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">212</td>
 148             <td class="snns italic cyan">characters</td>
 149             <td class="snnn right italic cyan">213959</td>
 150             <td class="snns italic cyan">nodes</td>
 151             <td class="ssnn right italic cyan">1057531</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">62</td>
 157             <td class="snns italic green">lemmas</td>
 158             <td class="snnn right italic green">741</td>
 159             <td class="snns italic green">total</td>
 160             <td class="ssnn right italic green">803</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">31</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">109</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 October 17.</span>
 186          Exclusion binder in local environments.
 187          Syntactic component updated:
 188          syntax, relocation, s_transition, s_computation, static, i_static.
 189    </li>
 190     </ul>
 191     <ul xmlns:ld="http://lambdadelta.info/">
 192       <li>
 193         <span class="emph alpha">2017 April 16.</span>
 194          Strong rt-normalization
 195          for simply typed terms
 196          (anniversary milestone).
 197    </li>
 198     </ul>
 199     <ul xmlns:ld="http://lambdadelta.info/">
 200       <li>
 201         <span class="emph alpha">2017 March 16.</span>
 202          First behavioral component reconstructed:
 203          rt_transition.
 204    </li>
 205     </ul>
 206     <ul xmlns:ld="http://lambdadelta.info/">
 207       <li>
 208         <span class="emph alpha">2017 February 19.</span>
 209          Generic candidates of reducibility.
 210    </li>
 211     </ul>
 212     <ul xmlns:ld="http://lambdadelta.info/">
 213       <li>
 214         <span class="emph alpha">2017 January 17.</span>
 215          Confluence for parallel r-transition on referred entries of local environments.
 216    </li>
 217     </ul>
 218     <ul xmlns:ld="http://lambdadelta.info/">
 219       <li>
 220         <span class="emph alpha">2016 September 15.</span>
 221          Confluence for context-sensitive parallel r-transition on terms.
 222    </li>
 223     </ul>
 224     <ul xmlns:ld="http://lambdadelta.info/">
 225       <li>
 226         <span class="emph alpha">2016 April 16.</span>
 227          Syntactic component reconstructed:
 228          syntax, relocation, s_transition, s_computation, static
 229          (anniversary milestone).
 230    </li>
 231     </ul>
 232     <ul xmlns:ld="http://lambdadelta.info/">
 233       <li>
 234         <span class="emph alpha">2016 March 25.</span>
 235          Relocation with reference transforming maps (rtmap).
 236    </li>
 237     </ul>
 238     <ul xmlns:ld="http://lambdadelta.info/">
 239       <li>
 240         <span class="emph alpha">2015 October 9.</span>
 241          λδ version 2A2 is started.
 242    </li>
 243     </ul>
 244     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
 245     <ul xmlns:ld="http://lambdadelta.info/">
 246       <li>
 247         <span class="emph delta">2015 August 27.</span>
 248          λδ version 2A1 appears too complex and is dismissed.
 249    </li>
 250     </ul>
 251     <ul xmlns:ld="http://lambdadelta.info/">
 252       <li>
 253         <span class="emph gamma">2014 October 28.</span>
 254          λδ version 2A1 is released.
 255    </li>
 256     </ul>
 257     <ul xmlns:ld="http://lambdadelta.info/">
 258       <li>
 259         <span class="emph beta">2014 September 9.</span>
 260          Iterated static type assignment defined (more elegantly)
 261          as a primitive notion.
 262    </li>
 263     </ul>
 264     <ul xmlns:ld="http://lambdadelta.info/">
 265       <li>
 266         <span class="emph beta">2014 June 18.</span>
 267          Preservation of stratified native validity
 268          for context-sensitive computation on terms.
 269    </li>
 270     </ul>
 271     <ul xmlns:ld="http://lambdadelta.info/">
 272       <li>
 273         <span class="emph alpha">2014 June 9.</span>
 274          Strong qrst-normalization
 275          for simply typed terms.
 276    </li>
 277     </ul>
 278     <ul xmlns:ld="http://lambdadelta.info/">
 279       <li>
 280         <span class="emph alpha">2014 April 16.</span>
 281          Lazy equivalence on local environments
 282          added as q-step to rst-computation on closures
 283          (anniversary milestone).
 284    </li>
 285     </ul>
 286     <ul xmlns:ld="http://lambdadelta.info/">
 287       <li>
 288         <span class="emph alpha">2014 January 20.</span>
 289          Parametrized slicing on local environments
 290          comprises both versions of this operation
 291          (one from basic_1, the other used in basic_2 till now).
 292    </li>
 293     </ul>
 294     <ul xmlns:ld="http://lambdadelta.info/">
 295       <li>
 296         <span class="emph alpha">2013 August 7.</span>
 297          Passive support for global environments.
 298    </li>
 299     </ul>
 300     <ul xmlns:ld="http://lambdadelta.info/">
 301       <li>
 302         <span class="emph alpha">2013 July 27.</span>
 303          Reaxiomatized β-reductum as in rt-reduction.
 304    </li>
 305     </ul>
 306     <ul xmlns:ld="http://lambdadelta.info/">
 307       <li>
 308         <span class="emph alpha">2013 July 20.</span>
 309          Context-sensitive strong rt-normalization
 310          for simply typed terms.
 311    </li>
 312     </ul>
 313     <ul xmlns:ld="http://lambdadelta.info/">
 314       <li>
 315         <span class="emph alpha">2013 April 16.</span>
 316          Reaxiomatized substitution and reduction
 317          commute with respect to subclosure
 318          (anniversary milestone).
 319    </li>
 320     </ul>
 321     <ul xmlns:ld="http://lambdadelta.info/">
 322       <li>
 323         <span class="emph alpha">2013 March 16.</span>
 324          Mutual recursive preservation of stratified native validity
 325          for rst-computation on closures.
 326    </li>
 327     </ul>
 328     <ul xmlns:ld="http://lambdadelta.info/">
 329       <li>
 330         <span class="emph alpha">2012 October 16.</span>
 331          Confluence for context-free parallel reduction on closures.
 332    </li>
 333     </ul>
 334     <ul xmlns:ld="http://lambdadelta.info/">
 335       <li>
 336         <span class="emph alpha">2012 July 26.</span>
 337          Term binders polarized to control ζ-reduction (not released).
 338    </li>
 339     </ul>
 340     <ul xmlns:ld="http://lambdadelta.info/">
 341       <li>
 342         <span class="emph alpha">2012 April 16.</span>
 343          Context-sensitive subject equivalence
 344          for atomic arity assignment
 345          (anniversary milestone).
 346    </li>
 347     </ul>
 348     <ul xmlns:ld="http://lambdadelta.info/">
 349       <li>
 350         <span class="emph alpha">2012 March 15.</span>
 351          Context-sensitive strong normalization
 352          for simply typed terms.
 353    </li>
 354     </ul>
 355     <ul xmlns:ld="http://lambdadelta.info/">
 356       <li>
 357         <span class="emph alpha">2012 January 27.</span>
 358          Generic candidates of reducibility.
 359    </li>
 360     </ul>
 361     <ul xmlns:ld="http://lambdadelta.info/">
 362       <li>
 363         <span class="emph alpha">2011 September 21.</span>
 364          Confluence for context-sensitive parallel reduction on terms.
 365    </li>
 366     </ul>
 367     <ul xmlns:ld="http://lambdadelta.info/">
 368       <li>
 369         <span class="emph alpha">2011 September 6.</span>
 370          Confluence for context-free parallel reduction on terms.
 371    </li>
 372     </ul>
 373     <ul xmlns:ld="http://lambdadelta.info/">
 374       <li>
 375         <span class="emph alpha">2011 April 17.</span>
 376          λδ version 2 is started.
 377    </li>
 378     </ul>
 379     <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" />
 380     </div>
 381     <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
 382    </div>
 383     <div xmlns:ld="http://lambdadelta.info/" class="text">
 384       <table cellpadding="4" cellspacing="0">
 385         <tbody>
 386           <tr>
 387             <td class="snns top capitalize italic gray">component</td>
 388             <td class="snns top italic gray">plane</td>
 389             <td class="snns top gray">files</td>
 390             <td class="ssnn top gray">
 391               <br />
 392             </td>
 393           </tr>
 394           <tr>
 395             <td class="snns top capitalize italic cyan">rt-transition</td>
 396             <td class="snns top italic cyan">counted context-sensitive rt-transition</td>
 397             <td class="snns top cyan">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
 398             <td class="ssnn top cyan">cpg_simple cpg_drops cpg_lsubr</td>
 399           </tr>
 400           <tr>
 401             <td class="snns top capitalize italic water">iterated static typing</td>
 402             <td class="snns top italic water">iterated extension on referred entries</td>
 403             <td class="snns top water">tc_lfxs ( ? ⦻**[?,?] ? )</td>
 404             <td class="ssnn top water">tc_lfxs_length tc_lfxs_drops tc_lfxs_fqup tc_lfxs_tc_lfxs</td>
 405           </tr>
 406           <tr>
 407             <td class="snns top capitalize italic green">static typing</td>
 408             <td class="snns top italic green">generic reducibility</td>
 409             <td class="snns top green">lsubc ( ? ⊢ ? ⫃[?] ? )</td>
 410             <td class="ssnn top green">lsubc_drops lsubc_lsubr lsubc_lsuba</td>
 411           </tr>
 412           <tr>
 413             <td class="nnns top capitalize italic green">
 414               <br />
 415             </td>
 416             <td class="nnns top italic green">
 417               <br />
 418             </td>
 419             <td class="snns top green">gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
 420             <td class="ssnn top green">gcp_aaa</td>
 421           </tr>
 422           <tr>
 423             <td class="nnns top capitalize italic green">
 424               <br />
 425             </td>
 426             <td class="nnns top italic green">
 427               <br />
 428             </td>
 429             <td class="snns top green">gcp</td>
 430             <td class="ssnn top green">
 431               <br />
 432             </td>
 433           </tr>
 434           <tr>
 435             <td class="nnns top capitalize italic green">
 436               <br />
 437             </td>
 438             <td class="snns top italic green">atomic arity assignment</td>
 439             <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
 440             <td class="ssnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
 441           </tr>
 442           <tr>
 443             <td class="nnns top capitalize italic green">
 444               <br />
 445             </td>
 446             <td class="nnns top italic green">
 447               <br />
 448             </td>
 449             <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 450             <td class="ssnn top green">aaa_drops aaa_fqus aaa_lfdeq aaa_aaa</td>
 451           </tr>
 452           <tr>
 453             <td class="nnns top capitalize italic green">
 454               <br />
 455             </td>
 456             <td class="snns top italic green">degree-based equivalence on referred entries</td>
 457             <td class="snns top green">ffdeq ( ⦃?,?,?⦄ ≡[?,?] ⦃?,?,?⦄ )</td>
 458             <td class="ssnn top green">ffdeq_fqup ffdeq_ffdeq</td>
 459           </tr>
 460           <tr>
 461             <td class="nnns top capitalize italic green">
 462               <br />
 463             </td>
 464             <td class="nnns top italic green">
 465               <br />
 466             </td>
 467             <td class="snns top green">lfdeq ( ? ≡[?,?,?] ? )</td>
 468             <td class="ssnn top green">lfdeq_length lfdeq_drops lfdeq_fqup lfdeq_fqus lfdeq_lfdeq</td>
 469           </tr>
 470           <tr>
 471             <td class="nnns top capitalize italic green">
 472               <br />
 473             </td>
 474             <td class="snns top italic green">generic extension on referred entries</td>
 475             <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
 476             <td class="ssnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
 477           </tr>
 478           <tr>
 479             <td class="nnns top capitalize italic green">
 480               <br />
 481             </td>
 482             <td class="snns top italic green">context-sensitive free variables</td>
 483             <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
 484             <td class="ssnn top green">lsubf_lsubr lsubf_frees lsubf_lsubf</td>
 485           </tr>
 486           <tr>
 487             <td class="nnns top capitalize italic green">
 488               <br />
 489             </td>
 490             <td class="nnns top italic green">
 491               <br />
 492             </td>
 493             <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 494             <td class="ssnn top green">frees_drops frees_fqup frees_frees</td>
 495           </tr>
 496           <tr>
 497             <td class="nnns top capitalize italic green">
 498               <br />
 499             </td>
 500             <td class="snns top italic green">restricted ref. for local env.</td>
 501             <td class="snns top green">lsubr ( ? ⫃ ? )</td>
 502             <td class="ssnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
 503           </tr>
 504           <tr>
 505             <td class="snns top capitalize italic grass">s-computation</td>
 506             <td class="snns top italic grass">iterated structural successor for closures</td>
 507             <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐*[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
 508             <td class="ssnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
 509           </tr>
 510           <tr>
 511             <td class="nnns top capitalize italic grass">
 512               <br />
 513             </td>
 514             <td class="nnns top italic grass">
 515               <br />
 516             </td>
 517             <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
 518             <td class="ssnn top grass">fqup_weight fqup_drops fqup_fqup</td>
 519           </tr>
 520           <tr>
 521             <td class="snns top capitalize italic yellow">s-transition</td>
 522             <td class="snns top italic yellow">structural successor for closures</td>
 523             <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
 524             <td class="ssnn top yellow">fquq_length fquq_weight</td>
 525           </tr>
 526           <tr>
 527             <td class="nnns top capitalize italic yellow">
 528               <br />
 529             </td>
 530             <td class="nnns top italic yellow">
 531               <br />
 532             </td>
 533             <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
 534             <td class="ssnn top yellow">fqu_length fqu_weight</td>
 535           </tr>
 536           <tr>
 537             <td class="snns top capitalize italic orange">relocation</td>
 538             <td class="snns top italic orange">generic slicing for local environments</td>
 539             <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 540             <td class="ssnn top orange">
 541               <br />
 542             </td>
 543           </tr>
 544           <tr>
 545             <td class="nnns top capitalize italic orange">
 546               <br />
 547             </td>
 548             <td class="nnns top italic orange">
 549               <br />
 550             </td>
 551             <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 552             <td class="ssnn top orange">drops_lstar drops_weight drops_length drops_ext2 drops_lexs drops_lreq drops_drops</td>
 553           </tr>
 554           <tr>
 555             <td class="nnns top capitalize italic orange">
 556               <br />
 557             </td>
 558             <td class="snns top italic orange">generic relocation</td>
 559             <td class="snns top orange">lifts_bind ( ⬆*[?] ? ≡ ? )</td>
 560             <td class="ssnn top orange">lifts_weight_bind lifts_lifts_bind</td>
 561           </tr>
 562           <tr>
 563             <td class="nnns top capitalize italic orange">
 564               <br />
 565             </td>
 566             <td class="nnns top italic orange">
 567               <br />
 568             </td>
 569             <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 570             <td class="ssnn top orange">lifts_lifts_vector</td>
 571           </tr>
 572           <tr>
 573             <td class="nnns top capitalize italic orange">
 574               <br />
 575             </td>
 576             <td class="nnns top italic orange">
 577               <br />
 578             </td>
 579             <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
 580             <td class="ssnn top orange">lifts_simple lifts_weight lifts_tdeq lifts_lifts</td>
 581           </tr>
 582           <tr>
 583             <td class="nnns top capitalize italic orange">
 584               <br />
 585             </td>
 586             <td class="snns top italic orange">ranged equivalence for local environments</td>
 587             <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
 588             <td class="ssnn top orange">lreq_length lreq_lreq</td>
 589           </tr>
 590           <tr>
 591             <td class="nnns top capitalize italic orange">
 592               <br />
 593             </td>
 594             <td class="snns top italic orange">generic entrywise extension</td>
 595             <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
 596             <td class="ssnn top orange">lexs_length lexs_lexs</td>
 597           </tr>
 598           <tr>
 599             <td class="snns top capitalize italic red">syntax</td>
 600             <td class="snns top italic red">append for local environments</td>
 601             <td class="snns top red">append ( ? @@ ? )</td>
 602             <td class="ssnn top red">append_length</td>
 603           </tr>
 604           <tr>
 605             <td class="nnns top capitalize italic red">
 606               <br />
 607             </td>
 608             <td class="snns top italic red">head equivalence for terms</td>
 609             <td class="snns top red">theq ( ? ⩳[?,?] ? )</td>
 610             <td class="ssnn top red">theq_simple theq_tdeq theq_theq theq_simple_vector</td>
 611           </tr>
 612           <tr>
 613             <td class="nnns top capitalize italic red">
 614               <br />
 615             </td>
 616             <td class="snns top italic red">degree-based equivalence</td>
 617             <td class="snns top red">tdeq_ext ( ? ≡[?,?] ? )</td>
 618             <td class="ssnn top red">
 619               <br />
 620             </td>
 621           </tr>
 622           <tr>
 623             <td class="nnns top capitalize italic red">
 624               <br />
 625             </td>
 626             <td class="nnns top italic red">
 627               <br />
 628             </td>
 629             <td class="snns top red">tdeq ( ? ≡[?,?] ? )</td>
 630             <td class="ssnn top red">tdeq_tdeq</td>
 631           </tr>
 632           <tr>
 633             <td class="nnns top capitalize italic red">
 634               <br />
 635             </td>
 636             <td class="snns top italic red">closures</td>
 637             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 638             <td class="ssnn top red">
 639               <br />
 640             </td>
 641           </tr>
 642           <tr>
 643             <td class="nnns top capitalize italic red">
 644               <br />
 645             </td>
 646             <td class="nnns top italic red">
 647               <br />
 648             </td>
 649             <td class="snns top red">cl_restricted_weight ( ♯{?,?} )</td>
 650             <td class="ssnn top red">
 651               <br />
 652             </td>
 653           </tr>
 654           <tr>
 655             <td class="nnns top capitalize italic red">
 656               <br />
 657             </td>
 658             <td class="snns top italic red">global environments</td>
 659             <td class="snns top red">genv</td>
 660             <td class="ssnn top red">
 661               <br />
 662             </td>
 663           </tr>
 664           <tr>
 665             <td class="nnns top capitalize italic red">
 666               <br />
 667             </td>
 668             <td class="snns top italic red">local environments</td>
 669             <td class="snns top red">lenv_ext2</td>
 670             <td class="ssnn top red">
 671               <br />
 672             </td>
 673           </tr>
 674           <tr>
 675             <td class="nnns top capitalize italic red">
 676               <br />
 677             </td>
 678             <td class="nnns top italic red">
 679               <br />
 680             </td>
 681             <td class="snns top red">lenv_length ( |?| )</td>
 682             <td class="ssnn top red">
 683               <br />
 684             </td>
 685           </tr>
 686           <tr>
 687             <td class="nnns top capitalize italic red">
 688               <br />
 689             </td>
 690             <td class="nnns top italic red">
 691               <br />
 692             </td>
 693             <td class="snns top red">lenv_weight ( ♯{?} )</td>
 694             <td class="ssnn top red">
 695               <br />
 696             </td>
 697           </tr>
 698           <tr>
 699             <td class="nnns top capitalize italic red">
 700               <br />
 701             </td>
 702             <td class="nnns top italic red">
 703               <br />
 704             </td>
 705             <td class="snns top red">lenv</td>
 706             <td class="ssnn top red">
 707               <br />
 708             </td>
 709           </tr>
 710           <tr>
 711             <td class="nnns top capitalize italic red">
 712               <br />
 713             </td>
 714             <td class="snns top italic red">binders for local environments</td>
 715             <td class="snns top red">ext2</td>
 716             <td class="ssnn top red">ext2_ext2</td>
 717           </tr>
 718           <tr>
 719             <td class="nnns top capitalize italic red">
 720               <br />
 721             </td>
 722             <td class="nnns top italic red">
 723               <br />
 724             </td>
 725             <td class="snns top red">bind</td>
 726             <td class="ssnn top red">bind_weight</td>
 727           </tr>
 728           <tr>
 729             <td class="nnns top capitalize italic red">
 730               <br />
 731             </td>
 732             <td class="snns top italic red">terms</td>
 733             <td class="snns top red">term_vector ( Ⓐ?.? )</td>
 734             <td class="ssnn top red">
 735               <br />
 736             </td>
 737           </tr>
 738           <tr>
 739             <td class="nnns top capitalize italic red">
 740               <br />
 741             </td>
 742             <td class="nnns top italic red">
 743               <br />
 744             </td>
 745             <td class="snns top red">term_simple ( 𝐒⦃?⦄ )</td>
 746             <td class="ssnn top red">
 747               <br />
 748             </td>
 749           </tr>
 750           <tr>
 751             <td class="nnns top capitalize italic red">
 752               <br />
 753             </td>
 754             <td class="nnns top italic red">
 755               <br />
 756             </td>
 757             <td class="snns top red">term_weight ( ♯{?} )</td>
 758             <td class="ssnn top red">
 759               <br />
 760             </td>
 761           </tr>
 762           <tr>
 763             <td class="nnns top capitalize italic red">
 764               <br />
 765             </td>
 766             <td class="nnns top italic red">
 767               <br />
 768             </td>
 769             <td class="snns top red">term</td>
 770             <td class="ssnn top red">
 771               <br />
 772             </td>
 773           </tr>
 774           <tr>
 775             <td class="nnns top capitalize italic red">
 776               <br />
 777             </td>
 778             <td class="snns top italic red">items</td>
 779             <td class="snns top red">item_sd</td>
 780             <td class="ssnn top red">
 781               <br />
 782             </td>
 783           </tr>
 784           <tr>
 785             <td class="nnns top capitalize italic red">
 786               <br />
 787             </td>
 788             <td class="nnns top italic red">
 789               <br />
 790             </td>
 791             <td class="snns top red">item_sh</td>
 792             <td class="ssnn top red">
 793               <br />
 794             </td>
 795           </tr>
 796           <tr>
 797             <td class="nnns top capitalize italic red">
 798               <br />
 799             </td>
 800             <td class="nnns top italic red">
 801               <br />
 802             </td>
 803             <td class="snns top red">item</td>
 804             <td class="ssnn top red">
 805               <br />
 806             </td>
 807           </tr>
 808           <tr>
 809             <td class="nnss top capitalize italic red">
 810               <br />
 811             </td>
 812             <td class="snss top italic red">atomic arities</td>
 813             <td class="snss top red">aarity</td>
 814             <td class="sssn top red">
 815               <br />
 816             </td>
 817           </tr>
 818         </tbody>
 819       </table>
 820     </div>
 821     <div class="spacer">
 822       <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 823     </div>
 824     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 825       <br />
 826     </div>
 827     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 828       <a href="http://validator.w3.org/check?uri=referer">
 829         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
 830       </a>
 831       <a href="http://jigsaw.w3.org/css-validator/check/referer">
 832         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
 833       </a>
 834       <a href="http://www.w3.org/XML/">
 835         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
 836       </a>
 837       <a href="http://www.w3.org/Graphics/PNG/">
 838         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 839       </a>
 840       <a href="http://www.anybrowser.org/campaign/">
 841         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
 842       </a>
 843     </div>
 844     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 845       <br />
 846     </div>
 847     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Tue, 17 Oct 2017 20:34:24 +0200</div>
 848   </body>
 849 </html>