helm/www/lambdadelta/basic_2.html

   1 <?xml version="1.0" encoding="UTF-8"?>
   2 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN" "http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd">
   3 <html xmlns="http://www.w3.org/1999/xhtml" dir="ltr" lang="en-us">
   4   <head>
   5     <meta http-equiv="Content-Language" content="en-us" />
   6     <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
   7     <meta http-equiv="Content-Style-Type" content="text/css" />
   8     <meta name="author" content="Ferruccio Guidi" />
   9     <meta name="description" content="\lambda\delta home page" />
  10     <title>\lambda\delta home page</title>
  11     <link rel="stylesheet" type="text/css" href="http://lambdadelta.info/css/ld_web.css" />
  12     <link rel="stylesheet" type="text/css" href="http://lambdadelta.info/css/lddl.css" />
  13     <link rel="stylesheet" type="text/css" href="http://lambdadelta.info/css/xhtbl.css" />
  14     <link rel="shortcut icon" href="http://lambdadelta.info/images/crux_16.ico" />
  15   </head>
  16   <body lang="en-US">
  17     <div class="spacer">
  18       <a href="http://lambdadelta.info/">
  19         <img class="icon32" alt="[\lambda\delta home]" title="\lambda\delta home" src="http://lambdadelta.info/images/crux_32.png" />
  20       </a>
  21     </div>
  22     <div class="head1">cic:/matita/lambdadelta/basic_2/ (core λδ version 2)</div>
  23     <div class="spacer">
  24       <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
  25     </div>
  26     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
  27       <br />
  28     </div>
  29     <div xmlns:ld="http://lambdadelta.info/" class="text">
  30       <table cellpadding="4" cellspacing="0">
  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     <!--
 106    <section>System's Syntax and Behavior</section>
 107    <body>This is a summary of the "block structure"
 108          of the System's syntactic items and reductions.
 109    </body>
 110    <table name="basic_2_blk"/>
 111    <body>* In terms only.
 112          ** In terms and local environments only.
 113          *** In global environments only.
 114          **** Sort level k in terms only.
 115    </body>
 116 -->
 117     <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="summary">Summary of the Specification <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png" />
 118     </div>
 119     <div xmlns:ld="http://lambdadelta.info/" class="text">Here is a numerical account of the specification's contents
 120          and its timeline.
 121    </div>
 122     <div xmlns:ld="http://lambdadelta.info/" class="text">
 123       <table cellpadding="4" cellspacing="0">
 124         <tbody>
 125           <tr>
 126             <td class="snns capitalize italic gray">category</td>
 127             <td class="snns italic gray">objects</td>
 128             <td class="snnn right italic gray">
 129               <br />
 130             </td>
 131             <td class="snnn italic gray">
 132               <br />
 133             </td>
 134             <td class="snnn right italic gray">
 135               <br />
 136             </td>
 137             <td class="snnn italic gray">
 138               <br />
 139             </td>
 140             <td class="ssnn right italic gray">
 141               <br />
 142             </td>
 143           </tr>
 144           <tr>
 145             <td class="snns capitalize italic cyan">sizes</td>
 146             <td class="snns italic cyan">files</td>
 147             <td class="snnn right italic cyan">268</td>
 148             <td class="snns italic cyan">characters</td>
 149             <td class="snnn right italic cyan">269075</td>
 150             <td class="snns italic cyan">nodes</td>
 151             <td class="ssnn right italic cyan">1271298</td>
 152           </tr>
 153           <tr>
 154             <td class="snns capitalize italic green">propositions</td>
 155             <td class="snns italic green">theorems</td>
 156             <td class="snnn right italic green">71</td>
 157             <td class="snns italic green">lemmas</td>
 158             <td class="snnn right italic green">928</td>
 159             <td class="snns italic green">total</td>
 160             <td class="ssnn right italic green">999</td>
 161           </tr>
 162           <tr>
 163             <td class="snss capitalize italic yellow">concepts</td>
 164             <td class="snss italic yellow">declared</td>
 165             <td class="snsn right italic yellow">33</td>
 166             <td class="snss italic yellow">defined</td>
 167             <td class="snsn right italic yellow">78</td>
 168             <td class="snss italic yellow">total</td>
 169             <td class="sssn right italic yellow">111</td>
 170           </tr>
 171         </tbody>
 172       </table>
 173     </div>
 174     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="B">Stage "B"</div>
 175     <ul xmlns:ld="http://lambdadelta.info/">
 176       <li>
 177         <span class="emph alpha">Ongoing.</span>
 178          Context-sensitive subject equivalence
 179          for native type assignment.
 180    </li>
 181     </ul>
 182     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A2">Stage "A2": "Extending the Applicability Condition"</div>
 183     <ul xmlns:ld="http://lambdadelta.info/">
 184       <li>
 185         <span class="emph alpha">2017 April 16.</span>
 186          Strong rt-normalization
 187          for simply typed terms
 188          (anniversary milestone).
 189    </li>
 190     </ul>
 191     <ul xmlns:ld="http://lambdadelta.info/">
 192       <li>
 193         <span class="emph alpha">2017 March 16.</span>
 194          First behavioral component reconstructed:
 195          rt_transition.
 196    </li>
 197     </ul>
 198     <ul xmlns:ld="http://lambdadelta.info/">
 199       <li>
 200         <span class="emph alpha">2017 February 19.</span>
 201          Generic candidates of reducibility.
 202    </li>
 203     </ul>
 204     <ul xmlns:ld="http://lambdadelta.info/">
 205       <li>
 206         <span class="emph alpha">2017 January 17.</span>
 207          Confluence for parallel r-transition on referred entries of local environments.
 208    </li>
 209     </ul>
 210     <ul xmlns:ld="http://lambdadelta.info/">
 211       <li>
 212         <span class="emph alpha">2016 September 15.</span>
 213          Confluence for context-sensitive parallel r-transition on terms.
 214    </li>
 215     </ul>
 216     <ul xmlns:ld="http://lambdadelta.info/">
 217       <li>
 218         <span class="emph alpha">2016 April 16.</span>
 219          Syntactic component reconstructed:
 220          syntax, relocation, s_transition, s_computation, static
 221          (anniversary milestone).
 222    </li>
 223     </ul>
 224     <ul xmlns:ld="http://lambdadelta.info/">
 225       <li>
 226         <span class="emph alpha">2016 March 25.</span>
 227          Relocation with reference transforming maps (rtmap).
 228    </li>
 229     </ul>
 230     <ul xmlns:ld="http://lambdadelta.info/">
 231       <li>
 232         <span class="emph alpha">2015 October 9.</span>
 233          λδ version 2A2 is started.
 234    </li>
 235     </ul>
 236     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
 237     <ul xmlns:ld="http://lambdadelta.info/">
 238       <li>
 239         <span class="emph delta">2015 August 27.</span>
 240          λδ version 2A1 appears too complex and is dismissed.
 241    </li>
 242     </ul>
 243     <ul xmlns:ld="http://lambdadelta.info/">
 244       <li>
 245         <span class="emph gamma">2014 October 28.</span>
 246          λδ version 2A1 is released.
 247    </li>
 248     </ul>
 249     <ul xmlns:ld="http://lambdadelta.info/">
 250       <li>
 251         <span class="emph beta">2014 September 9.</span>
 252          Iterated static type assignment defined (more elegantly)
 253          as a primitive notion.
 254    </li>
 255     </ul>
 256     <ul xmlns:ld="http://lambdadelta.info/">
 257       <li>
 258         <span class="emph beta">2014 June 18.</span>
 259          Preservation of stratified native validity
 260          for context-sensitive computation on terms.
 261    </li>
 262     </ul>
 263     <ul xmlns:ld="http://lambdadelta.info/">
 264       <li>
 265         <span class="emph alpha">2014 June 9.</span>
 266          Strong qrst-normalization
 267          for simply typed terms.
 268    </li>
 269     </ul>
 270     <ul xmlns:ld="http://lambdadelta.info/">
 271       <li>
 272         <span class="emph alpha">2014 April 16.</span>
 273          Lazy equivalence on local environments
 274          added as q-step to rst-computation on closures
 275          (anniversary milestone).
 276    </li>
 277     </ul>
 278     <ul xmlns:ld="http://lambdadelta.info/">
 279       <li>
 280         <span class="emph alpha">2014 January 20.</span>
 281          Parametrized slicing on local environments
 282          comprises both versions of this operation
 283          (one from basic_1, the other used in basic_2 till now).
 284    </li>
 285     </ul>
 286     <ul xmlns:ld="http://lambdadelta.info/">
 287       <li>
 288         <span class="emph alpha">2013 August 7.</span>
 289          Passive support for global environments.
 290    </li>
 291     </ul>
 292     <ul xmlns:ld="http://lambdadelta.info/">
 293       <li>
 294         <span class="emph alpha">2013 July 27.</span>
 295          Reaxiomatized β-reductum as in rt-reduction.
 296    </li>
 297     </ul>
 298     <ul xmlns:ld="http://lambdadelta.info/">
 299       <li>
 300         <span class="emph alpha">2013 July 20.</span>
 301          Context-sensitive strong rt-normalization
 302          for simply typed terms.
 303    </li>
 304     </ul>
 305     <ul xmlns:ld="http://lambdadelta.info/">
 306       <li>
 307         <span class="emph alpha">2013 April 16.</span>
 308          Reaxiomatized substitution and reduction
 309          commute with respect to subclosure
 310          (anniversary milestone).
 311    </li>
 312     </ul>
 313     <ul xmlns:ld="http://lambdadelta.info/">
 314       <li>
 315         <span class="emph alpha">2013 March 16.</span>
 316          Mutual recursive preservation of stratified native validity
 317          for rst-computation on closures.
 318    </li>
 319     </ul>
 320     <ul xmlns:ld="http://lambdadelta.info/">
 321       <li>
 322         <span class="emph alpha">2012 October 16.</span>
 323          Confluence for context-free parallel reduction on closures.
 324    </li>
 325     </ul>
 326     <ul xmlns:ld="http://lambdadelta.info/">
 327       <li>
 328         <span class="emph alpha">2012 July 26.</span>
 329          Term binders polarized to control ζ-reduction (not released).
 330    </li>
 331     </ul>
 332     <ul xmlns:ld="http://lambdadelta.info/">
 333       <li>
 334         <span class="emph alpha">2012 April 16.</span>
 335          Context-sensitive subject equivalence
 336          for atomic arity assignment
 337          (anniversary milestone).
 338    </li>
 339     </ul>
 340     <ul xmlns:ld="http://lambdadelta.info/">
 341       <li>
 342         <span class="emph alpha">2012 March 15.</span>
 343          Context-sensitive strong normalization
 344          for simply typed terms.
 345    </li>
 346     </ul>
 347     <ul xmlns:ld="http://lambdadelta.info/">
 348       <li>
 349         <span class="emph alpha">2012 January 27.</span>
 350          Generic candidates of reducibility.
 351    </li>
 352     </ul>
 353     <ul xmlns:ld="http://lambdadelta.info/">
 354       <li>
 355         <span class="emph alpha">2011 September 21.</span>
 356          Confluence for context-sensitive parallel reduction on terms.
 357    </li>
 358     </ul>
 359     <ul xmlns:ld="http://lambdadelta.info/">
 360       <li>
 361         <span class="emph alpha">2011 September 6.</span>
 362          Confluence for context-free parallel reduction on terms.
 363    </li>
 364     </ul>
 365     <ul xmlns:ld="http://lambdadelta.info/">
 366       <li>
 367         <span class="emph alpha">2011 April 17.</span>
 368          λδ version 2 is started.
 369    </li>
 370     </ul>
 371     <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="structure">Logical Structure of the Specification <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png" />
 372     </div>
 373     <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
 374    </div>
 375     <div xmlns:ld="http://lambdadelta.info/" class="text">
 376       <table cellpadding="4" cellspacing="0">
 377         <tbody>
 378           <tr>
 379             <td class="snns top capitalize italic gray">component</td>
 380             <td class="snns top italic gray">plane</td>
 381             <td class="snns top gray">files</td>
 382             <td class="ssnn top gray">
 383               <br />
 384             </td>
 385           </tr>
 386           <tr>
 387             <td class="snns top capitalize italic blue">conversion</td>
 388             <td class="snns top italic blue">context-sensitive r-conversion</td>
 389             <td class="snns top blue">cpc ( ⦃?,?⦄ ⊢ ? ⬌[?] ? )</td>
 390             <td class="ssnn top blue">cpc_cpc</td>
 391           </tr>
 392           <tr>
 393             <td class="snns top capitalize italic sky">rt-computation</td>
 394             <td class="snns top italic sky">uncounted context-sensitive rt-computation</td>
 395             <td class="snns top sky">lfsx ( ? ⊢ ⬈*[?,?,?] 𝐒⦃?⦄ )</td>
 396             <td class="ssnn top sky">lfsx_fqup lfsx_lfpxs lfsx_lfsx</td>
 397           </tr>
 398           <tr>
 399             <td class="nnns top capitalize italic sky">
 400               <br />
 401             </td>
 402             <td class="nnns top italic sky">
 403               <br />
 404             </td>
 405             <td class="snns top sky">csx_vector ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )</td>
 406             <td class="ssnn top sky">csx_cnx_vector csx_csx_vector</td>
 407           </tr>
 408           <tr>
 409             <td class="nnns top capitalize italic sky">
 410               <br />
 411             </td>
 412             <td class="nnns top italic sky">
 413               <br />
 414             </td>
 415             <td class="snns top sky">csx ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )</td>
 416             <td class="ssnn top sky">csx_simple csx_simple_theq csx_drops csx_lsubr csx_aaa csx_gcp csx_gcr csx_lfpx csx_cnx csx_cpxs csx_csx</td>
 417           </tr>
 418           <tr>
 419             <td class="nnns top capitalize italic sky">
 420               <br />
 421             </td>
 422             <td class="nnns top italic sky">
 423               <br />
 424             </td>
 425             <td class="snns top sky">lfpxs ( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )</td>
 426             <td class="ssnn top sky">lfpxs_length lfpxs_drops lfpxs_fqup lfpxs_lfdeq lfpxs_aaa lfpxs_cpxs lfpxs_lfpxs</td>
 427           </tr>
 428           <tr>
 429             <td class="nnns top capitalize italic sky">
 430               <br />
 431             </td>
 432             <td class="nnns top italic sky">
 433               <br />
 434             </td>
 435             <td class="snns top sky">cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )</td>
 436             <td class="ssnn top sky">cpxs_tdeq cpxs_theq cpxs_theq_vector cpxs_drops cpxs_lsubr cpxs_aaa cpxs_lfpx cpxs_cnx cpxs_cpxs</td>
 437           </tr>
 438           <tr>
 439             <td class="snns top capitalize italic cyan">rt-transition</td>
 440             <td class="snns top italic cyan">uncounted rst-transition</td>
 441             <td class="snns top cyan">fpbq ( ⦃?,?,?⦄ ≽[?] ⦃?,?,?⦄ )</td>
 442             <td class="ssnn top cyan">fpbq_aaa</td>
 443           </tr>
 444           <tr>
 445             <td class="nnns top capitalize italic cyan">
 446               <br />
 447             </td>
 448             <td class="nnns top italic cyan">
 449               <br />
 450             </td>
 451             <td class="snns top cyan">fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )</td>
 452             <td class="ssnn top cyan">fpb_lfdeq</td>
 453           </tr>
 454           <tr>
 455             <td class="nnns top capitalize italic cyan">
 456               <br />
 457             </td>
 458             <td class="snns top italic cyan">t-bound context-sensitive rt-transition</td>
 459             <td class="snns top cyan">lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
 460             <td class="ssnn top cyan">lfpr_length lfpr_drops lfpr_fquq lfpr_fqup lfpr_frees lfpr_aaa lfpr_lfpx lfpr_lfpr</td>
 461           </tr>
 462           <tr>
 463             <td class="nnns top capitalize italic cyan">
 464               <br />
 465             </td>
 466             <td class="nnns top italic cyan">
 467               <br />
 468             </td>
 469             <td class="snns top cyan">cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 470             <td class="ssnn top cyan">cpr_drops</td>
 471           </tr>
 472           <tr>
 473             <td class="nnns top capitalize italic cyan">
 474               <br />
 475             </td>
 476             <td class="nnns top italic cyan">
 477               <br />
 478             </td>
 479             <td class="snns top cyan">cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
 480             <td class="ssnn top cyan">cpm_simple cpm_drops cpm_lsubr cpm_lfxs cpm_cpx</td>
 481           </tr>
 482           <tr>
 483             <td class="nnns top capitalize italic cyan">
 484               <br />
 485             </td>
 486             <td class="snns top italic cyan">uncounted context-sensitive rt-transition</td>
 487             <td class="snns top cyan">cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )</td>
 488             <td class="ssnn top cyan">cnx_simple cnx_drops cnx_cnx</td>
 489           </tr>
 490           <tr>
 491             <td class="nnns top capitalize italic cyan">
 492               <br />
 493             </td>
 494             <td class="nnns top italic cyan">
 495               <br />
 496             </td>
 497             <td class="snns top cyan">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
 498             <td class="ssnn top cyan">lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_lfdeq lfpx_aaa lfpx_lfpx</td>
 499           </tr>
 500           <tr>
 501             <td class="nnns top capitalize italic cyan">
 502               <br />
 503             </td>
 504             <td class="nnns top italic cyan">
 505               <br />
 506             </td>
 507             <td class="snns top cyan">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
 508             <td class="ssnn top cyan">cpx_simple cpx_drops cpx_fqus cpx_lsubr cpx_lfxs</td>
 509           </tr>
 510           <tr>
 511             <td class="nnns top capitalize italic cyan">
 512               <br />
 513             </td>
 514             <td class="snns top italic cyan">counted context-sensitive rt-transition</td>
 515             <td class="snns top cyan">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
 516             <td class="ssnn top cyan">cpg_simple cpg_drops cpg_lsubr</td>
 517           </tr>
 518           <tr>
 519             <td class="snns top capitalize italic water">iterated static typing</td>
 520             <td class="snns top italic water">iterated extension on referred entries</td>
 521             <td class="snns top water">tc_lfxs ( ? ⦻**[?,?] ? )</td>
 522             <td class="ssnn top water">tc_lfxs_length tc_lfxs_drops tc_lfxs_fqup tc_lfxs_tc_lfxs</td>
 523           </tr>
 524           <tr>
 525             <td class="snns top capitalize italic green">static typing</td>
 526             <td class="snns top italic green">generic reducibility</td>
 527             <td class="snns top green">lsubc ( ? ⊢ ? ⫃[?] ? )</td>
 528             <td class="ssnn top green">lsubc_drops lsubc_lsubr lsubc_lsuba</td>
 529           </tr>
 530           <tr>
 531             <td class="nnns top capitalize italic green">
 532               <br />
 533             </td>
 534             <td class="nnns top italic green">
 535               <br />
 536             </td>
 537             <td class="snns top green">gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
 538             <td class="ssnn top green">gcp_aaa</td>
 539           </tr>
 540           <tr>
 541             <td class="nnns top capitalize italic green">
 542               <br />
 543             </td>
 544             <td class="nnns top italic green">
 545               <br />
 546             </td>
 547             <td class="snns top green">gcp</td>
 548             <td class="ssnn top green">
 549               <br />
 550             </td>
 551           </tr>
 552           <tr>
 553             <td class="nnns top capitalize italic green">
 554               <br />
 555             </td>
 556             <td class="snns top italic green">atomic arity assignment</td>
 557             <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
 558             <td class="ssnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
 559           </tr>
 560           <tr>
 561             <td class="nnns top capitalize italic green">
 562               <br />
 563             </td>
 564             <td class="nnns top italic green">
 565               <br />
 566             </td>
 567             <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 568             <td class="ssnn top green">aaa_drops aaa_fqus aaa_lfdeq aaa_aaa</td>
 569           </tr>
 570           <tr>
 571             <td class="nnns top capitalize italic green">
 572               <br />
 573             </td>
 574             <td class="snns top italic green">degree-based equivalence on referred entries</td>
 575             <td class="snns top green">ffdeq ( ⦃?,?,?⦄ ≡[?,?] ⦃?,?,?⦄ )</td>
 576             <td class="ssnn top green">ffdeq_fqup ffdeq_ffdeq</td>
 577           </tr>
 578           <tr>
 579             <td class="nnns top capitalize italic green">
 580               <br />
 581             </td>
 582             <td class="nnns top italic green">
 583               <br />
 584             </td>
 585             <td class="snns top green">lfdeq ( ? ≡[?,?,?] ? )</td>
 586             <td class="ssnn top green">lfdeq_length lfdeq_drops lfdeq_fqup lfdeq_fqus lfdeq_lfdeq</td>
 587           </tr>
 588           <tr>
 589             <td class="nnns top capitalize italic green">
 590               <br />
 591             </td>
 592             <td class="snns top italic green">generic extension on referred entries</td>
 593             <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
 594             <td class="ssnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
 595           </tr>
 596           <tr>
 597             <td class="nnns top capitalize italic green">
 598               <br />
 599             </td>
 600             <td class="snns top italic green">context-sensitive free variables</td>
 601             <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
 602             <td class="ssnn top green">lsubf_frees</td>
 603           </tr>
 604           <tr>
 605             <td class="nnns top capitalize italic green">
 606               <br />
 607             </td>
 608             <td class="nnns top italic green">
 609               <br />
 610             </td>
 611             <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 612             <td class="ssnn top green">frees_drops frees_fqup frees_frees</td>
 613           </tr>
 614           <tr>
 615             <td class="nnns top capitalize italic green">
 616               <br />
 617             </td>
 618             <td class="snns top italic green">restricted ref. for local env.</td>
 619             <td class="snns top green">lsubr ( ? ⫃ ? )</td>
 620             <td class="ssnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
 621           </tr>
 622           <tr>
 623             <td class="snns top capitalize italic grass">s-computation</td>
 624             <td class="snns top italic grass">iterated structural successor for closures</td>
 625             <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
 626             <td class="ssnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
 627           </tr>
 628           <tr>
 629             <td class="nnns top capitalize italic grass">
 630               <br />
 631             </td>
 632             <td class="nnns top italic grass">
 633               <br />
 634             </td>
 635             <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
 636             <td class="ssnn top grass">fqup_weight fqup_drops fqup_fqup</td>
 637           </tr>
 638           <tr>
 639             <td class="snns top capitalize italic yellow">s-transition</td>
 640             <td class="snns top italic yellow">structural successor for closures</td>
 641             <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
 642             <td class="ssnn top yellow">fquq_length fquq_weight</td>
 643           </tr>
 644           <tr>
 645             <td class="nnns top capitalize italic yellow">
 646               <br />
 647             </td>
 648             <td class="nnns top italic yellow">
 649               <br />
 650             </td>
 651             <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
 652             <td class="ssnn top yellow">fqu_length fqu_weight</td>
 653           </tr>
 654           <tr>
 655             <td class="snns top capitalize italic orange">relocation</td>
 656             <td class="snns top italic orange">generic slicing for local environments</td>
 657             <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 658             <td class="ssnn top orange">
 659               <br />
 660             </td>
 661           </tr>
 662           <tr>
 663             <td class="nnns top capitalize italic orange">
 664               <br />
 665             </td>
 666             <td class="nnns top italic orange">
 667               <br />
 668             </td>
 669             <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 670             <td class="ssnn top orange">drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops</td>
 671           </tr>
 672           <tr>
 673             <td class="nnns top capitalize italic orange">
 674               <br />
 675             </td>
 676             <td class="snns top italic orange">generic relocation</td>
 677             <td class="snns top orange">lifts_bind ( ⬆*[?] ? ≡ ? )</td>
 678             <td class="ssnn top orange">lifts_weight_bind lifts_lifts_bind</td>
 679           </tr>
 680           <tr>
 681             <td class="nnns top capitalize italic orange">
 682               <br />
 683             </td>
 684             <td class="nnns top italic orange">
 685               <br />
 686             </td>
 687             <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 688             <td class="ssnn top orange">lifts_lifts_vector</td>
 689           </tr>
 690           <tr>
 691             <td class="nnns top capitalize italic orange">
 692               <br />
 693             </td>
 694             <td class="nnns top italic orange">
 695               <br />
 696             </td>
 697             <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
 698             <td class="ssnn top orange">lifts_simple lifts_weight lifts_tdeq lifts_lifts</td>
 699           </tr>
 700           <tr>
 701             <td class="nnns top capitalize italic orange">
 702               <br />
 703             </td>
 704             <td class="snns top italic orange">ranged equivalence for local environments</td>
 705             <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
 706             <td class="ssnn top orange">lreq_length lreq_lreq</td>
 707           </tr>
 708           <tr>
 709             <td class="nnns top capitalize italic orange">
 710               <br />
 711             </td>
 712             <td class="snns top italic orange">generic entrywise extension</td>
 713             <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
 714             <td class="ssnn top orange">lexs_length lexs_lexs</td>
 715           </tr>
 716           <tr>
 717             <td class="snns top capitalize italic red">syntax</td>
 718             <td class="snns top italic red">append for local environments</td>
 719             <td class="snns top red">append ( ? @@ ? )</td>
 720             <td class="ssnn top red">append_length</td>
 721           </tr>
 722           <tr>
 723             <td class="nnns top capitalize italic red">
 724               <br />
 725             </td>
 726             <td class="snns top italic red">head equivalence for terms</td>
 727             <td class="snns top red">theq ( ? ⩳[?,?] ? )</td>
 728             <td class="ssnn top red">theq_simple theq_tdeq theq_theq theq_simple_vector</td>
 729           </tr>
 730           <tr>
 731             <td class="nnns top capitalize italic red">
 732               <br />
 733             </td>
 734             <td class="snns top italic red">degree-based equivalence for terms</td>
 735             <td class="snns top red">deq ( ? ≡[?,?] ? ) </td>
 736             <td class="ssnn top red">deq_deq</td>
 737           </tr>
 738           <tr>
 739             <td class="nnns top capitalize italic red">
 740               <br />
 741             </td>
 742             <td class="snns top italic red">closures</td>
 743             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 744             <td class="ssnn top red">
 745               <br />
 746             </td>
 747           </tr>
 748           <tr>
 749             <td class="nnns top capitalize italic red">
 750               <br />
 751             </td>
 752             <td class="nnns top italic red">
 753               <br />
 754             </td>
 755             <td class="snns top red">cl_restricted_weight ( ♯{?,?} )</td>
 756             <td class="ssnn top red">
 757               <br />
 758             </td>
 759           </tr>
 760           <tr>
 761             <td class="nnns top capitalize italic red">
 762               <br />
 763             </td>
 764             <td class="snns top italic red">global environments</td>
 765             <td class="snns top red">genv</td>
 766             <td class="ssnn top red">
 767               <br />
 768             </td>
 769           </tr>
 770           <tr>
 771             <td class="nnns top capitalize italic red">
 772               <br />
 773             </td>
 774             <td class="snns top italic red">local environments</td>
 775             <td class="snns top red">lenv_ext2</td>
 776             <td class="ssnn top red">
 777               <br />
 778             </td>
 779           </tr>
 780           <tr>
 781             <td class="nnns top capitalize italic red">
 782               <br />
 783             </td>
 784             <td class="nnns top italic red">
 785               <br />
 786             </td>
 787             <td class="snns top red">lenv_length ( |?| )</td>
 788             <td class="ssnn top red">
 789               <br />
 790             </td>
 791           </tr>
 792           <tr>
 793             <td class="nnns top capitalize italic red">
 794               <br />
 795             </td>
 796             <td class="nnns top italic red">
 797               <br />
 798             </td>
 799             <td class="snns top red">lenv_weight ( ♯{?} )</td>
 800             <td class="ssnn top red">
 801               <br />
 802             </td>
 803           </tr>
 804           <tr>
 805             <td class="nnns top capitalize italic red">
 806               <br />
 807             </td>
 808             <td class="nnns top italic red">
 809               <br />
 810             </td>
 811             <td class="snns top red">lenv</td>
 812             <td class="ssnn top red">
 813               <br />
 814             </td>
 815           </tr>
 816           <tr>
 817             <td class="nnns top capitalize italic red">
 818               <br />
 819             </td>
 820             <td class="snns top italic red">binders for local environments</td>
 821             <td class="snns top red">bind_ext2</td>
 822             <td class="ssnn top red">
 823               <br />
 824             </td>
 825           </tr>
 826           <tr>
 827             <td class="nnns top capitalize italic red">
 828               <br />
 829             </td>
 830             <td class="nnns top italic red">
 831               <br />
 832             </td>
 833             <td class="snns top red">bind</td>
 834             <td class="ssnn top red">bind_weight</td>
 835           </tr>
 836           <tr>
 837             <td class="nnns top capitalize italic red">
 838               <br />
 839             </td>
 840             <td class="snns top italic red">terms</td>
 841             <td class="snns top red">term_vector ( Ⓐ?.? )</td>
 842             <td class="ssnn top red">
 843               <br />
 844             </td>
 845           </tr>
 846           <tr>
 847             <td class="nnns top capitalize italic red">
 848               <br />
 849             </td>
 850             <td class="nnns top italic red">
 851               <br />
 852             </td>
 853             <td class="snns top red">term_simple ( 𝐒⦃?⦄ )</td>
 854             <td class="ssnn top red">
 855               <br />
 856             </td>
 857           </tr>
 858           <tr>
 859             <td class="nnns top capitalize italic red">
 860               <br />
 861             </td>
 862             <td class="nnns top italic red">
 863               <br />
 864             </td>
 865             <td class="snns top red">term_weight ( ♯{?} )</td>
 866             <td class="ssnn top red">
 867               <br />
 868             </td>
 869           </tr>
 870           <tr>
 871             <td class="nnns top capitalize italic red">
 872               <br />
 873             </td>
 874             <td class="nnns top italic red">
 875               <br />
 876             </td>
 877             <td class="snns top red">term</td>
 878             <td class="ssnn top red">
 879               <br />
 880             </td>
 881           </tr>
 882           <tr>
 883             <td class="nnns top capitalize italic red">
 884               <br />
 885             </td>
 886             <td class="snns top italic red">items</td>
 887             <td class="snns top red">item_sd</td>
 888             <td class="ssnn top red">
 889               <br />
 890             </td>
 891           </tr>
 892           <tr>
 893             <td class="nnns top capitalize italic red">
 894               <br />
 895             </td>
 896             <td class="nnns top italic red">
 897               <br />
 898             </td>
 899             <td class="snns top red">item_sh</td>
 900             <td class="ssnn top red">
 901               <br />
 902             </td>
 903           </tr>
 904           <tr>
 905             <td class="nnns top capitalize italic red">
 906               <br />
 907             </td>
 908             <td class="nnns top italic red">
 909               <br />
 910             </td>
 911             <td class="snns top red">item</td>
 912             <td class="ssnn top red">
 913               <br />
 914             </td>
 915           </tr>
 916           <tr>
 917             <td class="nnss top capitalize italic red">
 918               <br />
 919             </td>
 920             <td class="snss top italic red">atomic arities</td>
 921             <td class="snss top red">aarity</td>
 922             <td class="sssn top red">
 923               <br />
 924             </td>
 925           </tr>
 926         </tbody>
 927       </table>
 928     </div>
 929     <div class="spacer">
 930       <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 931     </div>
 932     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 933       <br />
 934     </div>
 935     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 936       <a href="http://validator.w3.org/check?uri=referer">
 937         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
 938       </a>
 939       <a href="http://jigsaw.w3.org/css-validator/check/referer">
 940         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
 941       </a>
 942       <a href="http://www.w3.org/XML/">
 943         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
 944       </a>
 945       <a href="http://www.w3.org/Graphics/PNG/">
 946         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 947       </a>
 948       <a href="http://www.anybrowser.org/campaign/">
 949         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
 950       </a>
 951     </div>
 952     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 953       <br />
 954     </div>
 955     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Tue, 10 Oct 2017 22:45:09 +0200</div>
 956   </body>
 957 </html>