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">229</td>
 148             <td class="snns italic cyan">characters</td>
 149             <td class="snnn right italic cyan">240969</td>
 150             <td class="snns italic cyan">nodes</td>
 151             <td class="ssnn right italic cyan">1182308</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">61</td>
 157             <td class="snns italic green">lemmas</td>
 158             <td class="snnn right italic green">805</td>
 159             <td class="snns italic green">total</td>
 160             <td class="ssnn right italic green">866</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">30</td>
 166             <td class="snss italic yellow">defined</td>
 167             <td class="snsn right italic yellow">66</td>
 168             <td class="snss italic yellow">total</td>
 169             <td class="sssn right italic yellow">96</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 March 16.</span>
 186          First behavioral component reconstructed:
 187          rt_transition.
 188    </li>
 189     </ul>
 190     <ul xmlns:ld="http://lambdadelta.info/">
 191       <li>
 192         <span class="emph alpha">2017 February 19.</span>
 193          Generic candidates of reducibility.
 194    </li>
 195     </ul>
 196     <ul xmlns:ld="http://lambdadelta.info/">
 197       <li>
 198         <span class="emph alpha">2017 January 17.</span>
 199          Confluence for parallel r-transition on referred entries of local environments.
 200    </li>
 201     </ul>
 202     <ul xmlns:ld="http://lambdadelta.info/">
 203       <li>
 204         <span class="emph alpha">2016 September 15.</span>
 205          Confluence for context-sensitive parallel r-transition on terms.
 206    </li>
 207     </ul>
 208     <ul xmlns:ld="http://lambdadelta.info/">
 209       <li>
 210         <span class="emph alpha">2016 April 16.</span>
 211          Syntactic component reconstructed:
 212          syntax, relocation, s_transition, s_computation, static
 213          (anniversary milestone).
 214    </li>
 215     </ul>
 216     <ul xmlns:ld="http://lambdadelta.info/">
 217       <li>
 218         <span class="emph alpha">2016 March 25.</span>
 219          Relocation with reference transforming maps (rtmap).
 220    </li>
 221     </ul>
 222     <ul xmlns:ld="http://lambdadelta.info/">
 223       <li>
 224         <span class="emph alpha">2015 October 9.</span>
 225          λδ version 2A2 is started.
 226    </li>
 227     </ul>
 228     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
 229     <ul xmlns:ld="http://lambdadelta.info/">
 230       <li>
 231         <span class="emph delta">2015 August 27.</span>
 232          λδ version 2A1 appears too complex and is dismissed.
 233    </li>
 234     </ul>
 235     <ul xmlns:ld="http://lambdadelta.info/">
 236       <li>
 237         <span class="emph gamma">2014 October 28.</span>
 238          λδ version 2A1 is released.
 239    </li>
 240     </ul>
 241     <ul xmlns:ld="http://lambdadelta.info/">
 242       <li>
 243         <span class="emph beta">2014 September 9.</span>
 244          Iterated static type assignment defined (more elegantly)
 245          as a primitive notion.
 246    </li>
 247     </ul>
 248     <ul xmlns:ld="http://lambdadelta.info/">
 249       <li>
 250         <span class="emph beta">2014 June 18.</span>
 251          Preservation of stratified native validity
 252          for context-sensitive computation on terms.
 253    </li>
 254     </ul>
 255     <ul xmlns:ld="http://lambdadelta.info/">
 256       <li>
 257         <span class="emph alpha">2014 June 9.</span>
 258          Strong qrst-normalization
 259          for simply typed terms.
 260    </li>
 261     </ul>
 262     <ul xmlns:ld="http://lambdadelta.info/">
 263       <li>
 264         <span class="emph alpha">2014 April 16.</span>
 265          Lazy equivalence on local environments
 266          added as q-step to rst-computation on closures
 267          (anniversary milestone).
 268    </li>
 269     </ul>
 270     <ul xmlns:ld="http://lambdadelta.info/">
 271       <li>
 272         <span class="emph alpha">2014 January 20.</span>
 273          Parametrized slicing of local environments
 274          comprises both versions of this operation
 275          (one from basic_1, the other used in basic_2 till now).
 276    </li>
 277     </ul>
 278     <ul xmlns:ld="http://lambdadelta.info/">
 279       <li>
 280         <span class="emph alpha">2013 August 7.</span>
 281          Passive support for global environments.
 282    </li>
 283     </ul>
 284     <ul xmlns:ld="http://lambdadelta.info/">
 285       <li>
 286         <span class="emph alpha">2013 July 27.</span>
 287          Reaxiomatized β-reductum as in rt-reduction.
 288    </li>
 289     </ul>
 290     <ul xmlns:ld="http://lambdadelta.info/">
 291       <li>
 292         <span class="emph alpha">2013 July 20.</span>
 293          Context-sensitive strong rt-normalization
 294          for simply typed terms.
 295    </li>
 296     </ul>
 297     <ul xmlns:ld="http://lambdadelta.info/">
 298       <li>
 299         <span class="emph alpha">2013 April 16.</span>
 300          Reaxiomatized substitution and reduction
 301          commute with respect to subclosure
 302          (anniversary milestone).
 303    </li>
 304     </ul>
 305     <ul xmlns:ld="http://lambdadelta.info/">
 306       <li>
 307         <span class="emph alpha">2013 March 16.</span>
 308          Mutual recursive preservation of stratified native validity
 309          for rst-computation on closures.
 310    </li>
 311     </ul>
 312     <ul xmlns:ld="http://lambdadelta.info/">
 313       <li>
 314         <span class="emph alpha">2012 October 16.</span>
 315          Confluence for context-free parallel reduction on closures.
 316    </li>
 317     </ul>
 318     <ul xmlns:ld="http://lambdadelta.info/">
 319       <li>
 320         <span class="emph alpha">2012 July 26.</span>
 321          Term binders polarized to control ζ-reduction (not released).
 322    </li>
 323     </ul>
 324     <ul xmlns:ld="http://lambdadelta.info/">
 325       <li>
 326         <span class="emph alpha">2012 April 16.</span>
 327          Context-sensitive subject equivalence
 328          for atomic arity assignment
 329          (anniversary milestone).
 330    </li>
 331     </ul>
 332     <ul xmlns:ld="http://lambdadelta.info/">
 333       <li>
 334         <span class="emph alpha">2012 March 15.</span>
 335          Context-sensitive strong normalization
 336          for simply typed terms.
 337    </li>
 338     </ul>
 339     <ul xmlns:ld="http://lambdadelta.info/">
 340       <li>
 341         <span class="emph alpha">2012 January 27.</span>
 342          Generic candidates of reducibility.
 343    </li>
 344     </ul>
 345     <ul xmlns:ld="http://lambdadelta.info/">
 346       <li>
 347         <span class="emph alpha">2011 September 21.</span>
 348          Confluence for context-sensitive parallel reduction on terms.
 349    </li>
 350     </ul>
 351     <ul xmlns:ld="http://lambdadelta.info/">
 352       <li>
 353         <span class="emph alpha">2011 September 6.</span>
 354          Confluence for context-free parallel reduction on terms.
 355    </li>
 356     </ul>
 357     <ul xmlns:ld="http://lambdadelta.info/">
 358       <li>
 359         <span class="emph alpha">2011 April 17.</span>
 360          λδ version 2 is started.
 361    </li>
 362     </ul>
 363     <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" />
 364     </div>
 365     <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
 366    </div>
 367     <div xmlns:ld="http://lambdadelta.info/" class="text">
 368       <table cellpadding="4" cellspacing="0">
 369         <tbody>
 370           <tr>
 371             <td class="snns top capitalize italic gray">component</td>
 372             <td class="snns top italic gray">plane</td>
 373             <td class="snns top gray">files</td>
 374             <td class="ssnn top gray">
 375               <br />
 376             </td>
 377           </tr>
 378           <tr>
 379             <td class="snns top capitalize italic sky">rt-computation</td>
 380             <td class="snns top italic sky">uncounted context-sensitive rt-computation</td>
 381             <td class="snns top sky">csx_vector ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )</td>
 382             <td class="ssnn top sky">
 383               <br />
 384             </td>
 385           </tr>
 386           <tr>
 387             <td class="nnns top capitalize italic sky">
 388               <br />
 389             </td>
 390             <td class="nnns top italic sky">
 391               <br />
 392             </td>
 393             <td class="snns top sky">csx ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )</td>
 394             <td class="ssnn top sky">csx_cnx csx_cpxs csx_csx</td>
 395           </tr>
 396           <tr>
 397             <td class="nnns top capitalize italic sky">
 398               <br />
 399             </td>
 400             <td class="nnns top italic sky">
 401               <br />
 402             </td>
 403             <td class="snns top sky">lfpxs ( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )</td>
 404             <td class="ssnn top sky">lfpxs_length lfpxs_fqup lfpxs_cpxs</td>
 405           </tr>
 406           <tr>
 407             <td class="nnns top capitalize italic sky">
 408               <br />
 409             </td>
 410             <td class="nnns top italic sky">
 411               <br />
 412             </td>
 413             <td class="snns top sky">cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )</td>
 414             <td class="ssnn top sky">cpxs_tdeq cpxs_tsts cpxs_tsts_vector cpxs_drops cpxs_lsubr cpxs_lfpx cpxs_cnx cpxs_cpxs</td>
 415           </tr>
 416           <tr>
 417             <td class="snns top capitalize italic cyan">rt-transition</td>
 418             <td class="snns top italic cyan">parallel rst-transition</td>
 419             <td class="snns top cyan">fpbq ( ⦃?,?,?⦄ ≽[?] ⦃?,?,?⦄ )</td>
 420             <td class="ssnn top cyan">fpbq_aaa</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">fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )</td>
 430             <td class="ssnn top cyan">fpb_lfdeq</td>
 431           </tr>
 432           <tr>
 433             <td class="nnns top capitalize italic cyan">
 434               <br />
 435             </td>
 436             <td class="snns top italic cyan">t-bound context-sensitive rt-transition</td>
 437             <td class="snns top cyan">lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
 438             <td class="ssnn top cyan">lfpr_length lfpr_drops lfpr_fquq lfpr_fqup lfpr_frees lfpr_aaa lfpr_lfpx lfpr_lfpr</td>
 439           </tr>
 440           <tr>
 441             <td class="nnns top capitalize italic cyan">
 442               <br />
 443             </td>
 444             <td class="nnns top italic cyan">
 445               <br />
 446             </td>
 447             <td class="snns top cyan">cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 448             <td class="ssnn top cyan">cpr_drops</td>
 449           </tr>
 450           <tr>
 451             <td class="nnns top capitalize italic cyan">
 452               <br />
 453             </td>
 454             <td class="nnns top italic cyan">
 455               <br />
 456             </td>
 457             <td class="snns top cyan">cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
 458             <td class="ssnn top cyan">cpm_simple cpm_drops cpm_lsubr cpm_lfxs cpm_cpx</td>
 459           </tr>
 460           <tr>
 461             <td class="nnns top capitalize italic cyan">
 462               <br />
 463             </td>
 464             <td class="snns top italic cyan">uncounted context-sensitive rt-transition</td>
 465             <td class="snns top cyan">cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )</td>
 466             <td class="ssnn top cyan">cnx_simple cnx_drops cnx_cnx</td>
 467           </tr>
 468           <tr>
 469             <td class="nnns top capitalize italic cyan">
 470               <br />
 471             </td>
 472             <td class="nnns top italic cyan">
 473               <br />
 474             </td>
 475             <td class="snns top cyan">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
 476             <td class="ssnn top cyan">lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_lfdeq lfpx_aaa lfpx_lfpx</td>
 477           </tr>
 478           <tr>
 479             <td class="nnns top capitalize italic cyan">
 480               <br />
 481             </td>
 482             <td class="nnns top italic cyan">
 483               <br />
 484             </td>
 485             <td class="snns top cyan">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
 486             <td class="ssnn top cyan">cpx_simple cpx_drops cpx_fqus cpx_lsubr cpx_lfxs</td>
 487           </tr>
 488           <tr>
 489             <td class="nnns top capitalize italic cyan">
 490               <br />
 491             </td>
 492             <td class="snns top italic cyan">counted context-sensitive rt-transition</td>
 493             <td class="snns top cyan">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
 494             <td class="ssnn top cyan">cpg_simple cpg_drops cpg_lsubr</td>
 495           </tr>
 496           <tr>
 497             <td class="snns top capitalize italic water">iterated static typing</td>
 498             <td class="snns top italic water">iterated extension on referred entries</td>
 499             <td class="snns top water">tc_lfxs ( ? ⦻**[?,?] ? )</td>
 500             <td class="ssnn top water">
 501               <br />
 502             </td>
 503           </tr>
 504           <tr>
 505             <td class="snns top capitalize italic green">static typing</td>
 506             <td class="snns top italic green">generic reducibility</td>
 507             <td class="snns top green">lsubc ( ? ⊢ ? ⫃[?] ? )</td>
 508             <td class="ssnn top green">lsubc_drops lsubc_lsubr lsubc_lsuba</td>
 509           </tr>
 510           <tr>
 511             <td class="nnns top capitalize italic green">
 512               <br />
 513             </td>
 514             <td class="nnns top italic green">
 515               <br />
 516             </td>
 517             <td class="snns top green">gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
 518             <td class="ssnn top green">gcp_aaa</td>
 519           </tr>
 520           <tr>
 521             <td class="nnns top capitalize italic green">
 522               <br />
 523             </td>
 524             <td class="nnns top italic green">
 525               <br />
 526             </td>
 527             <td class="snns top green">gcp</td>
 528             <td class="ssnn top green">
 529               <br />
 530             </td>
 531           </tr>
 532           <tr>
 533             <td class="nnns top capitalize italic green">
 534               <br />
 535             </td>
 536             <td class="snns top italic green">atomic arity assignment</td>
 537             <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
 538             <td class="ssnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
 539           </tr>
 540           <tr>
 541             <td class="nnns top capitalize italic green">
 542               <br />
 543             </td>
 544             <td class="nnns top italic green">
 545               <br />
 546             </td>
 547             <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 548             <td class="ssnn top green">aaa_drops aaa_fqus aaa_lfdeq aaa_aaa</td>
 549           </tr>
 550           <tr>
 551             <td class="nnns top capitalize italic green">
 552               <br />
 553             </td>
 554             <td class="snns top italic green">degree-based equivalence on referred entries</td>
 555             <td class="snns top green">ffdeq ( ⦃?,?,?⦄ ≡[?,?] ⦃?,?,?⦄ )</td>
 556             <td class="ssnn top green">ffdeq_fqup ffdeq_ffdeq</td>
 557           </tr>
 558           <tr>
 559             <td class="nnns top capitalize italic green">
 560               <br />
 561             </td>
 562             <td class="nnns top italic green">
 563               <br />
 564             </td>
 565             <td class="snns top green">lfdeq ( ? ≡[?,?,?] ? )</td>
 566             <td class="ssnn top green">lfdeq_length lfdeq_drops lfdeq_fqup lfdeq_fqus lfdeq_lfdeq</td>
 567           </tr>
 568           <tr>
 569             <td class="nnns top capitalize italic green">
 570               <br />
 571             </td>
 572             <td class="snns top italic green">generic extension on referred entries</td>
 573             <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
 574             <td class="ssnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
 575           </tr>
 576           <tr>
 577             <td class="nnns top capitalize italic green">
 578               <br />
 579             </td>
 580             <td class="snns top italic green">context-sensitive free variables</td>
 581             <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
 582             <td class="ssnn top green">lsubf_frees</td>
 583           </tr>
 584           <tr>
 585             <td class="nnns top capitalize italic green">
 586               <br />
 587             </td>
 588             <td class="nnns top italic green">
 589               <br />
 590             </td>
 591             <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 592             <td class="ssnn top green">frees_drops frees_fqup frees_frees</td>
 593           </tr>
 594           <tr>
 595             <td class="nnns top capitalize italic green">
 596               <br />
 597             </td>
 598             <td class="snns top italic green">restricted ref. for local env.</td>
 599             <td class="snns top green">lsubr ( ? ⫃ ? )</td>
 600             <td class="ssnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
 601           </tr>
 602           <tr>
 603             <td class="snns top capitalize italic grass">s-computation</td>
 604             <td class="snns top italic grass">iterated structural successor for closures</td>
 605             <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
 606             <td class="ssnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
 607           </tr>
 608           <tr>
 609             <td class="nnns top capitalize italic grass">
 610               <br />
 611             </td>
 612             <td class="nnns top italic grass">
 613               <br />
 614             </td>
 615             <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
 616             <td class="ssnn top grass">fqup_weight fqup_drops fqup_fqup</td>
 617           </tr>
 618           <tr>
 619             <td class="snns top capitalize italic yellow">s-transition</td>
 620             <td class="snns top italic yellow">structural successor for closures</td>
 621             <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
 622             <td class="ssnn top yellow">fquq_length fquq_weight</td>
 623           </tr>
 624           <tr>
 625             <td class="nnns top capitalize italic yellow">
 626               <br />
 627             </td>
 628             <td class="nnns top italic yellow">
 629               <br />
 630             </td>
 631             <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
 632             <td class="ssnn top yellow">fqu_length fqu_weight</td>
 633           </tr>
 634           <tr>
 635             <td class="snns top capitalize italic orange">relocation</td>
 636             <td class="snns top italic orange">generic slicing for local environments</td>
 637             <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 638             <td class="ssnn top orange">
 639               <br />
 640             </td>
 641           </tr>
 642           <tr>
 643             <td class="nnns top capitalize italic orange">
 644               <br />
 645             </td>
 646             <td class="nnns top italic orange">
 647               <br />
 648             </td>
 649             <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 650             <td class="ssnn top orange">drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops</td>
 651           </tr>
 652           <tr>
 653             <td class="nnns top capitalize italic orange">
 654               <br />
 655             </td>
 656             <td class="snns top italic orange">generic relocation for terms</td>
 657             <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 658             <td class="ssnn top orange">lifts_lifts_vector</td>
 659           </tr>
 660           <tr>
 661             <td class="nnns top capitalize italic orange">
 662               <br />
 663             </td>
 664             <td class="nnns top italic orange">
 665               <br />
 666             </td>
 667             <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
 668             <td class="ssnn top orange">lifts_simple lifts_weight lifts_tdeq lifts_lifts</td>
 669           </tr>
 670           <tr>
 671             <td class="nnns top capitalize italic orange">
 672               <br />
 673             </td>
 674             <td class="snns top italic orange">ranged equivalence for local environments</td>
 675             <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
 676             <td class="ssnn top orange">lreq_length lreq_lreq</td>
 677           </tr>
 678           <tr>
 679             <td class="nnns top capitalize italic orange">
 680               <br />
 681             </td>
 682             <td class="snns top italic orange">generic entrywise extension</td>
 683             <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
 684             <td class="ssnn top orange">lexs_length lexs_lexs</td>
 685           </tr>
 686           <tr>
 687             <td class="snns top capitalize italic red">syntax</td>
 688             <td class="snns top italic red">append for local environments</td>
 689             <td class="snns top red">append ( ? @@ ? )</td>
 690             <td class="ssnn top red">append_length</td>
 691           </tr>
 692           <tr>
 693             <td class="nnns top capitalize italic red">
 694               <br />
 695             </td>
 696             <td class="snns top italic red">same top term structure</td>
 697             <td class="snns top red">tsts ( ? ⩳[?,?] ? )</td>
 698             <td class="ssnn top red">tsts_simple tsts_tdeq tsts_tsts tsts_simple_vector</td>
 699           </tr>
 700           <tr>
 701             <td class="nnns top capitalize italic red">
 702               <br />
 703             </td>
 704             <td class="snns top italic red">degree-based equivalence for terms</td>
 705             <td class="snns top red">deq ( ? ≡[?,?] ? ) </td>
 706             <td class="ssnn top red">deq_deq</td>
 707           </tr>
 708           <tr>
 709             <td class="nnns top capitalize italic red">
 710               <br />
 711             </td>
 712             <td class="snns top italic red">closures</td>
 713             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 714             <td class="ssnn top red">
 715               <br />
 716             </td>
 717           </tr>
 718           <tr>
 719             <td class="nnns top capitalize italic red">
 720               <br />
 721             </td>
 722             <td class="nnns top italic red">
 723               <br />
 724             </td>
 725             <td class="snns top red">cl_restricted_weight ( ♯{?,?} )</td>
 726             <td class="ssnn top red">
 727               <br />
 728             </td>
 729           </tr>
 730           <tr>
 731             <td class="nnns top capitalize italic red">
 732               <br />
 733             </td>
 734             <td class="snns top italic red">global environments</td>
 735             <td class="snns top red">genv</td>
 736             <td class="ssnn top red">
 737               <br />
 738             </td>
 739           </tr>
 740           <tr>
 741             <td class="nnns top capitalize italic red">
 742               <br />
 743             </td>
 744             <td class="snns top italic red">local environments</td>
 745             <td class="snns top red">lenv_length ( |?| )</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="nnns top italic red">
 755               <br />
 756             </td>
 757             <td class="snns top red">lenv_weight ( ♯{?} )</td>
 758             <td class="ssnn top red">
 759               <br />
 760             </td>
 761           </tr>
 762           <tr>
 763             <td class="nnns top capitalize italic red">
 764               <br />
 765             </td>
 766             <td class="nnns top italic red">
 767               <br />
 768             </td>
 769             <td class="snns top red">lenv</td>
 770             <td class="ssnn top red">
 771               <br />
 772             </td>
 773           </tr>
 774           <tr>
 775             <td class="nnns top capitalize italic red">
 776               <br />
 777             </td>
 778             <td class="snns top italic red">terms</td>
 779             <td class="snns top red">term_vector ( Ⓐ?.? )</td>
 780             <td class="ssnn top red">
 781               <br />
 782             </td>
 783           </tr>
 784           <tr>
 785             <td class="nnns top capitalize italic red">
 786               <br />
 787             </td>
 788             <td class="nnns top italic red">
 789               <br />
 790             </td>
 791             <td class="snns top red">term_simple ( 𝐒⦃?⦄ )</td>
 792             <td class="ssnn top red">
 793               <br />
 794             </td>
 795           </tr>
 796           <tr>
 797             <td class="nnns top capitalize italic red">
 798               <br />
 799             </td>
 800             <td class="nnns top italic red">
 801               <br />
 802             </td>
 803             <td class="snns top red">term_weight ( ♯{?} )</td>
 804             <td class="ssnn top red">
 805               <br />
 806             </td>
 807           </tr>
 808           <tr>
 809             <td class="nnns top capitalize italic red">
 810               <br />
 811             </td>
 812             <td class="nnns top italic red">
 813               <br />
 814             </td>
 815             <td class="snns top red">term</td>
 816             <td class="ssnn top red">
 817               <br />
 818             </td>
 819           </tr>
 820           <tr>
 821             <td class="nnns top capitalize italic red">
 822               <br />
 823             </td>
 824             <td class="snns top italic red">items</td>
 825             <td class="snns top red">item_sd</td>
 826             <td class="ssnn top red">
 827               <br />
 828             </td>
 829           </tr>
 830           <tr>
 831             <td class="nnns top capitalize italic red">
 832               <br />
 833             </td>
 834             <td class="nnns top italic red">
 835               <br />
 836             </td>
 837             <td class="snns top red">item_sh</td>
 838             <td class="ssnn top red">
 839               <br />
 840             </td>
 841           </tr>
 842           <tr>
 843             <td class="nnns top capitalize italic red">
 844               <br />
 845             </td>
 846             <td class="nnns top italic red">
 847               <br />
 848             </td>
 849             <td class="snns top red">item</td>
 850             <td class="ssnn top red">
 851               <br />
 852             </td>
 853           </tr>
 854           <tr>
 855             <td class="nnss top capitalize italic red">
 856               <br />
 857             </td>
 858             <td class="snss top italic red">atomic arities</td>
 859             <td class="snss top red">aarity</td>
 860             <td class="sssn top red">
 861               <br />
 862             </td>
 863           </tr>
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