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 January 17.</span>
 186          Confluence for parallel r-transition on referred entries of local environments.
 187    </li>
 188     </ul>
 189     <ul xmlns:ld="http://lambdadelta.info/">
 190       <li>
 191         <span class="emph alpha">2016 September 15.</span>
 192          Confluence for context-sensitive parallel r-transition on terms.
 193    </li>
 194     </ul>
 195     <ul xmlns:ld="http://lambdadelta.info/">
 196       <li>
 197         <span class="emph alpha">2016 April 16.</span>
 198          Grammatical component reconstructed:
 199          grammar, relocation, s_transition, s_computation, static
 200          (anniversary milestone).
 201    </li>
 202     </ul>
 203     <ul xmlns:ld="http://lambdadelta.info/">
 204       <li>
 205         <span class="emph alpha">2016 March 25.</span>
 206          Relocation with reference transforming maps (rtmap).
 207    </li>
 208     </ul>
 209     <ul xmlns:ld="http://lambdadelta.info/">
 210       <li>
 211         <span class="emph alpha">2015 October 9.</span>
 212          λδ version 2A2 is started.
 213    </li>
 214     </ul>
 215     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
 216     <ul xmlns:ld="http://lambdadelta.info/">
 217       <li>
 218         <span class="emph delta">2015 August 27.</span>
 219          λδ version 2A1 appears too complex and is dismissed.
 220    </li>
 221     </ul>
 222     <ul xmlns:ld="http://lambdadelta.info/">
 223       <li>
 224         <span class="emph gamma">2014 October 28.</span>
 225          λδ version 2A1 is released.
 226    </li>
 227     </ul>
 228     <ul xmlns:ld="http://lambdadelta.info/">
 229       <li>
 230         <span class="emph beta">2014 September 9.</span>
 231          Iterated static type assignment defined (more elegantly)
 232          as a primitive notion.
 233    </li>
 234     </ul>
 235     <ul xmlns:ld="http://lambdadelta.info/">
 236       <li>
 237         <span class="emph beta">2014 June 18.</span>
 238          Preservation of stratified native validity
 239          for context-sensitive computation on terms.
 240    </li>
 241     </ul>
 242     <ul xmlns:ld="http://lambdadelta.info/">
 243       <li>
 244         <span class="emph alpha">2014 June 9.</span>
 245          Strong qrst-normalization
 246          for simply typed terms.
 247    </li>
 248     </ul>
 249     <ul xmlns:ld="http://lambdadelta.info/">
 250       <li>
 251         <span class="emph alpha">2014 April 16.</span>
 252          Lazy equivalence on local environments
 253          added as q-step to rst-computation on closures
 254          (anniversary milestone).
 255    </li>
 256     </ul>
 257     <ul xmlns:ld="http://lambdadelta.info/">
 258       <li>
 259         <span class="emph alpha">2014 January 20.</span>
 260          Parametrized slicing of local environments
 261          comprises both versions of this operation
 262          (one from basic_1, the other used in basic_2 till now).
 263    </li>
 264     </ul>
 265     <ul xmlns:ld="http://lambdadelta.info/">
 266       <li>
 267         <span class="emph alpha">2013 August 7.</span>
 268          Passive support for global environments.
 269    </li>
 270     </ul>
 271     <ul xmlns:ld="http://lambdadelta.info/">
 272       <li>
 273         <span class="emph alpha">2013 July 27.</span>
 274          Reaxiomatized β-reductum as in rt-reduction.
 275    </li>
 276     </ul>
 277     <ul xmlns:ld="http://lambdadelta.info/">
 278       <li>
 279         <span class="emph alpha">2013 July 20.</span>
 280          Context-sensitive strong rt-normalization
 281          for simply typed terms.
 282    </li>
 283     </ul>
 284     <ul xmlns:ld="http://lambdadelta.info/">
 285       <li>
 286         <span class="emph alpha">2013 April 16.</span>
 287          Reaxiomatized substitution and reduction
 288          commute with respect to subclosure
 289          (anniversary milestone).
 290    </li>
 291     </ul>
 292     <ul xmlns:ld="http://lambdadelta.info/">
 293       <li>
 294         <span class="emph alpha">2013 March 16.</span>
 295          Mutual recursive preservation of stratified native validity
 296          for rst-computation on closures.
 297    </li>
 298     </ul>
 299     <ul xmlns:ld="http://lambdadelta.info/">
 300       <li>
 301         <span class="emph alpha">2012 October 16.</span>
 302          Confluence for context-free parallel reduction on closures.
 303    </li>
 304     </ul>
 305     <ul xmlns:ld="http://lambdadelta.info/">
 306       <li>
 307         <span class="emph alpha">2012 July 26.</span>
 308          Term binders polarized to control ζ-reduction (not released).
 309    </li>
 310     </ul>
 311     <ul xmlns:ld="http://lambdadelta.info/">
 312       <li>
 313         <span class="emph alpha">2012 April 16.</span>
 314          Context-sensitive subject equivalence
 315          for atomic arity assignment
 316          (anniversary milestone).
 317    </li>
 318     </ul>
 319     <ul xmlns:ld="http://lambdadelta.info/">
 320       <li>
 321         <span class="emph alpha">2012 March 15.</span>
 322          Context-sensitive strong normalization
 323          for simply typed terms.
 324    </li>
 325     </ul>
 326     <ul xmlns:ld="http://lambdadelta.info/">
 327       <li>
 328         <span class="emph alpha">2012 January 27.</span>
 329          Support for abstract candidates of reducibility.
 330    </li>
 331     </ul>
 332     <ul xmlns:ld="http://lambdadelta.info/">
 333       <li>
 334         <span class="emph alpha">2011 September 21.</span>
 335          Confluence for context-sensitive parallel reduction on terms.
 336    </li>
 337     </ul>
 338     <ul xmlns:ld="http://lambdadelta.info/">
 339       <li>
 340         <span class="emph alpha">2011 September 6.</span>
 341          Confluence for context-free parallel reduction on terms.
 342    </li>
 343     </ul>
 344     <ul xmlns:ld="http://lambdadelta.info/">
 345       <li>
 346         <span class="emph alpha">2011 April 17.</span>
 347          λδ version 2 is started.
 348    </li>
 349     </ul>
 350     <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" />
 351     </div>
 352     <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
 353    </div>
 354     <div xmlns:ld="http://lambdadelta.info/" class="text">
 355       <table cellpadding="4" cellspacing="0">
 356         <tbody>
 357           <tr>
 358             <td class="snns top capitalize italic gray">component</td>
 359             <td class="snns top italic gray">plane</td>
 360             <td class="snns top gray">files</td>
 361             <td class="snnn top gray">
 362               <br />
 363             </td>
 364             <td class="ssnn top gray">
 365               <br />
 366             </td>
 367           </tr>
 368           <tr>
 369             <td class="snns top capitalize italic cyan">rt-computation</td>
 370             <td class="snns top italic cyan">uncounted context-sensitive rt-transition</td>
 371             <td class="snns top cyan">cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )</td>
 372             <td class="snnn top cyan">
 373               <br />
 374             </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="snnn top cyan">lsubc_drop lsubc_drops lsubc_lsubr lsubc_lsuba</td>
 386             <td class="ssnn top cyan">
 387               <br />
 388             </td>
 389           </tr>
 390           <tr>
 391             <td class="nnns top capitalize italic cyan">
 392               <br />
 393             </td>
 394             <td class="nnns top italic cyan">
 395               <br />
 396             </td>
 397             <td class="snns top cyan">gcp</td>
 398             <td class="snnn top cyan">gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
 399             <td class="ssnn top cyan">gcp_aaa</td>
 400           </tr>
 401           <tr>
 402             <td class="snns top capitalize italic water">rt-transition</td>
 403             <td class="snns top italic water">parallel qrst-rtransition</td>
 404             <td class="snns top water">fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )</td>
 405             <td class="snnn top water">
 406               <br />
 407             </td>
 408             <td class="ssnn top water">
 409               <br />
 410             </td>
 411           </tr>
 412           <tr>
 413             <td class="nnns top capitalize italic water">
 414               <br />
 415             </td>
 416             <td class="snns top italic water">t-bound context-sensitive rt-transition</td>
 417             <td class="snns top water">lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
 418             <td class="snnn top water">lfpr_length lfpr_drops lfpr_fqup lfpr_frees lfpr_aaa lfpr_lfpx lfpr_lfpr</td>
 419             <td class="ssnn top water">
 420               <br />
 421             </td>
 422           </tr>
 423           <tr>
 424             <td class="nnns top capitalize italic water">
 425               <br />
 426             </td>
 427             <td class="nnns top italic water">
 428               <br />
 429             </td>
 430             <td class="snns top water">cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 431             <td class="snnn top water">cpr_drops</td>
 432             <td class="ssnn top water">
 433               <br />
 434             </td>
 435           </tr>
 436           <tr>
 437             <td class="nnns top capitalize italic water">
 438               <br />
 439             </td>
 440             <td class="nnns top italic water">
 441               <br />
 442             </td>
 443             <td class="snns top water">cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
 444             <td class="snnn top water">cpm_simple cpm_drops cpm_lsubr cpm_lfxs cpm_cpx</td>
 445             <td class="ssnn top water">
 446               <br />
 447             </td>
 448           </tr>
 449           <tr>
 450             <td class="nnns top capitalize italic water">
 451               <br />
 452             </td>
 453             <td class="snns top italic water">uncounted context-sensitive rt-transition</td>
 454             <td class="snns top water">cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )</td>
 455             <td class="snnn top water">cnx_simple cnx_drops</td>
 456             <td class="ssnn top water">
 457               <br />
 458             </td>
 459           </tr>
 460           <tr>
 461             <td class="nnns top capitalize italic water">
 462               <br />
 463             </td>
 464             <td class="nnns top italic water">
 465               <br />
 466             </td>
 467             <td class="snns top water">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
 468             <td class="snnn top water">lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_aaa</td>
 469             <td class="ssnn top water">
 470               <br />
 471             </td>
 472           </tr>
 473           <tr>
 474             <td class="nnns top capitalize italic water">
 475               <br />
 476             </td>
 477             <td class="nnns top italic water">
 478               <br />
 479             </td>
 480             <td class="snns top water">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
 481             <td class="snnn top water">cpx_simple cpx_drops cpx_fqus cpx_lsubr cpx_lfxs cpx_lfdeq</td>
 482             <td class="ssnn top water">
 483               <br />
 484             </td>
 485           </tr>
 486           <tr>
 487             <td class="nnns top capitalize italic water">
 488               <br />
 489             </td>
 490             <td class="snns top italic water">counted context-sensitive rt-transition</td>
 491             <td class="snns top water">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
 492             <td class="snnn top water">cpg_simple cpg_drops cpg_lsubr</td>
 493             <td class="ssnn top water">
 494               <br />
 495             </td>
 496           </tr>
 497           <tr>
 498             <td class="snns top capitalize italic green">static typing</td>
 499             <td class="snns top italic green">atomic arity assignment</td>
 500             <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
 501             <td class="snnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
 502             <td class="ssnn top green">
 503               <br />
 504             </td>
 505           </tr>
 506           <tr>
 507             <td class="nnns top capitalize italic green">
 508               <br />
 509             </td>
 510             <td class="nnns top italic green">
 511               <br />
 512             </td>
 513             <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 514             <td class="snnn top green">aaa_drops aaa_fqus aaa_lfdeq aaa_aaa</td>
 515             <td class="ssnn top green">
 516               <br />
 517             </td>
 518           </tr>
 519           <tr>
 520             <td class="nnns top capitalize italic green">
 521               <br />
 522             </td>
 523             <td class="snns top italic green">degree-based equivalence on referred entries</td>
 524             <td class="snns top green">ffdeq ( ⦃?,?,?⦄ ≡[?,?] ⦃?,?,?⦄ )</td>
 525             <td class="snnn top green">ffdeq_fqup ffdeq_ffdeq</td>
 526             <td class="ssnn top green">
 527               <br />
 528             </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">lfdeq ( ? ≡[?,?,?] ? )</td>
 538             <td class="snnn top green">lfdeq_length lfdeq_fqup lfdeq_lfdeq</td>
 539             <td class="ssnn top green">
 540               <br />
 541             </td>
 542           </tr>
 543           <tr>
 544             <td class="nnns top capitalize italic green">
 545               <br />
 546             </td>
 547             <td class="snns top italic green">generic extension on referred entries</td>
 548             <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
 549             <td class="snnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
 550             <td class="ssnn top green">
 551               <br />
 552             </td>
 553           </tr>
 554           <tr>
 555             <td class="nnns top capitalize italic green">
 556               <br />
 557             </td>
 558             <td class="snns top italic green">context-sensitive free variables</td>
 559             <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
 560             <td class="snnn top green">lsubf_frees</td>
 561             <td class="ssnn top green">
 562               <br />
 563             </td>
 564           </tr>
 565           <tr>
 566             <td class="nnns top capitalize italic green">
 567               <br />
 568             </td>
 569             <td class="nnns top italic green">
 570               <br />
 571             </td>
 572             <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 573             <td class="snnn top green">frees_weight frees_drops frees_fqup frees_frees</td>
 574             <td class="ssnn top green">
 575               <br />
 576             </td>
 577           </tr>
 578           <tr>
 579             <td class="nnns top capitalize italic green">
 580               <br />
 581             </td>
 582             <td class="snns top italic green">restricted ref. for local env.</td>
 583             <td class="snns top green">lsubr ( ? ⫃ ? )</td>
 584             <td class="snnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
 585             <td class="ssnn top green">
 586               <br />
 587             </td>
 588           </tr>
 589           <tr>
 590             <td class="snns top capitalize italic grass">s-computation</td>
 591             <td class="snns top italic grass">iterated structural successor for closures</td>
 592             <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
 593             <td class="snnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
 594             <td class="ssnn top grass">
 595               <br />
 596             </td>
 597           </tr>
 598           <tr>
 599             <td class="nnns top capitalize italic grass">
 600               <br />
 601             </td>
 602             <td class="nnns top italic grass">
 603               <br />
 604             </td>
 605             <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
 606             <td class="snnn top grass">fqup_weight fqup_drops fqup_fqup</td>
 607             <td class="ssnn top grass">
 608               <br />
 609             </td>
 610           </tr>
 611           <tr>
 612             <td class="snns top capitalize italic yellow">s-transition</td>
 613             <td class="snns top italic yellow">structural successor for closures</td>
 614             <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
 615             <td class="snnn top yellow">fquq_length fquq_weight</td>
 616             <td class="ssnn top yellow">
 617               <br />
 618             </td>
 619           </tr>
 620           <tr>
 621             <td class="nnns top capitalize italic yellow">
 622               <br />
 623             </td>
 624             <td class="nnns top italic yellow">
 625               <br />
 626             </td>
 627             <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
 628             <td class="snnn top yellow">fqu_length fqu_weight</td>
 629             <td class="ssnn top yellow">
 630               <br />
 631             </td>
 632           </tr>
 633           <tr>
 634             <td class="snns top capitalize italic orange">relocation</td>
 635             <td class="snns top italic orange">generic slicing for local environments</td>
 636             <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 637             <td class="snnn top orange">
 638               <br />
 639             </td>
 640             <td class="ssnn top orange">
 641               <br />
 642             </td>
 643           </tr>
 644           <tr>
 645             <td class="nnns top capitalize italic orange">
 646               <br />
 647             </td>
 648             <td class="nnns top italic orange">
 649               <br />
 650             </td>
 651             <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 652             <td class="snnn top orange">drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops</td>
 653             <td class="ssnn top orange">
 654               <br />
 655             </td>
 656           </tr>
 657           <tr>
 658             <td class="nnns top capitalize italic orange">
 659               <br />
 660             </td>
 661             <td class="snns top italic orange">generic relocation for terms</td>
 662             <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 663             <td class="snnn top orange">lifts_lifts_vector</td>
 664             <td class="ssnn top orange">
 665               <br />
 666             </td>
 667           </tr>
 668           <tr>
 669             <td class="nnns top capitalize italic orange">
 670               <br />
 671             </td>
 672             <td class="nnns top italic orange">
 673               <br />
 674             </td>
 675             <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
 676             <td class="snnn top orange">lifts_simple lifts_weight lifts_tdeq lifts_lifts</td>
 677             <td class="ssnn top orange">
 678               <br />
 679             </td>
 680           </tr>
 681           <tr>
 682             <td class="nnns top capitalize italic orange">
 683               <br />
 684             </td>
 685             <td class="snns top italic orange">ranged equivalence for local environments</td>
 686             <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
 687             <td class="snnn top orange">lreq_length lreq_lreq</td>
 688             <td class="ssnn top orange">
 689               <br />
 690             </td>
 691           </tr>
 692           <tr>
 693             <td class="nnns top capitalize italic orange">
 694               <br />
 695             </td>
 696             <td class="snns top italic orange">generic entrywise extension</td>
 697             <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
 698             <td class="snnn top orange">lexs_length lexs_lexs</td>
 699             <td class="ssnn top orange">
 700               <br />
 701             </td>
 702           </tr>
 703           <tr>
 704             <td class="snns top capitalize italic red">syntax</td>
 705             <td class="snns top italic red">append for local environments</td>
 706             <td class="snns top red">append ( ? @@ ? )</td>
 707             <td class="snnn top red">append_length</td>
 708             <td class="ssnn top red">
 709               <br />
 710             </td>
 711           </tr>
 712           <tr>
 713             <td class="nnns top capitalize italic red">
 714               <br />
 715             </td>
 716             <td class="snns top italic red">degree-based equivalence for terms</td>
 717             <td class="snns top red">deq ( ? ≡[?,?] ? ) </td>
 718             <td class="snnn top red">deq_deq</td>
 719             <td class="ssnn top red">
 720               <br />
 721             </td>
 722           </tr>
 723           <tr>
 724             <td class="nnns top capitalize italic red">
 725               <br />
 726             </td>
 727             <td class="snns top italic red">same top term structure</td>
 728             <td class="snns top red">tsts ( ? ≂ ? )</td>
 729             <td class="snnn top red">tsts_tsts tsts_vector</td>
 730             <td class="ssnn top red">
 731               <br />
 732             </td>
 733           </tr>
 734           <tr>
 735             <td class="nnns top capitalize italic red">
 736               <br />
 737             </td>
 738             <td class="snns top italic red">closures</td>
 739             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 740             <td class="snnn top red">
 741               <br />
 742             </td>
 743             <td class="ssnn top red">
 744               <br />
 745             </td>
 746           </tr>
 747           <tr>
 748             <td class="nnns top capitalize italic red">
 749               <br />
 750             </td>
 751             <td class="nnns top italic red">
 752               <br />
 753             </td>
 754             <td class="snns top red">cl_restricted_weight ( ♯{?,?} )</td>
 755             <td class="snnn top red">
 756               <br />
 757             </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="snns top italic red">global environments</td>
 767             <td class="snns top red">genv</td>
 768             <td class="snnn top red">
 769               <br />
 770             </td>
 771             <td class="ssnn top red">
 772               <br />
 773             </td>
 774           </tr>
 775           <tr>
 776             <td class="nnns top capitalize italic red">
 777               <br />
 778             </td>
 779             <td class="snns top italic red">local environments</td>
 780             <td class="snns top red">lenv_length ( |?| )</td>
 781             <td class="snnn top red">
 782               <br />
 783             </td>
 784             <td class="ssnn top red">
 785               <br />
 786             </td>
 787           </tr>
 788           <tr>
 789             <td class="nnns top capitalize italic red">
 790               <br />
 791             </td>
 792             <td class="nnns top italic red">
 793               <br />
 794             </td>
 795             <td class="snns top red">lenv_weight ( ♯{?} )</td>
 796             <td class="snnn top red">
 797               <br />
 798             </td>
 799             <td class="ssnn top red">
 800               <br />
 801             </td>
 802           </tr>
 803           <tr>
 804             <td class="nnns top capitalize italic red">
 805               <br />
 806             </td>
 807             <td class="nnns top italic red">
 808               <br />
 809             </td>
 810             <td class="snns top red">lenv</td>
 811             <td class="snnn top red">
 812               <br />
 813             </td>
 814             <td class="ssnn top red">
 815               <br />
 816             </td>
 817           </tr>
 818           <tr>
 819             <td class="nnns top capitalize italic red">
 820               <br />
 821             </td>
 822             <td class="snns top italic red">terms</td>
 823             <td class="snns top red">term_vector ( Ⓐ?.? )</td>
 824             <td class="snnn top red">
 825               <br />
 826             </td>
 827             <td class="ssnn top red">
 828               <br />
 829             </td>
 830           </tr>
 831           <tr>
 832             <td class="nnns top capitalize italic red">
 833               <br />
 834             </td>
 835             <td class="nnns top italic red">
 836               <br />
 837             </td>
 838             <td class="snns top red">term_simple ( 𝐒⦃?⦄ )</td>
 839             <td class="snnn top red">
 840               <br />
 841             </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_weight ( ♯{?} )</td>
 854             <td class="snnn top red">
 855               <br />
 856             </td>
 857             <td class="ssnn top red">
 858               <br />
 859             </td>
 860           </tr>
 861           <tr>
 862             <td class="nnns top capitalize italic red">
 863               <br />
 864             </td>
 865             <td class="nnns top italic red">
 866               <br />
 867             </td>
 868             <td class="snns top red">term</td>
 869             <td class="snnn top red">
 870               <br />
 871             </td>
 872             <td class="ssnn top red">
 873               <br />
 874             </td>
 875           </tr>
 876           <tr>
 877             <td class="nnns top capitalize italic red">
 878               <br />
 879             </td>
 880             <td class="snns top italic red">items</td>
 881             <td class="snns top red">item_sd</td>
 882             <td class="snnn top red">
 883               <br />
 884             </td>
 885             <td class="ssnn top red">
 886               <br />
 887             </td>
 888           </tr>
 889           <tr>
 890             <td class="nnns top capitalize italic red">
 891               <br />
 892             </td>
 893             <td class="nnns top italic red">
 894               <br />
 895             </td>
 896             <td class="snns top red">item_sh</td>
 897             <td class="snnn top red">
 898               <br />
 899             </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="snnn top red">
 913               <br />
 914             </td>
 915             <td class="ssnn top red">
 916               <br />
 917             </td>
 918           </tr>
 919           <tr>
 920             <td class="nnss top capitalize italic red">
 921               <br />
 922             </td>
 923             <td class="snss top italic red">atomic arities</td>
 924             <td class="snss top red">aarity</td>
 925             <td class="snsn top red">
 926               <br />
 927             </td>
 928             <td class="sssn top red">
 929               <br />
 930             </td>
 931           </tr>
 932         </tbody>
 933       </table>
 934     </div>
 935     <div class="spacer">
 936       <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 937     </div>
 938     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 939       <br />
 940     </div>
 941     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 942       <a href="http://validator.w3.org/check?uri=referer">
 943         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
 944       </a>
 945       <a href="http://jigsaw.w3.org/css-validator/check/referer">
 946         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
 947       </a>
 948       <a href="http://www.w3.org/XML/">
 949         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
 950       </a>
 951       <a href="http://www.w3.org/Graphics/PNG/">
 952         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 953       </a>
 954       <a href="http://www.anybrowser.org/campaign/">
 955         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
 956       </a>
 957     </div>
 958     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 959       <br />
 960     </div>
 961     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sun, 19 Feb 2017 16:24:37 +0100</div>
 962   </body>
 963 </html>