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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>
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- 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.
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- (revised <span class="emph alpha">2012-09</span>).
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- <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" />
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- <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="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 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>
- <!-- ===================================================================== -->
- <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" />
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- 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 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 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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projects / helm.git / blobdiff