdadelta.info/basic_1.html">core</a>)</td>
+ <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
+ <td class="snss capitalize orange">
+ <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
+ </td>
+ <td class="snss capitalize green">
+ <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
+ </td>
+ <td class="sssn capitalize green">
+ <br />
</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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- <div xmlns:ld="http://lambdadelta.info/" class="text">
+ <div xmlns:ld="http://lambdadelta.info/" class="text">
+ The formal systems of the λδ (\lambda\delta) family are typed λ-calculi aiming to support
+ the foundational frameworks for Mathematics that require an underlying specification language
+ (for example the <a href="http://www.math.unipd.it/~maietti/">Minimalist Foundation</a>
+ and its predecessors).
+ </div>
+ <div xmlns:ld="http://lambdadelta.info/" class="text">
+ The λδ family is developed within the
+ <a href="http://helm.cs.unibo.it/">Hypertextual Electronic Library of Mathematics</a>
+ as a set of machine-checked digital specifications.
+ </div>
+ <div xmlns:ld="http://lambdadelta.info/" class="text">
+ This is the family logo: <a href="http://lambdadelta.info/images/crux_177.png">crux_177.png</a>
+ (revised <span class="emph alpha">2012-09</span>).
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-
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+ <!-- ===================================================================== -->
+ <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="citations">Citations <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b9.png" />
+ </div>
+ <div xmlns:ld="http://lambdadelta.info/" class="text">
+ This is a list of publications citing λδ documentation.
+ </div>
+ <ul xmlns:ld="http://lambdadelta.info/" id="C7">
+ <li>
+ C. Dunchev, F. Guidi, C. Sacerdoti Coen, E. Tassi:
+ <span class="emph alpha">ELPI: fast, Embeddable, λProlog Interpreter</span>
+ (2015). In proc. of LPAR 20. Lecture Notes in Computer Science, 9450, pp. 460-468. Springer.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/" id="C6">
+ <li>
+ A. Asperti, W. Ricciotti, C. Sacerdoti Coen, E. Tassi:
+ <span class="emph alpha">Formal metatheory of programming languages in the Matita interactive theorem prover</span>
+ (2012). In Journal of Automated Reasoning, 49(3), pp. 427-451. Springer.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/" id="C5">
+ <li>
+ M.E. Maietti:
+ <span class="emph alpha">Consistency of the minimalist foundation with Church thesis and Bar Induction</span>
+ (2012). Submitted article.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/" id="C4">
+ <li>
+ W. Ricciotti:
+ <span class="emph alpha">Theoretical and implementation aspects in the mechanization of the metatheory of programming languages</span>
+ (July 2011). Ph.D. Thesis in Computer Science, Technical Report UBLCS-2011-09, University of Bologna.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/" id="C3">
+ <li>
+ C.E. Brown:
+ <span class="emph alpha">Faithful Reproductions of the Automath Landau Formalization</span>
+ (2011). Technical report.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/" id="C2">
+ <li>
+ M.E. Maietti:
+ <span class="emph alpha">A minimalist two-level foundation for constructive mathematics</span>
+ (2009). In Annals of Pure and Applied Logic, 160(3), pp. 319-354. Elsevier.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/" id="C1">
+ <li>
+ V. Rahili:
+ <span class="emph alpha">First Year Report: Realisability methods of proof and semantics with application to expansion</span>
+ (July 2007). Technical report.
+ </li>
+ </ul>
+ <!-- ===================================================================== -->
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+ </div>
+ <div xmlns:ld="http://lambdadelta.info/" class="text">
+ The systens of the λδ family <span class="emph alpha">are not</span> related intentionally to any other system
+ having (variations of) the symbols λ and δ in its name or syntax.
+ Examples include (but are not limited to):
+ </div>
+ <ul xmlns:ld="http://lambdadelta.info/" id="D1">
+ <li>
+ <span class="emph alpha">λ-δ</span> of
+ A. Church:
+ <span class="emph alpha">The calculi of lambda-conversion</span>
+ (1941).
+ Annals of Mathematics Studies 6.
+ Princeton University Press.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/" id="D2">
+ <li>
+ <span class="emph alpha">∆Λ</span> of
+ N.G. de Bruijn:
+ <span class="emph alpha">Generalizing Automath by means of a lambda-typed lambda calculus</span>
+ (1987).
+ In Lecture Notes in Pure and Applied Mathematics 106, pp. 71-92.
+ Marcel Dekker.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/" id="D3">
+ <li>
+ <span class="emph alpha">λ<sub>∆</sub>
+ </span> of
+ N.J. Rehof, M.H. Sørensen:
+ <span class="emph alpha">The λ<sub>∆</sub>-calculus</span>
+ (1994).
+ In Lecture Notes in Computer Science, 789, pp. 516–542.
+ Springer.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/" id="D4">
+ <li>
+ <span class="emph alpha">λ∆</span> of
+ S. Ronchi Della Rocca, L. Paolini:
+ <span class="emph alpha">The Parametric Lambda Calculus</span>
+ (2004).
+ Texts in Theoretical Computer Science, An EATCS Series.
+ Springer.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/" id="D5">
+ <li>
+ <span class="emph alpha">λD</span> of
+ R. Nederpelt, H. Geuvers:
+ <span class="emph alpha">Type Theory and Formal Proof</span>
+ (2014).
+ Cambridge University Press.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/" id="D6">
+ <li>
+ <span class="emph alpha">Cλξ</span> of
+ N.G. de Bruijn:
+ <span class="emph alpha">A namefree lambda calculus with facilities for internal definition of expressions and segments</span>
+ (1978).
+ TH-report 78-WSK-03.
+ Eindhoven University of Technology, Eindhoven.
+ </li>
+ </ul>
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