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  22     <div class="head1">The Formal Systems of the λδ (\lambda\delta) Family</div>
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  31         <tbody>
  32           <tr>
  33             <td class="snns capitalize italic sky">
  34               <a href="http://lambdadelta.info/home.html">home</a>
  35             </td>
  36             <td class="snns capitalize italic magenta">
  37               <a href="http://lambdadelta.info/news.html">news</a>
  38             </td>
  39             <td class="snns capitalize italic white">
  40               <a href="http://lambdadelta.info/specification.html">specification</a>
  41             </td>
  42             <td class="snnn capitalize italic white">
  43               <br />
  44             </td>
  45             <td class="snnn capitalize italic white">
  46               <br />
  47             </td>
  48             <td class="snns capitalize italic orange">
  49               <a href="http://lambdadelta.info/documentation.html">documentation</a>
  50             </td>
  51             <td class="snns capitalize italic green">
  52               <a href="http://lambdadelta.info/implementation.html">implementation</a>
  53             </td>
  54             <td class="ssnn capitalize italic green">
  55               <br />
  56             </td>
  57           </tr>
  58           <tr>
  59             <td class="snns capitalize sky">
  60               <a href="http://lambdadelta.info/home.html#foreword">foreword</a>
  61             </td>
  62             <td class="snns capitalize magenta">
  63               <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
  64             </td>
  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>
  69             <td class="snnn capitalize white">
  70               <br />
  71             </td>
  72             <td class="snns capitalize orange">
  73               <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
  74             </td>
  75             <td class="snns capitalize green">
  76               <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
  77             </td>
  78             <td class="ssnn capitalize green">
  79               <a href="http://lambdadelta.info/osn/">Open Symbolic Notation (OSN)</a>
  80             </td>
  81           </tr>
  82           <tr>
  83             <td class="snss capitalize sky">
  84               <a href="http://lambdadelta.info/home.html#citations">citations</a>
  85             </td>
  86             <td class="snss capitalize magenta">
  87               <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
  88             </td>
  89             <td class="snss capitalize white">
  90               <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
  91             </td>
  92             <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>
  93             <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
  94             <td class="snss capitalize orange">
  95               <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
  96             </td>
  97             <td class="snss capitalize green">
  98               <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
  99             </td>
 100             <td class="sssn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
 101           </tr>
 102         </tbody>
 103       </table>
 104     </div>
 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" />
 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>
 118     <div xmlns:ld="http://lambdadelta.info/" class="text">
 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>
 122     <div xmlns:ld="http://lambdadelta.info/" class="text">
 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="[butterfly]" title="\lambda\delta 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="C9">
 137       <li>
 138       Matthias Weber:
 139       <span class="emph alpha">An extended type system with lambda-typed lambda-expressions (extended version)</span>
 140       (2017). Technical report. Faculty of Computer Science, Technical University of Berlin.
 141    </li>
 142     </ul>
 143     <ul xmlns:ld="http://lambdadelta.info/" id="C8">
 144       <li>
 145       M.E. Maietti, S. Maschio:
 146       <span class="emph alpha">An extensional Kleene realizability semantics for the Minimalist Foundation</span>
 147       (2015). In Leibniz International Proceedings in Informatics, 39, pp 162-186. Schloss Dagstuhl, Leibniz-Zentrum für Informatik.
 148    </li>
 149     </ul>
 150     <ul xmlns:ld="http://lambdadelta.info/" id="C7">
 151       <li>
 152       C. Dunchev, F. Guidi, C. Sacerdoti Coen, E. Tassi:
 153       <span class="emph alpha">ELPI: Fast, Embeddable, λProlog Interpreter</span>
 154       (2015). In proc. of LPAR 20. Lecture Notes in Computer Science, 9450, pp. 460-468. Springer.
 155    </li>
 156     </ul>
 157     <ul xmlns:ld="http://lambdadelta.info/" id="C6">
 158       <li>
 159       A. Asperti, W. Ricciotti, C. Sacerdoti Coen, E. Tassi:
 160       <span class="emph alpha">Formal metatheory of programming languages in the Matita interactive theorem prover</span>
 161       (2012). In Journal of Automated Reasoning, 49(3), pp. 427-451. Springer.
 162    </li>
 163     </ul>
 164     <ul xmlns:ld="http://lambdadelta.info/" id="C5">
 165       <li>
 166       M.E. Maietti:
 167       <span class="emph alpha">Consistency of the minimalist foundation with Church thesis and Bar Induction</span>
 168       (2012). Submitted article.
 169    </li>
 170     </ul>
 171     <ul xmlns:ld="http://lambdadelta.info/" id="C4">
 172       <li>
 173       W. Ricciotti:
 174       <span class="emph alpha">Theoretical and implementation aspects in the mechanization of the metatheory of programming languages</span>
 175       (July 2011). Ph.D. Thesis in Computer Science, Technical Report UBLCS-2011-09, University of Bologna.
 176    </li>
 177     </ul>
 178     <ul xmlns:ld="http://lambdadelta.info/" id="C3">
 179       <li>
 180       C.E. Brown:
 181       <span class="emph alpha">Faithful Reproductions of the Automath Landau Formalization</span>
 182       (2011). Technical report.
 183    </li>
 184     </ul>
 185     <ul xmlns:ld="http://lambdadelta.info/" id="C2">
 186       <li>
 187       M.E. Maietti:
 188       <span class="emph alpha">A minimalist two-level foundation for constructive mathematics</span>
 189       (2009). In Annals of Pure and Applied Logic, 160(3), pp. 319-354. Elsevier.
 190    </li>
 191     </ul>
 192     <ul xmlns:ld="http://lambdadelta.info/" id="C1">
 193       <li>
 194       V. Rahili:
 195       <span class="emph alpha">First Year Report: Realisability methods of proof and semantics with application to expansion</span>
 196       (July 2007). Technical report.
 197    </li>
 198     </ul>
 199     <!-- ===================================================================== -->
 200     <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" />
 201     </div>
 202     <div xmlns:ld="http://lambdadelta.info/" class="text">
 203       The systems of the λδ family <span class="emph alpha">are not</span> related intentionally to
 204       any other system having (variations of) the symbols λ and δ in its name or syntax.
 205       Examples include (but are not limited to):
 206    </div>
 207     <ul xmlns:ld="http://lambdadelta.info/" id="D1">
 208       <li>
 209         <span class="emph alpha">λ-δ</span> of
 210       A. Church:
 211       <span class="emph alpha">The calculi of lambda-conversion</span>
 212       (1941).
 213       Annals of Mathematics Studies 6.
 214       Princeton University Press.
 215    </li>
 216     </ul>
 217     <ul xmlns:ld="http://lambdadelta.info/" id="D2">
 218       <li>
 219         <span class="emph alpha">∆Λ</span> of
 220       N.G. de Bruijn:
 221       <span class="emph alpha">Generalizing Automath by means of a lambda-typed lambda calculus</span>
 222       (1987).
 223       In Lecture Notes in Pure and Applied Mathematics 106, pp. 71-92.
 224       Marcel Dekker.
 225    </li>
 226     </ul>
 227     <ul xmlns:ld="http://lambdadelta.info/" id="D3">
 228       <li>
 229         <span class="emph alpha">λ<sub>∆</sub>
 230         </span> of
 231       N.J. Rehof, M.H. Sørensen:
 232       <span class="emph alpha">The λ<sub>∆</sub>-calculus</span>
 233       (1994).
 234       In Lecture Notes in Computer Science, 789, pp. 516–542.
 235       Springer.
 236    </li>
 237     </ul>
 238     <ul xmlns:ld="http://lambdadelta.info/" id="D4">
 239       <li>
 240         <span class="emph alpha">λ∆</span> of
 241       S. Ronchi Della Rocca, L. Paolini:
 242       <span class="emph alpha">The Parametric Lambda Calculus</span>
 243       (2004).
 244       Texts in Theoretical Computer Science, An EATCS Series.
 245       Springer.
 246    </li>
 247     </ul>
 248     <ul xmlns:ld="http://lambdadelta.info/" id="D5">
 249       <li>
 250         <span class="emph alpha">λD</span> of
 251       R. Nederpelt, H. Geuvers:
 252       <span class="emph alpha">Type Theory and Formal Proof</span>
 253       (2014).
 254       Cambridge University Press.
 255    </li>
 256     </ul>
 257     <ul xmlns:ld="http://lambdadelta.info/" id="D6">
 258       <li>
 259         <span class="emph alpha">Cλξ</span> of
 260       N.G. de Bruijn:
 261       <span class="emph alpha">A namefree lambda calculus with facilities for internal definition of expressions and segments</span>
 262       (1978).
 263       TH-report 78-WSK-03.
 264       Eindhoven University of Technology, Eindhoven.
 265    </li>
 266     </ul>
 267     <div xmlns:ld="http://lambdadelta.info/" class="text">
 268       <img class="icon32" alt="[Smiling face]" title="Smile!" src="http://lambdadelta.info/images/smile.png" />
 269       Moreover, the systems of the λδ family <span class="emph alpha">are not</span> related intentionally to
 270       <a href="http://umineko.wikia.com/wiki/Lambdadelta">Lady Lambdadelta</a>,
 271       the Witch of Certainty of the sound novel
 272       <a href="https://it.wikipedia.org/wiki/Umineko_no_naku_koro_ni">Umineko no Naku Koro ni</a>.
 273    </div>
 274     <div class="spacer">
 275       <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
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