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22 <div class="head1">The Formal Systems of the λδ (\lambda\delta) Family</div>
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40 <a href="http://lambdadelta.info/specification.html">specification</a>
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76 <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
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79 <a href="http://lambdadelta.info/osn/">Open Symbolic Notation (OSN)</a>
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90 <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
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93 <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
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105 <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="foreword">Foreword <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b9.png" />
107 <div xmlns:ld="http://lambdadelta.info/" class="text">
108 The formal systems of the λδ (\lambda\delta) family are typed λ-calculi aiming to support
109 the foundational frameworks for Mathematics that require an underlying specification language
110 (for example the <a href="http://www.math.unipd.it/~maietti/">Minimalist Foundation</a>
111 and its predecessors).
113 <div xmlns:ld="http://lambdadelta.info/" class="text">
114 The λδ family is developed within the
115 <a href="http://helm.cs.unibo.it/">Hypertextual Electronic Library of Mathematics</a>
116 as a set of machine-checked digital specifications.
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120 (revised <span class="emph alpha">2012-09</span>).
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130 <!-- ===================================================================== -->
131 <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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134 This is a list of publications citing λδ documentation.
136 <ul xmlns:ld="http://lambdadelta.info/" id="C8">
138 M.E. Maietti, S. Maschio:
139 <span class="emph alpha">An extensional Kleene realizability semantics for the Minimalist Foundation</span>
140 (2015). In Leibniz International Proceedings in Informatics, 39, pp 162-186. Schloss Dagstuhl, Leibniz-Zentrum für Informatik.
143 <ul xmlns:ld="http://lambdadelta.info/" id="C7">
145 C. Dunchev, F. Guidi, C. Sacerdoti Coen, E. Tassi:
146 <span class="emph alpha">ELPI: Fast, Embeddable, λProlog Interpreter</span>
147 (2015). In proc. of LPAR 20. Lecture Notes in Computer Science, 9450, pp. 460-468. Springer.
150 <ul xmlns:ld="http://lambdadelta.info/" id="C6">
152 A. Asperti, W. Ricciotti, C. Sacerdoti Coen, E. Tassi:
153 <span class="emph alpha">Formal metatheory of programming languages in the Matita interactive theorem prover</span>
154 (2012). In Journal of Automated Reasoning, 49(3), pp. 427-451. Springer.
157 <ul xmlns:ld="http://lambdadelta.info/" id="C5">
160 <span class="emph alpha">Consistency of the minimalist foundation with Church thesis and Bar Induction</span>
161 (2012). Submitted article.
164 <ul xmlns:ld="http://lambdadelta.info/" id="C4">
167 <span class="emph alpha">Theoretical and implementation aspects in the mechanization of the metatheory of programming languages</span>
168 (July 2011). Ph.D. Thesis in Computer Science, Technical Report UBLCS-2011-09, University of Bologna.
171 <ul xmlns:ld="http://lambdadelta.info/" id="C3">
174 <span class="emph alpha">Faithful Reproductions of the Automath Landau Formalization</span>
175 (2011). Technical report.
178 <ul xmlns:ld="http://lambdadelta.info/" id="C2">
181 <span class="emph alpha">A minimalist two-level foundation for constructive mathematics</span>
182 (2009). In Annals of Pure and Applied Logic, 160(3), pp. 319-354. Elsevier.
185 <ul xmlns:ld="http://lambdadelta.info/" id="C1">
188 <span class="emph alpha">First Year Report: Realisability methods of proof and semantics with application to expansion</span>
189 (July 2007). Technical report.
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196 The systems of the λδ family <span class="emph alpha">are not</span> related intentionally to
197 any other system having (variations of) the symbols λ and δ in its name or syntax.
198 Examples include (but are not limited to):
200 <ul xmlns:ld="http://lambdadelta.info/" id="D1">
202 <span class="emph alpha">λ-δ</span> of
204 <span class="emph alpha">The calculi of lambda-conversion</span>
206 Annals of Mathematics Studies 6.
207 Princeton University Press.
210 <ul xmlns:ld="http://lambdadelta.info/" id="D2">
212 <span class="emph alpha">∆Λ</span> of
214 <span class="emph alpha">Generalizing Automath by means of a lambda-typed lambda calculus</span>
216 In Lecture Notes in Pure and Applied Mathematics 106, pp. 71-92.
220 <ul xmlns:ld="http://lambdadelta.info/" id="D3">
222 <span class="emph alpha">λ<sub>∆</sub>
224 N.J. Rehof, M.H. Sørensen:
225 <span class="emph alpha">The λ<sub>∆</sub>-calculus</span>
227 In Lecture Notes in Computer Science, 789, pp. 516–542.
231 <ul xmlns:ld="http://lambdadelta.info/" id="D4">
233 <span class="emph alpha">λ∆</span> of
234 S. Ronchi Della Rocca, L. Paolini:
235 <span class="emph alpha">The Parametric Lambda Calculus</span>
237 Texts in Theoretical Computer Science, An EATCS Series.
241 <ul xmlns:ld="http://lambdadelta.info/" id="D5">
243 <span class="emph alpha">λD</span> of
244 R. Nederpelt, H. Geuvers:
245 <span class="emph alpha">Type Theory and Formal Proof</span>
247 Cambridge University Press.
250 <ul xmlns:ld="http://lambdadelta.info/" id="D6">
252 <span class="emph alpha">Cλξ</span> of
254 <span class="emph alpha">A namefree lambda calculus with facilities for internal definition of expressions and segments</span>
257 Eindhoven University of Technology, Eindhoven.
260 <div xmlns:ld="http://lambdadelta.info/" class="text">
261 <img class="icon32" alt="[Smiling face]" title="Smile!" src="http://lambdadelta.info/images/smile.png" />
262 Moreover, the systems of the λδ family <span class="emph alpha">are not</span> related intentionally to
263 <a href="http://umineko.wikia.com/wiki/Lambdadelta">Lady Lambdadelta</a>,
264 the Witch of Certainty of the sound novel
265 <a href="https://it.wikipedia.org/wiki/Umineko_no_naku_koro_ni">Umineko no Naku Koro ni</a>.
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