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+ <div class="head1">The Formal Systems of the λδ (\lambda\delta) Family</div>
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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 class="text">
+ </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 class="text">
+ </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>).
- </div><div class="text"><span class="emph alpha">Notice for the user of Internet Explorer.</span>
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+ <div xmlns:ld="http://lambdadelta.info/" class="text">
+ <span class="emph alpha">Notice for the user of Internet Explorer.</span>
To view this site correctly, please select a font
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- </div><!-- ===================================================================== --><div class="head2dx" id="citations">Citations <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b9.png"/></div><div class="text">
+ </div>
+ <!-- ===================================================================== -->
+ <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="citations">Citations <img class="icon37" alt="[butterfly]" 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 documentation.
- </div><ul id="C8"><li>
+ </div>
+ <ul xmlns:ld="http://lambdadelta.info/" id="C9">
+ <li>
+ Matthias Weber:
+ <span class="emph alpha">An extended type system with lambda-typed lambda-expressions (extended version)</span>
+ (2017). Technical report. Faculty of Computer Science, Technical University of Berlin.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/" id="C8">
+ <li>
M.E. Maietti, S. Maschio:
<span class="emph alpha">An extensional Kleene realizability semantics for the Minimalist Foundation</span>
(2015). In Leibniz International Proceedings in Informatics, 39, pp 162-186. Schloss Dagstuhl, Leibniz-Zentrum für Informatik.
- </li></ul><ul id="C7"><li>
+ </li>
+ </ul>
+ <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 id="C6"><li>
+ </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 id="C5"><li>
+ </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 id="C4"><li>
+ </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 id="C3"><li>
+ </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 id="C2"><li>
+ </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 id="C1"><li>
+ </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><!-- ===================================================================== --><div class="head2dx" id="disclaimer">Disclaimer <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b9.png"/></div><div class="text">
+ </li>
+ </ul>
+ <!-- ===================================================================== -->
+ <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="disclaimer">Disclaimer <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b9.png" />
+ </div>
+ <div xmlns:ld="http://lambdadelta.info/" class="text">
The systems 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 id="D1"><li><span class="emph alpha">λ-δ</span> of
+ </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 id="D2"><li><span class="emph alpha">∆Λ</span> of
+ </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 id="D3"><li><span class="emph alpha">λ<sub>∆</sub></span> of
+ </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 id="D4"><li><span class="emph alpha">λ∆</span> of
+ </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 id="D5"><li><span class="emph alpha">λD</span> of
+ </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 id="D6"><li><span class="emph alpha">Cλξ</span> of
+ </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 class="text"><img class="icon32" alt="[Smiling face]" title="Smile!" src="http://lambdadelta.info/images/smile.png"/>
+ </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 systems 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>.
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