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  22     <div class="head1">The Formal Systems of the λδ (\lambda\delta) Family</div>
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  33             <td class="snns capitalize italic sky">
  34               <a href="http://lambdadelta.info/index.html">home</a>
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  49               <a href="http://lambdadelta.info/documentation.html">documentation</a>
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  52               <a href="http://lambdadelta.info/implementation.html">implementation</a>
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  60               <a href="http://lambdadelta.info/index.html#foreword">foreword</a>
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  63               <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
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  65             <td class="snns capitalize white">
  66               <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
  67             </td>
  68             <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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  73               <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
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  76               <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
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  78             <td class="ssnn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
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  82               <a href="http://lambdadelta.info/index.html#citations">citations</a>
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  88               <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
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  90             <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>
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  93               <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
  94             </td>
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  96               <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
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 105     <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="foreword">Foreword <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b9.png" />
 106     </div>
 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).
 112    </div>
 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.
 117    </div>
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 119       This is the family logo: <a href="http://lambdadelta.info/images/crux_177.png">crux_177.png</a>
 120       (revised <span class="emph alpha">2012-09</span>).
 121    </div>
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 123       <span class="emph alpha">Notice for the user of Internet Explorer.</span>
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 129    </div>
 130     <!-- ===================================================================== -->
 131     <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" />
 132     </div>
 133     <div xmlns:ld="http://lambdadelta.info/" class="text">
 134       This is a list of publications citing λδ documentation.
 135    </div>
 136     <ul xmlns:ld="http://lambdadelta.info/" id="C7">
 137       <li>
 138       C. Dunchev, F. Guidi, C. Sacerdoti Coen, E. Tassi:
 139       <span class="emph alpha">ELPI: Fast, Embeddable, λProlog Interpreter</span>
 140       (2015). In proc. of LPAR 20. Lecture Notes in Computer Science, 9450, pp. 460-468. Springer.
 141    </li>
 142     </ul>
 143     <ul xmlns:ld="http://lambdadelta.info/" id="C6">
 144       <li>
 145       A. Asperti, W. Ricciotti, C. Sacerdoti Coen, E. Tassi:
 146       <span class="emph alpha">Formal metatheory of programming languages in the Matita interactive theorem prover</span>
 147       (2012). In Journal of Automated Reasoning, 49(3), pp. 427-451. Springer.
 148    </li>
 149     </ul>
 150     <ul xmlns:ld="http://lambdadelta.info/" id="C5">
 151       <li>
 152       M.E. Maietti:
 153       <span class="emph alpha">Consistency of the minimalist foundation with Church thesis and Bar Induction</span>
 154       (2012). Submitted article.
 155    </li>
 156     </ul>
 157     <ul xmlns:ld="http://lambdadelta.info/" id="C4">
 158       <li>
 159       W. Ricciotti:
 160       <span class="emph alpha">Theoretical and implementation aspects in the mechanization of the metatheory of programming languages</span>
 161       (July 2011). Ph.D. Thesis in Computer Science, Technical Report UBLCS-2011-09, University of Bologna.
 162    </li>
 163     </ul>
 164     <ul xmlns:ld="http://lambdadelta.info/" id="C3">
 165       <li>
 166       C.E. Brown:
 167       <span class="emph alpha">Faithful Reproductions of the Automath Landau Formalization</span>
 168       (2011). Technical report.
 169    </li>
 170     </ul>
 171     <ul xmlns:ld="http://lambdadelta.info/" id="C2">
 172       <li>
 173       M.E. Maietti:
 174       <span class="emph alpha">A minimalist two-level foundation for constructive mathematics</span>
 175       (2009). In Annals of Pure and Applied Logic, 160(3), pp. 319-354. Elsevier.
 176    </li>
 177     </ul>
 178     <ul xmlns:ld="http://lambdadelta.info/" id="C1">
 179       <li>
 180       V. Rahili:
 181       <span class="emph alpha">First Year Report: Realisability methods of proof and semantics with application to expansion</span>
 182       (July 2007). Technical report.
 183    </li>
 184     </ul>
 185     <!-- ===================================================================== -->
 186     <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="disclaimer">Disclaimer <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b9.png" />
 187     </div>
 188     <div xmlns:ld="http://lambdadelta.info/" class="text">
 189       The systens of the λδ family <span class="emph alpha">are not</span> related intentionally to any other system
 190       having (variations of) the symbols λ and δ in its name or syntax.
 191       Examples include (but are not limited to):
 192    </div>
 193     <ul xmlns:ld="http://lambdadelta.info/" id="D1">
 194       <li>
 195         <span class="emph alpha">λ-δ</span> of
 196       A. Church:
 197       <span class="emph alpha">The calculi of lambda-conversion</span>
 198       (1941).
 199       Annals of Mathematics Studies 6.
 200       Princeton University Press.
 201    </li>
 202     </ul>
 203     <ul xmlns:ld="http://lambdadelta.info/" id="D2">
 204       <li>
 205         <span class="emph alpha">∆Λ</span> of
 206       N.G. de Bruijn:
 207       <span class="emph alpha">Generalizing Automath by means of a lambda-typed lambda calculus</span>
 208       (1987).
 209       In Lecture Notes in Pure and Applied Mathematics 106, pp. 71-92.
 210       Marcel Dekker.
 211    </li>
 212     </ul>
 213     <ul xmlns:ld="http://lambdadelta.info/" id="D3">
 214       <li>
 215         <span class="emph alpha">λ<sub>∆</sub>
 216         </span> of
 217       N.J. Rehof, M.H. Sørensen:
 218       <span class="emph alpha">The λ<sub>∆</sub>-calculus</span>
 219       (1994).
 220       In Lecture Notes in Computer Science, 789, pp. 516–542.
 221       Springer.
 222    </li>
 223     </ul>
 224     <ul xmlns:ld="http://lambdadelta.info/" id="D4">
 225       <li>
 226         <span class="emph alpha">λ∆</span> of
 227       S. Ronchi Della Rocca, L. Paolini:
 228       <span class="emph alpha">The Parametric Lambda Calculus</span>
 229       (2004).
 230       Texts in Theoretical Computer Science, An EATCS Series.
 231       Springer.
 232    </li>
 233     </ul>
 234     <ul xmlns:ld="http://lambdadelta.info/" id="D5">
 235       <li>
 236         <span class="emph alpha">λD</span> of
 237       R. Nederpelt, H. Geuvers:
 238       <span class="emph alpha">Type Theory and Formal Proof</span>
 239       (2014).
 240       Cambridge University Press.
 241    </li>
 242     </ul>
 243     <ul xmlns:ld="http://lambdadelta.info/" id="D6">
 244       <li>
 245         <span class="emph alpha">Cλξ</span> of
 246       N.G. de Bruijn:
 247       <span class="emph alpha">A namefree lambda calculus with facilities for internal definition of expressions and segments</span>
 248       (1978).
 249       TH-report 78-WSK-03.
 250       Eindhoven University of Technology, Eindhoven.
 251    </li>
 252     </ul>
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