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">214</td>
 148             <td class="snns italic cyan">characters</td>
 149             <td class="snnn right italic cyan">202530</td>
 150             <td class="snns italic cyan">nodes</td>
 151             <td class="ssnn right italic cyan">1010247</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">48</td>
 157             <td class="snns italic green">lemmas</td>
 158             <td class="snnn right italic green">675</td>
 159             <td class="snns italic green">total</td>
 160             <td class="ssnn right italic green">723</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">26</td>
 166             <td class="snss italic yellow">defined</td>
 167             <td class="snsn right italic yellow">46</td>
 168             <td class="snss italic yellow">total</td>
 169             <td class="sssn right italic yellow">72</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="ssnn top gray">
 362               <br />
 363             </td>
 364           </tr>
 365           <tr>
 366             <td class="snns top capitalize italic cyan">rt-computation</td>
 367             <td class="snns top italic cyan">uncounted context-sensitive rt-transition</td>
 368             <td class="snns top cyan">cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )</td>
 369             <td class="ssnn top cyan">
 370               <br />
 371             </td>
 372           </tr>
 373           <tr>
 374             <td class="snns top capitalize italic water">rt-transition</td>
 375             <td class="snns top italic water">parallel qrst-rtransition</td>
 376             <td class="snns top water">fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )</td>
 377             <td class="ssnn top water">
 378               <br />
 379             </td>
 380           </tr>
 381           <tr>
 382             <td class="nnns top capitalize italic water">
 383               <br />
 384             </td>
 385             <td class="snns top italic water">t-bound context-sensitive rt-transition</td>
 386             <td class="snns top water">lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
 387             <td class="ssnn top water">lfpr_length lfpr_drops lfpr_fqup lfpr_frees lfpr_aaa lfpr_lfpx lfpr_lfpr</td>
 388           </tr>
 389           <tr>
 390             <td class="nnns top capitalize italic water">
 391               <br />
 392             </td>
 393             <td class="nnns top italic water">
 394               <br />
 395             </td>
 396             <td class="snns top water">cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 397             <td class="ssnn top water">cpr_drops</td>
 398           </tr>
 399           <tr>
 400             <td class="nnns top capitalize italic water">
 401               <br />
 402             </td>
 403             <td class="nnns top italic water">
 404               <br />
 405             </td>
 406             <td class="snns top water">cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
 407             <td class="ssnn top water">cpm_simple cpm_drops cpm_lsubr cpm_lfxs cpm_cpx</td>
 408           </tr>
 409           <tr>
 410             <td class="nnns top capitalize italic water">
 411               <br />
 412             </td>
 413             <td class="snns top italic water">uncounted context-sensitive rt-transition</td>
 414             <td class="snns top water">cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )</td>
 415             <td class="ssnn top water">cnx_simple cnx_drops</td>
 416           </tr>
 417           <tr>
 418             <td class="nnns top capitalize italic water">
 419               <br />
 420             </td>
 421             <td class="nnns top italic water">
 422               <br />
 423             </td>
 424             <td class="snns top water">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
 425             <td class="ssnn top water">lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_aaa</td>
 426           </tr>
 427           <tr>
 428             <td class="nnns top capitalize italic water">
 429               <br />
 430             </td>
 431             <td class="nnns top italic water">
 432               <br />
 433             </td>
 434             <td class="snns top water">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
 435             <td class="ssnn top water">cpx_simple cpx_drops cpx_fqus cpx_lsubr cpx_lfxs cpx_lfdeq</td>
 436           </tr>
 437           <tr>
 438             <td class="nnns top capitalize italic water">
 439               <br />
 440             </td>
 441             <td class="snns top italic water">counted context-sensitive rt-transition</td>
 442             <td class="snns top water">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
 443             <td class="ssnn top water">cpg_simple cpg_drops cpg_lsubr</td>
 444           </tr>
 445           <tr>
 446             <td class="snns top capitalize italic green">static typing</td>
 447             <td class="snns top italic green">atomic arity assignment</td>
 448             <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
 449             <td class="ssnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
 450           </tr>
 451           <tr>
 452             <td class="nnns top capitalize italic green">
 453               <br />
 454             </td>
 455             <td class="nnns top italic green">
 456               <br />
 457             </td>
 458             <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 459             <td class="ssnn top green">aaa_drops aaa_fqus aaa_lfdeq aaa_aaa</td>
 460           </tr>
 461           <tr>
 462             <td class="nnns top capitalize italic green">
 463               <br />
 464             </td>
 465             <td class="snns top italic green">degree-based equivalence on referred entries</td>
 466             <td class="snns top green">ffdeq ( ⦃?,?,?⦄ ≡[?,?] ⦃?,?,?⦄ )</td>
 467             <td class="ssnn top green">ffdeq_fqup ffdeq_ffdeq</td>
 468           </tr>
 469           <tr>
 470             <td class="nnns top capitalize italic green">
 471               <br />
 472             </td>
 473             <td class="nnns top italic green">
 474               <br />
 475             </td>
 476             <td class="snns top green">lfdeq ( ? ≡[?,?,?] ? )</td>
 477             <td class="ssnn top green">lfdeq_length lfdeq_fqup lfdeq_lfdeq</td>
 478           </tr>
 479           <tr>
 480             <td class="nnns top capitalize italic green">
 481               <br />
 482             </td>
 483             <td class="snns top italic green">generic extension on referred entries</td>
 484             <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
 485             <td class="ssnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
 486           </tr>
 487           <tr>
 488             <td class="nnns top capitalize italic green">
 489               <br />
 490             </td>
 491             <td class="snns top italic green">context-sensitive free variables</td>
 492             <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
 493             <td class="ssnn top green">lsubf_frees</td>
 494           </tr>
 495           <tr>
 496             <td class="nnns top capitalize italic green">
 497               <br />
 498             </td>
 499             <td class="nnns top italic green">
 500               <br />
 501             </td>
 502             <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 503             <td class="ssnn top green">frees_weight frees_drops frees_fqup frees_frees</td>
 504           </tr>
 505           <tr>
 506             <td class="nnns top capitalize italic green">
 507               <br />
 508             </td>
 509             <td class="snns top italic green">restricted ref. for local env.</td>
 510             <td class="snns top green">lsubr ( ? ⫃ ? )</td>
 511             <td class="ssnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
 512           </tr>
 513           <tr>
 514             <td class="snns top capitalize italic grass">s-computation</td>
 515             <td class="snns top italic grass">iterated structural successor for closures</td>
 516             <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
 517             <td class="ssnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
 518           </tr>
 519           <tr>
 520             <td class="nnns top capitalize italic grass">
 521               <br />
 522             </td>
 523             <td class="nnns top italic grass">
 524               <br />
 525             </td>
 526             <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
 527             <td class="ssnn top grass">fqup_weight fqup_drops fqup_fqup</td>
 528           </tr>
 529           <tr>
 530             <td class="snns top capitalize italic yellow">s-transition</td>
 531             <td class="snns top italic yellow">structural successor for closures</td>
 532             <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
 533             <td class="ssnn top yellow">fquq_length fquq_weight</td>
 534           </tr>
 535           <tr>
 536             <td class="nnns top capitalize italic yellow">
 537               <br />
 538             </td>
 539             <td class="nnns top italic yellow">
 540               <br />
 541             </td>
 542             <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
 543             <td class="ssnn top yellow">fqu_length fqu_weight</td>
 544           </tr>
 545           <tr>
 546             <td class="snns top capitalize italic orange">relocation</td>
 547             <td class="snns top italic orange">generic slicing for local environments</td>
 548             <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 549             <td class="ssnn top orange">
 550               <br />
 551             </td>
 552           </tr>
 553           <tr>
 554             <td class="nnns top capitalize italic orange">
 555               <br />
 556             </td>
 557             <td class="nnns top italic orange">
 558               <br />
 559             </td>
 560             <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 561             <td class="ssnn top orange">drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops</td>
 562           </tr>
 563           <tr>
 564             <td class="nnns top capitalize italic orange">
 565               <br />
 566             </td>
 567             <td class="snns top italic orange">generic relocation for terms</td>
 568             <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 569             <td class="ssnn top orange">lifts_lifts_vector</td>
 570           </tr>
 571           <tr>
 572             <td class="nnns top capitalize italic orange">
 573               <br />
 574             </td>
 575             <td class="nnns top italic orange">
 576               <br />
 577             </td>
 578             <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
 579             <td class="ssnn top orange">lifts_simple lifts_weight lifts_tdeq lifts_lifts</td>
 580           </tr>
 581           <tr>
 582             <td class="nnns top capitalize italic orange">
 583               <br />
 584             </td>
 585             <td class="snns top italic orange">ranged equivalence for local environments</td>
 586             <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
 587             <td class="ssnn top orange">lreq_length lreq_lreq</td>
 588           </tr>
 589           <tr>
 590             <td class="nnns top capitalize italic orange">
 591               <br />
 592             </td>
 593             <td class="snns top italic orange">generic entrywise extension</td>
 594             <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
 595             <td class="ssnn top orange">lexs_length lexs_lexs</td>
 596           </tr>
 597           <tr>
 598             <td class="snns top capitalize italic red">syntax</td>
 599             <td class="snns top italic red">append for local environments</td>
 600             <td class="snns top red">append ( ? @@ ? )</td>
 601             <td class="ssnn top red">append_length</td>
 602           </tr>
 603           <tr>
 604             <td class="nnns top capitalize italic red">
 605               <br />
 606             </td>
 607             <td class="snns top italic red">degree-based equivalence for terms</td>
 608             <td class="snns top red">deq ( ? ≡[?,?] ? ) </td>
 609             <td class="ssnn top red">deq_deq</td>
 610           </tr>
 611           <tr>
 612             <td class="nnns top capitalize italic red">
 613               <br />
 614             </td>
 615             <td class="snns top italic red">same top term structure</td>
 616             <td class="snns top red">tsts ( ? ≂ ? )</td>
 617             <td class="ssnn top red">tsts_tsts tsts_vector</td>
 618           </tr>
 619           <tr>
 620             <td class="nnns top capitalize italic red">
 621               <br />
 622             </td>
 623             <td class="snns top italic red">closures</td>
 624             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 625             <td class="ssnn top red">
 626               <br />
 627             </td>
 628           </tr>
 629           <tr>
 630             <td class="nnns top capitalize italic red">
 631               <br />
 632             </td>
 633             <td class="nnns top italic red">
 634               <br />
 635             </td>
 636             <td class="snns top red">cl_restricted_weight ( ♯{?,?} )</td>
 637             <td class="ssnn top red">
 638               <br />
 639             </td>
 640           </tr>
 641           <tr>
 642             <td class="nnns top capitalize italic red">
 643               <br />
 644             </td>
 645             <td class="snns top italic red">global environments</td>
 646             <td class="snns top red">genv</td>
 647             <td class="ssnn top red">
 648               <br />
 649             </td>
 650           </tr>
 651           <tr>
 652             <td class="nnns top capitalize italic red">
 653               <br />
 654             </td>
 655             <td class="snns top italic red">local environments</td>
 656             <td class="snns top red">lenv_length ( |?| )</td>
 657             <td class="ssnn top red">
 658               <br />
 659             </td>
 660           </tr>
 661           <tr>
 662             <td class="nnns top capitalize italic red">
 663               <br />
 664             </td>
 665             <td class="nnns top italic red">
 666               <br />
 667             </td>
 668             <td class="snns top red">lenv_weight ( ♯{?} )</td>
 669             <td class="ssnn top red">
 670               <br />
 671             </td>
 672           </tr>
 673           <tr>
 674             <td class="nnns top capitalize italic red">
 675               <br />
 676             </td>
 677             <td class="nnns top italic red">
 678               <br />
 679             </td>
 680             <td class="snns top red">lenv</td>
 681             <td class="ssnn top red">
 682               <br />
 683             </td>
 684           </tr>
 685           <tr>
 686             <td class="nnns top capitalize italic red">
 687               <br />
 688             </td>
 689             <td class="snns top italic red">terms</td>
 690             <td class="snns top red">term_vector ( Ⓐ?.? )</td>
 691             <td class="ssnn top red">
 692               <br />
 693             </td>
 694           </tr>
 695           <tr>
 696             <td class="nnns top capitalize italic red">
 697               <br />
 698             </td>
 699             <td class="nnns top italic red">
 700               <br />
 701             </td>
 702             <td class="snns top red">term_simple ( 𝐒⦃?⦄ )</td>
 703             <td class="ssnn top red">
 704               <br />
 705             </td>
 706           </tr>
 707           <tr>
 708             <td class="nnns top capitalize italic red">
 709               <br />
 710             </td>
 711             <td class="nnns top italic red">
 712               <br />
 713             </td>
 714             <td class="snns top red">term_weight ( ♯{?} )</td>
 715             <td class="ssnn top red">
 716               <br />
 717             </td>
 718           </tr>
 719           <tr>
 720             <td class="nnns top capitalize italic red">
 721               <br />
 722             </td>
 723             <td class="nnns top italic red">
 724               <br />
 725             </td>
 726             <td class="snns top red">term</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="snns top italic red">items</td>
 736             <td class="snns top red">item_sd</td>
 737             <td class="ssnn top red">
 738               <br />
 739             </td>
 740           </tr>
 741           <tr>
 742             <td class="nnns top capitalize italic red">
 743               <br />
 744             </td>
 745             <td class="nnns top italic red">
 746               <br />
 747             </td>
 748             <td class="snns top red">item_sh</td>
 749             <td class="ssnn top red">
 750               <br />
 751             </td>
 752           </tr>
 753           <tr>
 754             <td class="nnns top capitalize italic red">
 755               <br />
 756             </td>
 757             <td class="nnns top italic red">
 758               <br />
 759             </td>
 760             <td class="snns top red">item</td>
 761             <td class="ssnn top red">
 762               <br />
 763             </td>
 764           </tr>
 765           <tr>
 766             <td class="nnss top capitalize italic red">
 767               <br />
 768             </td>
 769             <td class="snss top italic red">atomic arities</td>
 770             <td class="snss top red">aarity</td>
 771             <td class="sssn top red">
 772               <br />
 773             </td>
 774           </tr>
 775         </tbody>
 776       </table>
 777     </div>
 778     <div class="spacer">
 779       <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 780     </div>
 781     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 782       <br />
 783     </div>
 784     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 785       <a href="http://validator.w3.org/check?uri=referer">
 786         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
 787       </a>
 788       <a href="http://jigsaw.w3.org/css-validator/check/referer">
 789         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
 790       </a>
 791       <a href="http://www.w3.org/XML/">
 792         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
 793       </a>
 794       <a href="http://www.w3.org/Graphics/PNG/">
 795         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 796       </a>
 797       <a href="http://www.anybrowser.org/campaign/">
 798         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
 799       </a>
 800     </div>
 801     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 802       <br />
 803     </div>
 804     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Thu, 16 Feb 2017 12:23:40 +0100</div>
 805   </body>
 806 </html>