helm/www/lambdadelta/basic_2.html

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  10     <title>\lambda\delta home page</title>
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  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">175</td>
 148             <td class="snns italic cyan">characters</td>
 149             <td class="snnn right italic cyan">177083</td>
 150             <td class="snns italic cyan">nodes</td>
 151             <td class="ssnn right italic cyan">919341</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">609</td>
 159             <td class="snns italic green">total</td>
 160             <td class="ssnn right italic green">658</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">24</td>
 166             <td class="snss italic yellow">defined</td>
 167             <td class="snsn right italic yellow">42</td>
 168             <td class="snss italic yellow">total</td>
 169             <td class="sssn right italic yellow">66</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="snnn top gray">
 365               <br />
 366             </td>
 367             <td class="ssnn top gray">
 368               <br />
 369             </td>
 370           </tr>
 371           <tr>
 372             <td class="snns top capitalize italic water">rt-transition</td>
 373             <td class="snns top italic water">t-bound context-sensitive rt-transition</td>
 374             <td class="snns top water">lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
 375             <td class="snnn top water">lfpr_length lfpr_drops lfpr_fqup lfpr_frees lfpr_lfpx lfpr_lfpr</td>
 376             <td class="snnn top water">
 377               <br />
 378             </td>
 379             <td class="ssnn top water">
 380               <br />
 381             </td>
 382           </tr>
 383           <tr>
 384             <td class="nnns top capitalize italic water">
 385               <br />
 386             </td>
 387             <td class="nnns top italic water">
 388               <br />
 389             </td>
 390             <td class="snns top water">cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 391             <td class="snnn top water">cpr_drops</td>
 392             <td class="snnn top water">
 393               <br />
 394             </td>
 395             <td class="ssnn top water">
 396               <br />
 397             </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="snnn top water">cpm_simple cpm_drops cpm_lsubr cpm_cpx</td>
 408             <td class="snnn top water">
 409               <br />
 410             </td>
 411             <td class="ssnn top water">
 412               <br />
 413             </td>
 414           </tr>
 415           <tr>
 416             <td class="nnns top capitalize italic water">
 417               <br />
 418             </td>
 419             <td class="snns top italic water">uncounted context-sensitive rt-transition</td>
 420             <td class="snns top water">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
 421             <td class="snnn top water">lfpx_length lfpx_drops lfpx_fqup lfpx_frees</td>
 422             <td class="snnn top water">
 423               <br />
 424             </td>
 425             <td class="ssnn top water">
 426               <br />
 427             </td>
 428           </tr>
 429           <tr>
 430             <td class="nnns top capitalize italic water">
 431               <br />
 432             </td>
 433             <td class="nnns top italic water">
 434               <br />
 435             </td>
 436             <td class="snns top water">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
 437             <td class="snnn top water">cpx_simple cpx_drops cpx_lsubr</td>
 438             <td class="snnn top water">
 439               <br />
 440             </td>
 441             <td class="ssnn top water">
 442               <br />
 443             </td>
 444           </tr>
 445           <tr>
 446             <td class="nnns top capitalize italic water">
 447               <br />
 448             </td>
 449             <td class="snns top italic water">counted context-sensitive rt-transition</td>
 450             <td class="snns top water">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
 451             <td class="snnn top water">cpg_simple cpg_drops cpg_lsubr</td>
 452             <td class="snnn top water">
 453               <br />
 454             </td>
 455             <td class="ssnn top water">
 456               <br />
 457             </td>
 458           </tr>
 459           <tr>
 460             <td class="snns top capitalize italic green">static typing</td>
 461             <td class="snns top italic green">parameters</td>
 462             <td class="snns top green">sh</td>
 463             <td class="snnn top green">sd</td>
 464             <td class="snnn top green">
 465               <br />
 466             </td>
 467             <td class="ssnn top green">
 468               <br />
 469             </td>
 470           </tr>
 471           <tr>
 472             <td class="nnns top capitalize italic green">
 473               <br />
 474             </td>
 475             <td class="snns top italic green">restricted ref. for atomic arity assignment</td>
 476             <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
 477             <td class="snnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
 478             <td class="snnn top green">
 479               <br />
 480             </td>
 481             <td class="ssnn top green">
 482               <br />
 483             </td>
 484           </tr>
 485           <tr>
 486             <td class="nnns top capitalize italic green">
 487               <br />
 488             </td>
 489             <td class="snns top italic green">atomic arity assignment</td>
 490             <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 491             <td class="snnn top green">aaa_drops aaa_fqus aaa_lfeq aaa_aaa</td>
 492             <td class="snnn top green">
 493               <br />
 494             </td>
 495             <td class="ssnn top green">
 496               <br />
 497             </td>
 498           </tr>
 499           <tr>
 500             <td class="nnns top capitalize italic green">
 501               <br />
 502             </td>
 503             <td class="snns top italic green">equivalence for closures on referred entries</td>
 504             <td class="snns top green">ffeq ( ⦃?,?,?⦄ ≡ ⦃?,?,?⦄ )</td>
 505             <td class="snnn top green">ffeq_freq</td>
 506             <td class="snnn top green">
 507               <br />
 508             </td>
 509             <td class="ssnn top green">
 510               <br />
 511             </td>
 512           </tr>
 513           <tr>
 514             <td class="nnns top capitalize italic green">
 515               <br />
 516             </td>
 517             <td class="snns top italic green">equivalence for local environments on referred entries</td>
 518             <td class="snns top green">lfeq ( ? ≡[?] ? )</td>
 519             <td class="snnn top green">lfeq_length lfeq_lreq lfeq_fqup lfeq_lfeq</td>
 520             <td class="snnn top green">
 521               <br />
 522             </td>
 523             <td class="ssnn top green">
 524               <br />
 525             </td>
 526           </tr>
 527           <tr>
 528             <td class="nnns top capitalize italic green">
 529               <br />
 530             </td>
 531             <td class="snns top italic green">generic extension on referred entries</td>
 532             <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
 533             <td class="snnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
 534             <td class="snnn top green">
 535               <br />
 536             </td>
 537             <td class="ssnn top green">
 538               <br />
 539             </td>
 540           </tr>
 541           <tr>
 542             <td class="nnns top capitalize italic green">
 543               <br />
 544             </td>
 545             <td class="snns top italic green">restricted ref. for context-sensitive free variables</td>
 546             <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
 547             <td class="snnn top green">lsubf_frees</td>
 548             <td class="snnn top green">
 549               <br />
 550             </td>
 551             <td class="ssnn top green">
 552               <br />
 553             </td>
 554           </tr>
 555           <tr>
 556             <td class="nnns top capitalize italic green">
 557               <br />
 558             </td>
 559             <td class="snns top italic green">context-sensitive free variables</td>
 560             <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 561             <td class="snnn top green">frees_weight frees_lreq frees_drops frees_fqup frees_fqus frees_frees</td>
 562             <td class="snnn top green">
 563               <br />
 564             </td>
 565             <td class="ssnn top green">
 566               <br />
 567             </td>
 568           </tr>
 569           <tr>
 570             <td class="nnns top capitalize italic green">
 571               <br />
 572             </td>
 573             <td class="snns top italic green">restricted ref. for local env.</td>
 574             <td class="snns top green">lsubr ( ? ⫃ ? )</td>
 575             <td class="snnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
 576             <td class="snnn top green">
 577               <br />
 578             </td>
 579             <td class="ssnn top green">
 580               <br />
 581             </td>
 582           </tr>
 583           <tr>
 584             <td class="snns top capitalize italic grass">s-computation</td>
 585             <td class="snns top italic grass">iterated structural successor for closures</td>
 586             <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
 587             <td class="snnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
 588             <td class="snnn top grass">
 589               <br />
 590             </td>
 591             <td class="ssnn top grass">
 592               <br />
 593             </td>
 594           </tr>
 595           <tr>
 596             <td class="nnns top capitalize italic grass">
 597               <br />
 598             </td>
 599             <td class="nnns top italic grass">
 600               <br />
 601             </td>
 602             <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
 603             <td class="snnn top grass">fqup_weight fqup_drops fqup_fqup</td>
 604             <td class="snnn top grass">
 605               <br />
 606             </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="snnn top yellow">
 617               <br />
 618             </td>
 619             <td class="ssnn top yellow">
 620               <br />
 621             </td>
 622           </tr>
 623           <tr>
 624             <td class="nnns top capitalize italic yellow">
 625               <br />
 626             </td>
 627             <td class="nnns top italic yellow">
 628               <br />
 629             </td>
 630             <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
 631             <td class="snnn top yellow">fqu_length fqu_weight</td>
 632             <td class="snnn top yellow">
 633               <br />
 634             </td>
 635             <td class="ssnn top yellow">
 636               <br />
 637             </td>
 638           </tr>
 639           <tr>
 640             <td class="snns top capitalize italic orange">relocation</td>
 641             <td class="snns top italic orange">generic slicing for local environments</td>
 642             <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 643             <td class="snnn top orange">
 644               <br />
 645             </td>
 646             <td class="snnn top orange">
 647               <br />
 648             </td>
 649             <td class="ssnn top orange">
 650               <br />
 651             </td>
 652           </tr>
 653           <tr>
 654             <td class="nnns top capitalize italic orange">
 655               <br />
 656             </td>
 657             <td class="nnns top italic orange">
 658               <br />
 659             </td>
 660             <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 661             <td class="snnn top orange">drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops</td>
 662             <td class="snnn top orange">
 663               <br />
 664             </td>
 665             <td class="ssnn top orange">
 666               <br />
 667             </td>
 668           </tr>
 669           <tr>
 670             <td class="nnns top capitalize italic orange">
 671               <br />
 672             </td>
 673             <td class="snns top italic orange">generic relocation for terms</td>
 674             <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 675             <td class="snnn top orange">lifts_lifts_vector</td>
 676             <td class="snnn top orange">
 677               <br />
 678             </td>
 679             <td class="ssnn top orange">
 680               <br />
 681             </td>
 682           </tr>
 683           <tr>
 684             <td class="nnns top capitalize italic orange">
 685               <br />
 686             </td>
 687             <td class="nnns top italic orange">
 688               <br />
 689             </td>
 690             <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
 691             <td class="snnn top orange">lifts_simple lifts_weight lifts_lifts</td>
 692             <td class="snnn top orange">
 693               <br />
 694             </td>
 695             <td class="ssnn top orange">
 696               <br />
 697             </td>
 698           </tr>
 699           <tr>
 700             <td class="nnns top capitalize italic orange">
 701               <br />
 702             </td>
 703             <td class="snns top italic orange">ranged equivalence for local environments</td>
 704             <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
 705             <td class="snnn top orange">lreq_length lreq_lreq</td>
 706             <td class="snnn top orange">
 707               <br />
 708             </td>
 709             <td class="ssnn top orange">
 710               <br />
 711             </td>
 712           </tr>
 713           <tr>
 714             <td class="nnns top capitalize italic orange">
 715               <br />
 716             </td>
 717             <td class="snns top italic orange">generic entrywise extension</td>
 718             <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
 719             <td class="snnn top orange">lexs_length lexs_lexs</td>
 720             <td class="snnn top orange">
 721               <br />
 722             </td>
 723             <td class="ssnn top orange">
 724               <br />
 725             </td>
 726           </tr>
 727           <tr>
 728             <td class="snns top capitalize italic red">grammar</td>
 729             <td class="snns top italic red">append for local environments</td>
 730             <td class="snns top red">append ( ? @@ ? )</td>
 731             <td class="snnn top red">append_length</td>
 732             <td class="snnn top red">
 733               <br />
 734             </td>
 735             <td class="ssnn top red">
 736               <br />
 737             </td>
 738           </tr>
 739           <tr>
 740             <td class="nnns top capitalize italic red">
 741               <br />
 742             </td>
 743             <td class="snns top italic red">context-sensitive equivalences for terms</td>
 744             <td class="snns top red">ceq</td>
 745             <td class="snnn top red">ceq_ceq</td>
 746             <td class="snnn top red">
 747               <br />
 748             </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="snns top italic red">same top term structure</td>
 758             <td class="snns top red">tsts ( ? ≂ ? )</td>
 759             <td class="snnn top red">tsts_tsts tsts_vector</td>
 760             <td class="snnn top red">
 761               <br />
 762             </td>
 763             <td class="ssnn top red">
 764               <br />
 765             </td>
 766           </tr>
 767           <tr>
 768             <td class="nnns top capitalize italic red">
 769               <br />
 770             </td>
 771             <td class="snns top italic red">closures</td>
 772             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 773             <td class="snnn top red">cl_restricted_weight ( ♯{?,?} )</td>
 774             <td class="snnn top red">
 775               <br />
 776             </td>
 777             <td class="ssnn top red">
 778               <br />
 779             </td>
 780           </tr>
 781           <tr>
 782             <td class="nnns top capitalize italic red">
 783               <br />
 784             </td>
 785             <td class="snns top italic red">internal syntax</td>
 786             <td class="snns top red">genv</td>
 787             <td class="snnn top red">
 788               <br />
 789             </td>
 790             <td class="snnn top red">
 791               <br />
 792             </td>
 793             <td class="ssnn top red">
 794               <br />
 795             </td>
 796           </tr>
 797           <tr>
 798             <td class="nnns top capitalize italic red">
 799               <br />
 800             </td>
 801             <td class="nnns top italic red">
 802               <br />
 803             </td>
 804             <td class="snns top red">lenv</td>
 805             <td class="snnn top red">lenv_weight ( ♯{?} )</td>
 806             <td class="snnn top red">lenv_length ( |?| )</td>
 807             <td class="ssnn top red">
 808               <br />
 809             </td>
 810           </tr>
 811           <tr>
 812             <td class="nnns top capitalize italic red">
 813               <br />
 814             </td>
 815             <td class="nnns top italic red">
 816               <br />
 817             </td>
 818             <td class="snns top red">term</td>
 819             <td class="snnn top red">term_weight ( ♯{?} )</td>
 820             <td class="snnn top red">term_simple ( 𝐒⦃?⦄ )</td>
 821             <td class="ssnn top red">term_vector ( Ⓐ?.? )</td>
 822           </tr>
 823           <tr>
 824             <td class="nnns top capitalize italic red">
 825               <br />
 826             </td>
 827             <td class="nnns top italic red">
 828               <br />
 829             </td>
 830             <td class="snns top red">item</td>
 831             <td class="snnn top red">
 832               <br />
 833             </td>
 834             <td class="snnn top red">
 835               <br />
 836             </td>
 837             <td class="ssnn top red">
 838               <br />
 839             </td>
 840           </tr>
 841           <tr>
 842             <td class="nnss top capitalize italic red">
 843               <br />
 844             </td>
 845             <td class="snss top italic red">external syntax</td>
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