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">221</td>
 148             <td class="snns italic cyan">characters</td>
 149             <td class="snnn right italic cyan">212361</td>
 150             <td class="snns italic cyan">nodes</td>
 151             <td class="ssnn right italic cyan">1046022</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">49</td>
 157             <td class="snns italic green">lemmas</td>
 158             <td class="snnn right italic green">691</td>
 159             <td class="snns italic green">total</td>
 160             <td class="ssnn right italic green">740</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">29</td>
 166             <td class="snss italic yellow">defined</td>
 167             <td class="snsn right italic yellow">61</td>
 168             <td class="snss italic yellow">total</td>
 169             <td class="sssn right italic yellow">90</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 February 19.</span>
 186          Generic candidates of reducibility.
 187    </li>
 188     </ul>
 189     <ul xmlns:ld="http://lambdadelta.info/">
 190       <li>
 191         <span class="emph alpha">2017 January 17.</span>
 192          Confluence for parallel r-transition on referred entries of local environments.
 193    </li>
 194     </ul>
 195     <ul xmlns:ld="http://lambdadelta.info/">
 196       <li>
 197         <span class="emph alpha">2016 September 15.</span>
 198          Confluence for context-sensitive parallel r-transition on terms.
 199    </li>
 200     </ul>
 201     <ul xmlns:ld="http://lambdadelta.info/">
 202       <li>
 203         <span class="emph alpha">2016 April 16.</span>
 204          Grammatical component reconstructed:
 205          grammar, relocation, s_transition, s_computation, static
 206          (anniversary milestone).
 207    </li>
 208     </ul>
 209     <ul xmlns:ld="http://lambdadelta.info/">
 210       <li>
 211         <span class="emph alpha">2016 March 25.</span>
 212          Relocation with reference transforming maps (rtmap).
 213    </li>
 214     </ul>
 215     <ul xmlns:ld="http://lambdadelta.info/">
 216       <li>
 217         <span class="emph alpha">2015 October 9.</span>
 218          λδ version 2A2 is started.
 219    </li>
 220     </ul>
 221     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
 222     <ul xmlns:ld="http://lambdadelta.info/">
 223       <li>
 224         <span class="emph delta">2015 August 27.</span>
 225          λδ version 2A1 appears too complex and is dismissed.
 226    </li>
 227     </ul>
 228     <ul xmlns:ld="http://lambdadelta.info/">
 229       <li>
 230         <span class="emph gamma">2014 October 28.</span>
 231          λδ version 2A1 is released.
 232    </li>
 233     </ul>
 234     <ul xmlns:ld="http://lambdadelta.info/">
 235       <li>
 236         <span class="emph beta">2014 September 9.</span>
 237          Iterated static type assignment defined (more elegantly)
 238          as a primitive notion.
 239    </li>
 240     </ul>
 241     <ul xmlns:ld="http://lambdadelta.info/">
 242       <li>
 243         <span class="emph beta">2014 June 18.</span>
 244          Preservation of stratified native validity
 245          for context-sensitive computation on terms.
 246    </li>
 247     </ul>
 248     <ul xmlns:ld="http://lambdadelta.info/">
 249       <li>
 250         <span class="emph alpha">2014 June 9.</span>
 251          Strong qrst-normalization
 252          for simply typed terms.
 253    </li>
 254     </ul>
 255     <ul xmlns:ld="http://lambdadelta.info/">
 256       <li>
 257         <span class="emph alpha">2014 April 16.</span>
 258          Lazy equivalence on local environments
 259          added as q-step to rst-computation on closures
 260          (anniversary milestone).
 261    </li>
 262     </ul>
 263     <ul xmlns:ld="http://lambdadelta.info/">
 264       <li>
 265         <span class="emph alpha">2014 January 20.</span>
 266          Parametrized slicing of local environments
 267          comprises both versions of this operation
 268          (one from basic_1, the other used in basic_2 till now).
 269    </li>
 270     </ul>
 271     <ul xmlns:ld="http://lambdadelta.info/">
 272       <li>
 273         <span class="emph alpha">2013 August 7.</span>
 274          Passive support for global environments.
 275    </li>
 276     </ul>
 277     <ul xmlns:ld="http://lambdadelta.info/">
 278       <li>
 279         <span class="emph alpha">2013 July 27.</span>
 280          Reaxiomatized β-reductum as in rt-reduction.
 281    </li>
 282     </ul>
 283     <ul xmlns:ld="http://lambdadelta.info/">
 284       <li>
 285         <span class="emph alpha">2013 July 20.</span>
 286          Context-sensitive strong rt-normalization
 287          for simply typed terms.
 288    </li>
 289     </ul>
 290     <ul xmlns:ld="http://lambdadelta.info/">
 291       <li>
 292         <span class="emph alpha">2013 April 16.</span>
 293          Reaxiomatized substitution and reduction
 294          commute with respect to subclosure
 295          (anniversary milestone).
 296    </li>
 297     </ul>
 298     <ul xmlns:ld="http://lambdadelta.info/">
 299       <li>
 300         <span class="emph alpha">2013 March 16.</span>
 301          Mutual recursive preservation of stratified native validity
 302          for rst-computation on closures.
 303    </li>
 304     </ul>
 305     <ul xmlns:ld="http://lambdadelta.info/">
 306       <li>
 307         <span class="emph alpha">2012 October 16.</span>
 308          Confluence for context-free parallel reduction on closures.
 309    </li>
 310     </ul>
 311     <ul xmlns:ld="http://lambdadelta.info/">
 312       <li>
 313         <span class="emph alpha">2012 July 26.</span>
 314          Term binders polarized to control ζ-reduction (not released).
 315    </li>
 316     </ul>
 317     <ul xmlns:ld="http://lambdadelta.info/">
 318       <li>
 319         <span class="emph alpha">2012 April 16.</span>
 320          Context-sensitive subject equivalence
 321          for atomic arity assignment
 322          (anniversary milestone).
 323    </li>
 324     </ul>
 325     <ul xmlns:ld="http://lambdadelta.info/">
 326       <li>
 327         <span class="emph alpha">2012 March 15.</span>
 328          Context-sensitive strong normalization
 329          for simply typed terms.
 330    </li>
 331     </ul>
 332     <ul xmlns:ld="http://lambdadelta.info/">
 333       <li>
 334         <span class="emph alpha">2012 January 27.</span>
 335          Generic candidates of reducibility.
 336    </li>
 337     </ul>
 338     <ul xmlns:ld="http://lambdadelta.info/">
 339       <li>
 340         <span class="emph alpha">2011 September 21.</span>
 341          Confluence for context-sensitive parallel reduction on terms.
 342    </li>
 343     </ul>
 344     <ul xmlns:ld="http://lambdadelta.info/">
 345       <li>
 346         <span class="emph alpha">2011 September 6.</span>
 347          Confluence for context-free parallel reduction on terms.
 348    </li>
 349     </ul>
 350     <ul xmlns:ld="http://lambdadelta.info/">
 351       <li>
 352         <span class="emph alpha">2011 April 17.</span>
 353          λδ version 2 is started.
 354    </li>
 355     </ul>
 356     <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" />
 357     </div>
 358     <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
 359    </div>
 360     <div xmlns:ld="http://lambdadelta.info/" class="text">
 361       <table cellpadding="4" cellspacing="0">
 362         <tbody>
 363           <tr>
 364             <td class="snns top capitalize italic gray">component</td>
 365             <td class="snns top italic gray">plane</td>
 366             <td class="snns top gray">files</td>
 367             <td class="ssnn top gray">
 368               <br />
 369             </td>
 370           </tr>
 371           <tr>
 372             <td class="snns top capitalize italic cyan">rt-computation</td>
 373             <td class="snns top italic cyan">uncounted context-sensitive rt-transition</td>
 374             <td class="snns top cyan">cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )</td>
 375             <td class="ssnn top cyan">
 376               <br />
 377             </td>
 378           </tr>
 379           <tr>
 380             <td class="nnns top capitalize italic cyan">
 381               <br />
 382             </td>
 383             <td class="snns top italic cyan">generic reducibility</td>
 384             <td class="snns top cyan">lsubc ( ? ⊢ ? ⫃[?] ? )</td>
 385             <td class="ssnn top cyan">lsubc_drop lsubc_drops lsubc_lsubr lsubc_lsuba</td>
 386           </tr>
 387           <tr>
 388             <td class="nnns top capitalize italic cyan">
 389               <br />
 390             </td>
 391             <td class="nnns top italic cyan">
 392               <br />
 393             </td>
 394             <td class="snns top cyan">gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
 395             <td class="ssnn top cyan">gcp_aaa</td>
 396           </tr>
 397           <tr>
 398             <td class="nnns top capitalize italic cyan">
 399               <br />
 400             </td>
 401             <td class="nnns top italic cyan">
 402               <br />
 403             </td>
 404             <td class="snns top cyan">gcp</td>
 405             <td class="ssnn top cyan">
 406               <br />
 407             </td>
 408           </tr>
 409           <tr>
 410             <td class="snns top capitalize italic water">rt-transition</td>
 411             <td class="snns top italic water">parallel qrst-rtransition</td>
 412             <td class="snns top water">fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )</td>
 413             <td class="ssnn top water">
 414               <br />
 415             </td>
 416           </tr>
 417           <tr>
 418             <td class="nnns top capitalize italic water">
 419               <br />
 420             </td>
 421             <td class="snns top italic water">t-bound context-sensitive rt-transition</td>
 422             <td class="snns top water">lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
 423             <td class="ssnn top water">lfpr_length lfpr_drops lfpr_fqup lfpr_frees lfpr_aaa lfpr_lfpx lfpr_lfpr</td>
 424           </tr>
 425           <tr>
 426             <td class="nnns top capitalize italic water">
 427               <br />
 428             </td>
 429             <td class="nnns top italic water">
 430               <br />
 431             </td>
 432             <td class="snns top water">cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 433             <td class="ssnn top water">cpr_drops</td>
 434           </tr>
 435           <tr>
 436             <td class="nnns top capitalize italic water">
 437               <br />
 438             </td>
 439             <td class="nnns top italic water">
 440               <br />
 441             </td>
 442             <td class="snns top water">cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
 443             <td class="ssnn top water">cpm_simple cpm_drops cpm_lsubr cpm_lfxs cpm_cpx</td>
 444           </tr>
 445           <tr>
 446             <td class="nnns top capitalize italic water">
 447               <br />
 448             </td>
 449             <td class="snns top italic water">uncounted context-sensitive rt-transition</td>
 450             <td class="snns top water">cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )</td>
 451             <td class="ssnn top water">cnx_simple cnx_drops</td>
 452           </tr>
 453           <tr>
 454             <td class="nnns top capitalize italic water">
 455               <br />
 456             </td>
 457             <td class="nnns top italic water">
 458               <br />
 459             </td>
 460             <td class="snns top water">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
 461             <td class="ssnn top water">lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_aaa</td>
 462           </tr>
 463           <tr>
 464             <td class="nnns top capitalize italic water">
 465               <br />
 466             </td>
 467             <td class="nnns top italic water">
 468               <br />
 469             </td>
 470             <td class="snns top water">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
 471             <td class="ssnn top water">cpx_simple cpx_drops cpx_fqus cpx_lsubr cpx_lfxs cpx_lfdeq</td>
 472           </tr>
 473           <tr>
 474             <td class="nnns top capitalize italic water">
 475               <br />
 476             </td>
 477             <td class="snns top italic water">counted context-sensitive rt-transition</td>
 478             <td class="snns top water">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
 479             <td class="ssnn top water">cpg_simple cpg_drops cpg_lsubr</td>
 480           </tr>
 481           <tr>
 482             <td class="snns top capitalize italic green">static typing</td>
 483             <td class="snns top italic green">atomic arity assignment</td>
 484             <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
 485             <td class="ssnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
 486           </tr>
 487           <tr>
 488             <td class="nnns top capitalize italic green">
 489               <br />
 490             </td>
 491             <td class="nnns top italic green">
 492               <br />
 493             </td>
 494             <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 495             <td class="ssnn top green">aaa_drops aaa_fqus aaa_lfdeq aaa_aaa</td>
 496           </tr>
 497           <tr>
 498             <td class="nnns top capitalize italic green">
 499               <br />
 500             </td>
 501             <td class="snns top italic green">degree-based equivalence on referred entries</td>
 502             <td class="snns top green">ffdeq ( ⦃?,?,?⦄ ≡[?,?] ⦃?,?,?⦄ )</td>
 503             <td class="ssnn top green">ffdeq_fqup ffdeq_ffdeq</td>
 504           </tr>
 505           <tr>
 506             <td class="nnns top capitalize italic green">
 507               <br />
 508             </td>
 509             <td class="nnns top italic green">
 510               <br />
 511             </td>
 512             <td class="snns top green">lfdeq ( ? ≡[?,?,?] ? )</td>
 513             <td class="ssnn top green">lfdeq_length lfdeq_fqup lfdeq_lfdeq</td>
 514           </tr>
 515           <tr>
 516             <td class="nnns top capitalize italic green">
 517               <br />
 518             </td>
 519             <td class="snns top italic green">generic extension on referred entries</td>
 520             <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
 521             <td class="ssnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
 522           </tr>
 523           <tr>
 524             <td class="nnns top capitalize italic green">
 525               <br />
 526             </td>
 527             <td class="snns top italic green">context-sensitive free variables</td>
 528             <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
 529             <td class="ssnn top green">lsubf_frees</td>
 530           </tr>
 531           <tr>
 532             <td class="nnns top capitalize italic green">
 533               <br />
 534             </td>
 535             <td class="nnns top italic green">
 536               <br />
 537             </td>
 538             <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 539             <td class="ssnn top green">frees_weight frees_drops frees_fqup frees_frees</td>
 540           </tr>
 541           <tr>
 542             <td class="nnns top capitalize italic green">
 543               <br />
 544             </td>
 545             <td class="snns top italic green">restricted ref. for local env.</td>
 546             <td class="snns top green">lsubr ( ? ⫃ ? )</td>
 547             <td class="ssnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
 548           </tr>
 549           <tr>
 550             <td class="snns top capitalize italic grass">s-computation</td>
 551             <td class="snns top italic grass">iterated structural successor for closures</td>
 552             <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
 553             <td class="ssnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
 554           </tr>
 555           <tr>
 556             <td class="nnns top capitalize italic grass">
 557               <br />
 558             </td>
 559             <td class="nnns top italic grass">
 560               <br />
 561             </td>
 562             <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
 563             <td class="ssnn top grass">fqup_weight fqup_drops fqup_fqup</td>
 564           </tr>
 565           <tr>
 566             <td class="snns top capitalize italic yellow">s-transition</td>
 567             <td class="snns top italic yellow">structural successor for closures</td>
 568             <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
 569             <td class="ssnn top yellow">fquq_length fquq_weight</td>
 570           </tr>
 571           <tr>
 572             <td class="nnns top capitalize italic yellow">
 573               <br />
 574             </td>
 575             <td class="nnns top italic yellow">
 576               <br />
 577             </td>
 578             <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
 579             <td class="ssnn top yellow">fqu_length fqu_weight</td>
 580           </tr>
 581           <tr>
 582             <td class="snns top capitalize italic orange">relocation</td>
 583             <td class="snns top italic orange">generic slicing for local environments</td>
 584             <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 585             <td class="ssnn top orange">
 586               <br />
 587             </td>
 588           </tr>
 589           <tr>
 590             <td class="nnns top capitalize italic orange">
 591               <br />
 592             </td>
 593             <td class="nnns top italic orange">
 594               <br />
 595             </td>
 596             <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 597             <td class="ssnn top orange">drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops</td>
 598           </tr>
 599           <tr>
 600             <td class="nnns top capitalize italic orange">
 601               <br />
 602             </td>
 603             <td class="snns top italic orange">generic relocation for terms</td>
 604             <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 605             <td class="ssnn top orange">lifts_lifts_vector</td>
 606           </tr>
 607           <tr>
 608             <td class="nnns top capitalize italic orange">
 609               <br />
 610             </td>
 611             <td class="nnns top italic orange">
 612               <br />
 613             </td>
 614             <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
 615             <td class="ssnn top orange">lifts_simple lifts_weight lifts_tdeq lifts_lifts</td>
 616           </tr>
 617           <tr>
 618             <td class="nnns top capitalize italic orange">
 619               <br />
 620             </td>
 621             <td class="snns top italic orange">ranged equivalence for local environments</td>
 622             <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
 623             <td class="ssnn top orange">lreq_length lreq_lreq</td>
 624           </tr>
 625           <tr>
 626             <td class="nnns top capitalize italic orange">
 627               <br />
 628             </td>
 629             <td class="snns top italic orange">generic entrywise extension</td>
 630             <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
 631             <td class="ssnn top orange">lexs_length lexs_lexs</td>
 632           </tr>
 633           <tr>
 634             <td class="snns top capitalize italic red">syntax</td>
 635             <td class="snns top italic red">append for local environments</td>
 636             <td class="snns top red">append ( ? @@ ? )</td>
 637             <td class="ssnn top red">append_length</td>
 638           </tr>
 639           <tr>
 640             <td class="nnns top capitalize italic red">
 641               <br />
 642             </td>
 643             <td class="snns top italic red">degree-based equivalence for terms</td>
 644             <td class="snns top red">deq ( ? ≡[?,?] ? ) </td>
 645             <td class="ssnn top red">deq_deq</td>
 646           </tr>
 647           <tr>
 648             <td class="nnns top capitalize italic red">
 649               <br />
 650             </td>
 651             <td class="snns top italic red">same top term structure</td>
 652             <td class="snns top red">tsts ( ? ≂ ? )</td>
 653             <td class="ssnn top red">tsts_tsts tsts_vector</td>
 654           </tr>
 655           <tr>
 656             <td class="nnns top capitalize italic red">
 657               <br />
 658             </td>
 659             <td class="snns top italic red">closures</td>
 660             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 661             <td class="ssnn top red">
 662               <br />
 663             </td>
 664           </tr>
 665           <tr>
 666             <td class="nnns top capitalize italic red">
 667               <br />
 668             </td>
 669             <td class="nnns top italic red">
 670               <br />
 671             </td>
 672             <td class="snns top red">cl_restricted_weight ( ♯{?,?} )</td>
 673             <td class="ssnn top red">
 674               <br />
 675             </td>
 676           </tr>
 677           <tr>
 678             <td class="nnns top capitalize italic red">
 679               <br />
 680             </td>
 681             <td class="snns top italic red">global environments</td>
 682             <td class="snns top red">genv</td>
 683             <td class="ssnn top red">
 684               <br />
 685             </td>
 686           </tr>
 687           <tr>
 688             <td class="nnns top capitalize italic red">
 689               <br />
 690             </td>
 691             <td class="snns top italic red">local environments</td>
 692             <td class="snns top red">lenv_length ( |?| )</td>
 693             <td class="ssnn top red">
 694               <br />
 695             </td>
 696           </tr>
 697           <tr>
 698             <td class="nnns top capitalize italic red">
 699               <br />
 700             </td>
 701             <td class="nnns top italic red">
 702               <br />
 703             </td>
 704             <td class="snns top red">lenv_weight ( ♯{?} )</td>
 705             <td class="ssnn top red">
 706               <br />
 707             </td>
 708           </tr>
 709           <tr>
 710             <td class="nnns top capitalize italic red">
 711               <br />
 712             </td>
 713             <td class="nnns top italic red">
 714               <br />
 715             </td>
 716             <td class="snns top red">lenv</td>
 717             <td class="ssnn top red">
 718               <br />
 719             </td>
 720           </tr>
 721           <tr>
 722             <td class="nnns top capitalize italic red">
 723               <br />
 724             </td>
 725             <td class="snns top italic red">terms</td>
 726             <td class="snns top red">term_vector ( Ⓐ?.? )</td>
 727             <td class="ssnn top red">
 728               <br />
 729             </td>
 730           </tr>
 731           <tr>
 732             <td class="nnns top capitalize italic red">
 733               <br />
 734             </td>
 735             <td class="nnns top italic red">
 736               <br />
 737             </td>
 738             <td class="snns top red">term_simple ( 𝐒⦃?⦄ )</td>
 739             <td class="ssnn top red">
 740               <br />
 741             </td>
 742           </tr>
 743           <tr>
 744             <td class="nnns top capitalize italic red">
 745               <br />
 746             </td>
 747             <td class="nnns top italic red">
 748               <br />
 749             </td>
 750             <td class="snns top red">term_weight ( ♯{?} )</td>
 751             <td class="ssnn top red">
 752               <br />
 753             </td>
 754           </tr>
 755           <tr>
 756             <td class="nnns top capitalize italic red">
 757               <br />
 758             </td>
 759             <td class="nnns top italic red">
 760               <br />
 761             </td>
 762             <td class="snns top red">term</td>
 763             <td class="ssnn top red">
 764               <br />
 765             </td>
 766           </tr>
 767           <tr>
 768             <td class="nnns top capitalize italic red">
 769               <br />
 770             </td>
 771             <td class="snns top italic red">items</td>
 772             <td class="snns top red">item_sd</td>
 773             <td class="ssnn top red">
 774               <br />
 775             </td>
 776           </tr>
 777           <tr>
 778             <td class="nnns top capitalize italic red">
 779               <br />
 780             </td>
 781             <td class="nnns top italic red">
 782               <br />
 783             </td>
 784             <td class="snns top red">item_sh</td>
 785             <td class="ssnn top red">
 786               <br />
 787             </td>
 788           </tr>
 789           <tr>
 790             <td class="nnns top capitalize italic red">
 791               <br />
 792             </td>
 793             <td class="nnns top italic red">
 794               <br />
 795             </td>
 796             <td class="snns top red">item</td>
 797             <td class="ssnn top red">
 798               <br />
 799             </td>
 800           </tr>
 801           <tr>
 802             <td class="nnss top capitalize italic red">
 803               <br />
 804             </td>
 805             <td class="snss top italic red">atomic arities</td>
 806             <td class="snss top red">aarity</td>
 807             <td class="sssn top red">
 808               <br />
 809             </td>
 810           </tr>
 811         </tbody>
 812       </table>
 813     </div>
 814     <div class="spacer">
 815       <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 816     </div>
 817     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 818       <br />
 819     </div>
 820     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 821       <a href="http://validator.w3.org/check?uri=referer">
 822         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
 823       </a>
 824       <a href="http://jigsaw.w3.org/css-validator/check/referer">
 825         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
 826       </a>
 827       <a href="http://www.w3.org/XML/">
 828         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
 829       </a>
 830       <a href="http://www.w3.org/Graphics/PNG/">
 831         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 832       </a>
 833       <a href="http://www.anybrowser.org/campaign/">
 834         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
 835       </a>
 836     </div>
 837     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 838       <br />
 839     </div>
 840     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sun, 19 Feb 2017 16:52:48 +0100</div>
 841   </body>
 842 </html>