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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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+ <td class="snns capitalize italic white">
<a href="http://lambdadelta.info/specification.html">specification</a>
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+ <a href="http://lambdadelta.info/documentation.html">documentation</a>
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+ <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>
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- <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
+ <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
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+ <td class="ssnn capitalize green">
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- <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
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- <td class="ssnn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
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+ <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
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+ <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
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- <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
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- <td class="snsn capitalize green">(<a href="http://lambdadelta.info/basic_1.html">core</a>)</td>
- <td class="snsn capitalize green">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
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- <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
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- <br />
+ <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
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+ <td class="sssn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
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+ <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="foreword">Foreword <img class="icon37" alt="[spacer]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b9.png" />
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<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>
+ 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">
- λδ is developed in the context of the
+ The λδ family is developed within 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 previous informal material.
+ as a set of machine-checked digital specifications.
</div>
<div xmlns:ld="http://lambdadelta.info/" class="text">
- This is the System logo: <a href="http://lambdadelta.info/images/crux_177.png">crux_177.png</a>
+ 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>).
</div>
<div xmlns:ld="http://lambdadelta.info/" class="text">
"Tools" menu → "Internet Options" entry → "General" tab → "Fonts" button.
</div>
<!-- ===================================================================== -->
- <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 xmlns:ld="http://lambdadelta.info/" class="head2dx" id="citations">Citations <img class="icon37" alt="[spacer]" title="\lambda\delta 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 (not including our own).
+ 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 JAR 49(3), pp. 427-451.
+ (2012). In Journal of Automated Reasoning, 49(3), pp. 427-451. Springer.
</li>
</ul>
<ul xmlns:ld="http://lambdadelta.info/" id="C5">
<li>
C.E. Brown:
<span class="emph alpha">Faithful Reproductions of the Automath Landau Formalization</span>
- (2011). Typescript note.
+ (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 APAL 160(3), pp. 319-354.
+ (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). Typescript note.
+ (July 2007). Technical report.
+ </li>
+ </ul>
+ <!-- ===================================================================== -->
+ <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="disclaimer">Disclaimer <img class="icon37" alt="[spacer]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b9.png" />
+ </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>
+ <div xmlns:ld="http://lambdadelta.info/" class="text">
+ <img class="icon32" alt="[Smiling face]" title="Smile!" src="http://lambdadelta.info/images/smile.png" />
+ Moreover, the systens of the λδ family <span class="emph alpha">are not</span> related intentionally to
+ <a href="http://umineko.wikia.com/wiki/Lambdadelta">Lady Lambdadelta</a>,
+ the Witch of Certainty of the sound novel
+ <a href="https://it.wikipedia.org/wiki/Umineko_no_naku_koro_ni">Umineko no Naku Koro ni</a>.
+ </div>
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