helm/www/lambdadelta/basic_2.html

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   8     <meta name="author" content="Ferruccio Guidi" />
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  10     <title>\lambda\delta home page</title>
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  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">229</td>
 148             <td class="snns italic cyan">characters</td>
 149             <td class="snnn right italic cyan">234579</td>
 150             <td class="snns italic cyan">nodes</td>
 151             <td class="ssnn right italic cyan">1140037</td>
 152           </tr>
 153           <tr>
 154             <td class="snns capitalize italic green">propositions</td>
 155             <td class="snns italic green">theorems</td>
 156             <td class="snnn right italic green">62</td>
 157             <td class="snns italic green">lemmas</td>
 158             <td class="snnn right italic green">814</td>
 159             <td class="snns italic green">total</td>
 160             <td class="ssnn right italic green">876</td>
 161           </tr>
 162           <tr>
 163             <td class="snss capitalize italic yellow">concepts</td>
 164             <td class="snss italic yellow">declared</td>
 165             <td class="snsn right italic yellow">31</td>
 166             <td class="snss italic yellow">defined</td>
 167             <td class="snsn right italic yellow">79</td>
 168             <td class="snss italic yellow">total</td>
 169             <td class="sssn right italic yellow">110</td>
 170           </tr>
 171         </tbody>
 172       </table>
 173     </div>
 174     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="B">Stage "B"</div>
 175     <ul xmlns:ld="http://lambdadelta.info/">
 176       <li>
 177         <span class="emph alpha">Ongoing.</span>
 178          Context-sensitive subject equivalence
 179          for native type assignment.
 180    </li>
 181     </ul>
 182     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A2">Stage "A2": "Extending the Applicability Condition"</div>
 183     <ul xmlns:ld="http://lambdadelta.info/">
 184       <li>
 185         <span class="emph alpha">2017 October 17.</span>
 186          Exclusion binder in local environments.
 187          Syntactic component updated:
 188          syntax, relocation, s_transition, s_computation, static, i_static.
 189    </li>
 190     </ul>
 191     <ul xmlns:ld="http://lambdadelta.info/">
 192       <li>
 193         <span class="emph alpha">2017 April 16.</span>
 194          Strong rt-normalization
 195          for simply typed terms
 196          (anniversary milestone).
 197    </li>
 198     </ul>
 199     <ul xmlns:ld="http://lambdadelta.info/">
 200       <li>
 201         <span class="emph alpha">2017 March 16.</span>
 202          First behavioral component reconstructed:
 203          rt_transition.
 204    </li>
 205     </ul>
 206     <ul xmlns:ld="http://lambdadelta.info/">
 207       <li>
 208         <span class="emph alpha">2017 February 19.</span>
 209          Generic candidates of reducibility.
 210    </li>
 211     </ul>
 212     <ul xmlns:ld="http://lambdadelta.info/">
 213       <li>
 214         <span class="emph alpha">2017 January 17.</span>
 215          Confluence for parallel r-transition on referred entries of local environments.
 216    </li>
 217     </ul>
 218     <ul xmlns:ld="http://lambdadelta.info/">
 219       <li>
 220         <span class="emph alpha">2016 September 15.</span>
 221          Confluence for context-sensitive parallel r-transition on terms.
 222    </li>
 223     </ul>
 224     <ul xmlns:ld="http://lambdadelta.info/">
 225       <li>
 226         <span class="emph alpha">2016 April 16.</span>
 227          Syntactic component reconstructed:
 228          syntax, relocation, s_transition, s_computation, static
 229          (anniversary milestone).
 230    </li>
 231     </ul>
 232     <ul xmlns:ld="http://lambdadelta.info/">
 233       <li>
 234         <span class="emph alpha">2016 March 25.</span>
 235          Relocation with reference transforming maps (rtmap).
 236    </li>
 237     </ul>
 238     <ul xmlns:ld="http://lambdadelta.info/">
 239       <li>
 240         <span class="emph alpha">2015 October 9.</span>
 241          λδ version 2A2 is started.
 242    </li>
 243     </ul>
 244     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
 245     <ul xmlns:ld="http://lambdadelta.info/">
 246       <li>
 247         <span class="emph delta">2015 August 27.</span>
 248          λδ version 2A1 appears too complex and is dismissed.
 249    </li>
 250     </ul>
 251     <ul xmlns:ld="http://lambdadelta.info/">
 252       <li>
 253         <span class="emph gamma">2014 October 28.</span>
 254          λδ version 2A1 is released.
 255    </li>
 256     </ul>
 257     <ul xmlns:ld="http://lambdadelta.info/">
 258       <li>
 259         <span class="emph beta">2014 September 9.</span>
 260          Iterated static type assignment defined (more elegantly)
 261          as a primitive notion.
 262    </li>
 263     </ul>
 264     <ul xmlns:ld="http://lambdadelta.info/">
 265       <li>
 266         <span class="emph beta">2014 June 18.</span>
 267          Preservation of stratified native validity
 268          for context-sensitive computation on terms.
 269    </li>
 270     </ul>
 271     <ul xmlns:ld="http://lambdadelta.info/">
 272       <li>
 273         <span class="emph alpha">2014 June 9.</span>
 274          Strong qrst-normalization
 275          for simply typed terms.
 276    </li>
 277     </ul>
 278     <ul xmlns:ld="http://lambdadelta.info/">
 279       <li>
 280         <span class="emph alpha">2014 April 16.</span>
 281          Lazy equivalence on local environments
 282          added as q-step to rst-computation on closures
 283          (anniversary milestone).
 284    </li>
 285     </ul>
 286     <ul xmlns:ld="http://lambdadelta.info/">
 287       <li>
 288         <span class="emph alpha">2014 January 20.</span>
 289          Parametrized slicing on local environments
 290          comprises both versions of this operation
 291          (one from basic_1, the other used in basic_2 till now).
 292    </li>
 293     </ul>
 294     <ul xmlns:ld="http://lambdadelta.info/">
 295       <li>
 296         <span class="emph alpha">2013 August 7.</span>
 297          Passive support for global environments.
 298    </li>
 299     </ul>
 300     <ul xmlns:ld="http://lambdadelta.info/">
 301       <li>
 302         <span class="emph alpha">2013 July 27.</span>
 303          Reaxiomatized β-reductum as in rt-reduction.
 304    </li>
 305     </ul>
 306     <ul xmlns:ld="http://lambdadelta.info/">
 307       <li>
 308         <span class="emph alpha">2013 July 20.</span>
 309          Context-sensitive strong rt-normalization
 310          for simply typed terms.
 311    </li>
 312     </ul>
 313     <ul xmlns:ld="http://lambdadelta.info/">
 314       <li>
 315         <span class="emph alpha">2013 April 16.</span>
 316          Reaxiomatized substitution and reduction
 317          commute with respect to subclosure
 318          (anniversary milestone).
 319    </li>
 320     </ul>
 321     <ul xmlns:ld="http://lambdadelta.info/">
 322       <li>
 323         <span class="emph alpha">2013 March 16.</span>
 324          Mutual recursive preservation of stratified native validity
 325          for rst-computation on closures.
 326    </li>
 327     </ul>
 328     <ul xmlns:ld="http://lambdadelta.info/">
 329       <li>
 330         <span class="emph alpha">2012 October 16.</span>
 331          Confluence for context-free parallel reduction on closures.
 332    </li>
 333     </ul>
 334     <ul xmlns:ld="http://lambdadelta.info/">
 335       <li>
 336         <span class="emph alpha">2012 July 26.</span>
 337          Term binders polarized to control ζ-reduction (not released).
 338    </li>
 339     </ul>
 340     <ul xmlns:ld="http://lambdadelta.info/">
 341       <li>
 342         <span class="emph alpha">2012 April 16.</span>
 343          Context-sensitive subject equivalence
 344          for atomic arity assignment
 345          (anniversary milestone).
 346    </li>
 347     </ul>
 348     <ul xmlns:ld="http://lambdadelta.info/">
 349       <li>
 350         <span class="emph alpha">2012 March 15.</span>
 351          Context-sensitive strong normalization
 352          for simply typed terms.
 353    </li>
 354     </ul>
 355     <ul xmlns:ld="http://lambdadelta.info/">
 356       <li>
 357         <span class="emph alpha">2012 January 27.</span>
 358          Generic candidates of reducibility.
 359    </li>
 360     </ul>
 361     <ul xmlns:ld="http://lambdadelta.info/">
 362       <li>
 363         <span class="emph alpha">2011 September 21.</span>
 364          Confluence for context-sensitive parallel reduction on terms.
 365    </li>
 366     </ul>
 367     <ul xmlns:ld="http://lambdadelta.info/">
 368       <li>
 369         <span class="emph alpha">2011 September 6.</span>
 370          Confluence for context-free parallel reduction on terms.
 371    </li>
 372     </ul>
 373     <ul xmlns:ld="http://lambdadelta.info/">
 374       <li>
 375         <span class="emph alpha">2011 April 17.</span>
 376          λδ version 2 is started.
 377    </li>
 378     </ul>
 379     <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="structure">Logical Structure of the Specification <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png" />
 380     </div>
 381     <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
 382    </div>
 383     <div xmlns:ld="http://lambdadelta.info/" class="text">
 384       <table cellpadding="4" cellspacing="0">
 385         <tbody>
 386           <tr>
 387             <td class="snns top capitalize italic gray">component</td>
 388             <td class="snns top italic gray">plane</td>
 389             <td class="snns top gray">files</td>
 390             <td class="ssnn top gray">
 391               <br />
 392             </td>
 393           </tr>
 394           <tr>
 395             <td class="snns top capitalize italic cyan">rt-transition</td>
 396             <td class="snns top italic cyan">uncounted context-sensitive rt-transition</td>
 397             <td class="snns top cyan">cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )</td>
 398             <td class="ssnn top cyan">cnx_simple cnx_drops cnx_cnx</td>
 399           </tr>
 400           <tr>
 401             <td class="nnns top capitalize italic cyan">
 402               <br />
 403             </td>
 404             <td class="nnns top italic cyan">
 405               <br />
 406             </td>
 407             <td class="snns top cyan">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
 408             <td class="ssnn top cyan">lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_lfdeq lfpx_aaa lfpx_lfpx</td>
 409           </tr>
 410           <tr>
 411             <td class="nnns top capitalize italic cyan">
 412               <br />
 413             </td>
 414             <td class="nnns top italic cyan">
 415               <br />
 416             </td>
 417             <td class="snns top cyan">cpx_ext ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
 418             <td class="ssnn top cyan">
 419               <br />
 420             </td>
 421           </tr>
 422           <tr>
 423             <td class="nnns top capitalize italic cyan">
 424               <br />
 425             </td>
 426             <td class="nnns top italic cyan">
 427               <br />
 428             </td>
 429             <td class="snns top cyan">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
 430             <td class="ssnn top cyan">cpx_simple cpx_drops cpx_fqus cpx_lsubr cpx_lfxs</td>
 431           </tr>
 432           <tr>
 433             <td class="nnns top capitalize italic cyan">
 434               <br />
 435             </td>
 436             <td class="snns top italic cyan">counted context-sensitive rt-transition</td>
 437             <td class="snns top cyan">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
 438             <td class="ssnn top cyan">cpg_simple cpg_drops cpg_lsubr</td>
 439           </tr>
 440           <tr>
 441             <td class="snns top capitalize italic water">iterated static typing</td>
 442             <td class="snns top italic water">iterated extension on referred entries</td>
 443             <td class="snns top water">tc_lfxs ( ? ⦻**[?,?] ? )</td>
 444             <td class="ssnn top water">tc_lfxs_length tc_lfxs_drops tc_lfxs_fqup tc_lfxs_tc_lfxs</td>
 445           </tr>
 446           <tr>
 447             <td class="snns top capitalize italic green">static typing</td>
 448             <td class="snns top italic green">generic reducibility</td>
 449             <td class="snns top green">lsubc ( ? ⊢ ? ⫃[?] ? )</td>
 450             <td class="ssnn top green">lsubc_drops lsubc_lsubr lsubc_lsuba</td>
 451           </tr>
 452           <tr>
 453             <td class="nnns top capitalize italic green">
 454               <br />
 455             </td>
 456             <td class="nnns top italic green">
 457               <br />
 458             </td>
 459             <td class="snns top green">gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
 460             <td class="ssnn top green">gcp_aaa</td>
 461           </tr>
 462           <tr>
 463             <td class="nnns top capitalize italic green">
 464               <br />
 465             </td>
 466             <td class="nnns top italic green">
 467               <br />
 468             </td>
 469             <td class="snns top green">gcp</td>
 470             <td class="ssnn top green">
 471               <br />
 472             </td>
 473           </tr>
 474           <tr>
 475             <td class="nnns top capitalize italic green">
 476               <br />
 477             </td>
 478             <td class="snns top italic green">atomic arity assignment</td>
 479             <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
 480             <td class="ssnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
 481           </tr>
 482           <tr>
 483             <td class="nnns top capitalize italic green">
 484               <br />
 485             </td>
 486             <td class="nnns top italic green">
 487               <br />
 488             </td>
 489             <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 490             <td class="ssnn top green">aaa_drops aaa_fqus aaa_lfdeq aaa_aaa</td>
 491           </tr>
 492           <tr>
 493             <td class="nnns top capitalize italic green">
 494               <br />
 495             </td>
 496             <td class="snns top italic green">degree-based equivalence on referred entries</td>
 497             <td class="snns top green">ffdeq ( ⦃?,?,?⦄ ≡[?,?] ⦃?,?,?⦄ )</td>
 498             <td class="ssnn top green">ffdeq_fqup ffdeq_ffdeq</td>
 499           </tr>
 500           <tr>
 501             <td class="nnns top capitalize italic green">
 502               <br />
 503             </td>
 504             <td class="nnns top italic green">
 505               <br />
 506             </td>
 507             <td class="snns top green">lfdeq ( ? ≡[?,?,?] ? )</td>
 508             <td class="ssnn top green">lfdeq_length lfdeq_drops lfdeq_fqup lfdeq_fqus lfdeq_lfdeq</td>
 509           </tr>
 510           <tr>
 511             <td class="nnns top capitalize italic green">
 512               <br />
 513             </td>
 514             <td class="snns top italic green">generic extension on referred entries</td>
 515             <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
 516             <td class="ssnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
 517           </tr>
 518           <tr>
 519             <td class="nnns top capitalize italic green">
 520               <br />
 521             </td>
 522             <td class="snns top italic green">context-sensitive free variables</td>
 523             <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
 524             <td class="ssnn top green">lsubf_lsubr lsubf_frees lsubf_lsubf</td>
 525           </tr>
 526           <tr>
 527             <td class="nnns top capitalize italic green">
 528               <br />
 529             </td>
 530             <td class="nnns top italic green">
 531               <br />
 532             </td>
 533             <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 534             <td class="ssnn top green">frees_drops frees_fqup frees_frees</td>
 535           </tr>
 536           <tr>
 537             <td class="nnns top capitalize italic green">
 538               <br />
 539             </td>
 540             <td class="snns top italic green">restricted ref. for local env.</td>
 541             <td class="snns top green">lsubr ( ? ⫃ ? )</td>
 542             <td class="ssnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
 543           </tr>
 544           <tr>
 545             <td class="snns top capitalize italic grass">s-computation</td>
 546             <td class="snns top italic grass">iterated structural successor for closures</td>
 547             <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐*[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
 548             <td class="ssnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
 549           </tr>
 550           <tr>
 551             <td class="nnns top capitalize italic grass">
 552               <br />
 553             </td>
 554             <td class="nnns top italic grass">
 555               <br />
 556             </td>
 557             <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
 558             <td class="ssnn top grass">fqup_weight fqup_drops fqup_fqup</td>
 559           </tr>
 560           <tr>
 561             <td class="snns top capitalize italic yellow">s-transition</td>
 562             <td class="snns top italic yellow">structural successor for closures</td>
 563             <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
 564             <td class="ssnn top yellow">fquq_length fquq_weight</td>
 565           </tr>
 566           <tr>
 567             <td class="nnns top capitalize italic yellow">
 568               <br />
 569             </td>
 570             <td class="nnns top italic yellow">
 571               <br />
 572             </td>
 573             <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
 574             <td class="ssnn top yellow">fqu_length fqu_weight</td>
 575           </tr>
 576           <tr>
 577             <td class="snns top capitalize italic orange">relocation</td>
 578             <td class="snns top italic orange">generic slicing for local environments</td>
 579             <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 580             <td class="ssnn top orange">
 581               <br />
 582             </td>
 583           </tr>
 584           <tr>
 585             <td class="nnns top capitalize italic orange">
 586               <br />
 587             </td>
 588             <td class="nnns top italic orange">
 589               <br />
 590             </td>
 591             <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 592             <td class="ssnn top orange">drops_lstar drops_weight drops_length drops_ext2 drops_lexs drops_lreq drops_drops</td>
 593           </tr>
 594           <tr>
 595             <td class="nnns top capitalize italic orange">
 596               <br />
 597             </td>
 598             <td class="snns top italic orange">generic relocation</td>
 599             <td class="snns top orange">lifts_bind ( ⬆*[?] ? ≡ ? )</td>
 600             <td class="ssnn top orange">lifts_weight_bind lifts_lifts_bind</td>
 601           </tr>
 602           <tr>
 603             <td class="nnns top capitalize italic orange">
 604               <br />
 605             </td>
 606             <td class="nnns top italic orange">
 607               <br />
 608             </td>
 609             <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 610             <td class="ssnn top orange">lifts_lifts_vector</td>
 611           </tr>
 612           <tr>
 613             <td class="nnns top capitalize italic orange">
 614               <br />
 615             </td>
 616             <td class="nnns top italic orange">
 617               <br />
 618             </td>
 619             <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
 620             <td class="ssnn top orange">lifts_simple lifts_weight lifts_tdeq lifts_lifts</td>
 621           </tr>
 622           <tr>
 623             <td class="nnns top capitalize italic orange">
 624               <br />
 625             </td>
 626             <td class="snns top italic orange">ranged equivalence for local environments</td>
 627             <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
 628             <td class="ssnn top orange">lreq_length lreq_lreq</td>
 629           </tr>
 630           <tr>
 631             <td class="nnns top capitalize italic orange">
 632               <br />
 633             </td>
 634             <td class="snns top italic orange">generic entrywise extension</td>
 635             <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
 636             <td class="ssnn top orange">lexs_length lexs_lexs</td>
 637           </tr>
 638           <tr>
 639             <td class="snns top capitalize italic red">syntax</td>
 640             <td class="snns top italic red">append for local environments</td>
 641             <td class="snns top red">append ( ? @@ ? )</td>
 642             <td class="ssnn top red">append_length</td>
 643           </tr>
 644           <tr>
 645             <td class="nnns top capitalize italic red">
 646               <br />
 647             </td>
 648             <td class="snns top italic red">head equivalence for terms</td>
 649             <td class="snns top red">theq ( ? ⩳[?,?] ? )</td>
 650             <td class="ssnn top red">theq_simple theq_tdeq theq_theq theq_simple_vector</td>
 651           </tr>
 652           <tr>
 653             <td class="nnns top capitalize italic red">
 654               <br />
 655             </td>
 656             <td class="snns top italic red">degree-based equivalence</td>
 657             <td class="snns top red">tdeq_ext ( ? ≡[?,?] ? )</td>
 658             <td class="ssnn top red">
 659               <br />
 660             </td>
 661           </tr>
 662           <tr>
 663             <td class="nnns top capitalize italic red">
 664               <br />
 665             </td>
 666             <td class="nnns top italic red">
 667               <br />
 668             </td>
 669             <td class="snns top red">tdeq ( ? ≡[?,?] ? )</td>
 670             <td class="ssnn top red">tdeq_tdeq</td>
 671           </tr>
 672           <tr>
 673             <td class="nnns top capitalize italic red">
 674               <br />
 675             </td>
 676             <td class="snns top italic red">closures</td>
 677             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 678             <td class="ssnn top red">
 679               <br />
 680             </td>
 681           </tr>
 682           <tr>
 683             <td class="nnns top capitalize italic red">
 684               <br />
 685             </td>
 686             <td class="nnns top italic red">
 687               <br />
 688             </td>
 689             <td class="snns top red">cl_restricted_weight ( ♯{?,?} )</td>
 690             <td class="ssnn top red">
 691               <br />
 692             </td>
 693           </tr>
 694           <tr>
 695             <td class="nnns top capitalize italic red">
 696               <br />
 697             </td>
 698             <td class="snns top italic red">global environments</td>
 699             <td class="snns top red">genv</td>
 700             <td class="ssnn top red">
 701               <br />
 702             </td>
 703           </tr>
 704           <tr>
 705             <td class="nnns top capitalize italic red">
 706               <br />
 707             </td>
 708             <td class="snns top italic red">local environments</td>
 709             <td class="snns top red">lenv_ext2</td>
 710             <td class="ssnn top red">
 711               <br />
 712             </td>
 713           </tr>
 714           <tr>
 715             <td class="nnns top capitalize italic red">
 716               <br />
 717             </td>
 718             <td class="nnns top italic red">
 719               <br />
 720             </td>
 721             <td class="snns top red">lenv_length ( |?| )</td>
 722             <td class="ssnn top red">
 723               <br />
 724             </td>
 725           </tr>
 726           <tr>
 727             <td class="nnns top capitalize italic red">
 728               <br />
 729             </td>
 730             <td class="nnns top italic red">
 731               <br />
 732             </td>
 733             <td class="snns top red">lenv_weight ( ♯{?} )</td>
 734             <td class="ssnn top red">
 735               <br />
 736             </td>
 737           </tr>
 738           <tr>
 739             <td class="nnns top capitalize italic red">
 740               <br />
 741             </td>
 742             <td class="nnns top italic red">
 743               <br />
 744             </td>
 745             <td class="snns top red">lenv</td>
 746             <td class="ssnn top red">
 747               <br />
 748             </td>
 749           </tr>
 750           <tr>
 751             <td class="nnns top capitalize italic red">
 752               <br />
 753             </td>
 754             <td class="snns top italic red">binders for local environments</td>
 755             <td class="snns top red">ext2</td>
 756             <td class="ssnn top red">ext2_ext2</td>
 757           </tr>
 758           <tr>
 759             <td class="nnns top capitalize italic red">
 760               <br />
 761             </td>
 762             <td class="nnns top italic red">
 763               <br />
 764             </td>
 765             <td class="snns top red">bind</td>
 766             <td class="ssnn top red">bind_weight</td>
 767           </tr>
 768           <tr>
 769             <td class="nnns top capitalize italic red">
 770               <br />
 771             </td>
 772             <td class="snns top italic red">terms</td>
 773             <td class="snns top red">term_vector ( Ⓐ?.? )</td>
 774             <td class="ssnn top red">
 775               <br />
 776             </td>
 777           </tr>
 778           <tr>
 779             <td class="nnns top capitalize italic red">
 780               <br />
 781             </td>
 782             <td class="nnns top italic red">
 783               <br />
 784             </td>
 785             <td class="snns top red">term_simple ( 𝐒⦃?⦄ )</td>
 786             <td class="ssnn top red">
 787               <br />
 788             </td>
 789           </tr>
 790           <tr>
 791             <td class="nnns top capitalize italic red">
 792               <br />
 793             </td>
 794             <td class="nnns top italic red">
 795               <br />
 796             </td>
 797             <td class="snns top red">term_weight ( ♯{?} )</td>
 798             <td class="ssnn top red">
 799               <br />
 800             </td>
 801           </tr>
 802           <tr>
 803             <td class="nnns top capitalize italic red">
 804               <br />
 805             </td>
 806             <td class="nnns top italic red">
 807               <br />
 808             </td>
 809             <td class="snns top red">term</td>
 810             <td class="ssnn top red">
 811               <br />
 812             </td>
 813           </tr>
 814           <tr>
 815             <td class="nnns top capitalize italic red">
 816               <br />
 817             </td>
 818             <td class="snns top italic red">items</td>
 819             <td class="snns top red">item_sd</td>
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