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">238</td>
 148             <td class="snns italic cyan">characters</td>
 149             <td class="snnn right italic cyan">249398</td>
 150             <td class="snns italic cyan">nodes</td>
 151             <td class="ssnn right italic cyan">1213337</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">63</td>
 157             <td class="snns italic green">lemmas</td>
 158             <td class="snnn right italic green">838</td>
 159             <td class="snns italic green">total</td>
 160             <td class="ssnn right italic green">901</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">70</td>
 168             <td class="snss italic yellow">total</td>
 169             <td class="sssn right italic yellow">100</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">csx_cnx_vector csx_csx_vector</td>
 383           </tr>
 384           <tr>
 385             <td class="nnns top capitalize italic sky">
 386               <br />
 387             </td>
 388             <td class="nnns top italic sky">
 389               <br />
 390             </td>
 391             <td class="snns top sky">csx ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )</td>
 392             <td class="ssnn top sky">csx_simple csx_simple_theq csx_drops csx_lsubr csx_gcp csx_gcr csx_lfpx csx_cnx csx_cpxs csx_csx</td>
 393           </tr>
 394           <tr>
 395             <td class="nnns top capitalize italic sky">
 396               <br />
 397             </td>
 398             <td class="nnns top italic sky">
 399               <br />
 400             </td>
 401             <td class="snns top sky">lfpxs ( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )</td>
 402             <td class="ssnn top sky">lfpxs_length lfpxs_fqup lfpxs_cpxs</td>
 403           </tr>
 404           <tr>
 405             <td class="nnns top capitalize italic sky">
 406               <br />
 407             </td>
 408             <td class="nnns top italic sky">
 409               <br />
 410             </td>
 411             <td class="snns top sky">cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )</td>
 412             <td class="ssnn top sky">cpxs_tdeq cpxs_theq cpxs_theq_vector cpxs_drops cpxs_lsubr cpxs_lfpx cpxs_cnx cpxs_cpxs</td>
 413           </tr>
 414           <tr>
 415             <td class="snns top capitalize italic cyan">rt-transition</td>
 416             <td class="snns top italic cyan">parallel rst-transition</td>
 417             <td class="snns top cyan">fpbq ( ⦃?,?,?⦄ ≽[?] ⦃?,?,?⦄ )</td>
 418             <td class="ssnn top cyan">fpbq_aaa</td>
 419           </tr>
 420           <tr>
 421             <td class="nnns top capitalize italic cyan">
 422               <br />
 423             </td>
 424             <td class="nnns top italic cyan">
 425               <br />
 426             </td>
 427             <td class="snns top cyan">fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )</td>
 428             <td class="ssnn top cyan">fpb_lfdeq</td>
 429           </tr>
 430           <tr>
 431             <td class="nnns top capitalize italic cyan">
 432               <br />
 433             </td>
 434             <td class="snns top italic cyan">t-bound context-sensitive rt-transition</td>
 435             <td class="snns top cyan">lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
 436             <td class="ssnn top cyan">lfpr_length lfpr_drops lfpr_fquq lfpr_fqup lfpr_frees lfpr_aaa lfpr_lfpx lfpr_lfpr</td>
 437           </tr>
 438           <tr>
 439             <td class="nnns top capitalize italic cyan">
 440               <br />
 441             </td>
 442             <td class="nnns top italic cyan">
 443               <br />
 444             </td>
 445             <td class="snns top cyan">cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 446             <td class="ssnn top cyan">cpr_drops</td>
 447           </tr>
 448           <tr>
 449             <td class="nnns top capitalize italic cyan">
 450               <br />
 451             </td>
 452             <td class="nnns top italic cyan">
 453               <br />
 454             </td>
 455             <td class="snns top cyan">cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
 456             <td class="ssnn top cyan">cpm_simple cpm_drops cpm_lsubr cpm_lfxs cpm_cpx</td>
 457           </tr>
 458           <tr>
 459             <td class="nnns top capitalize italic cyan">
 460               <br />
 461             </td>
 462             <td class="snns top italic cyan">uncounted context-sensitive rt-transition</td>
 463             <td class="snns top cyan">cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )</td>
 464             <td class="ssnn top cyan">cnx_simple cnx_drops cnx_cnx</td>
 465           </tr>
 466           <tr>
 467             <td class="nnns top capitalize italic cyan">
 468               <br />
 469             </td>
 470             <td class="nnns top italic cyan">
 471               <br />
 472             </td>
 473             <td class="snns top cyan">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
 474             <td class="ssnn top cyan">lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_lfdeq lfpx_aaa lfpx_lfpx</td>
 475           </tr>
 476           <tr>
 477             <td class="nnns top capitalize italic cyan">
 478               <br />
 479             </td>
 480             <td class="nnns top italic cyan">
 481               <br />
 482             </td>
 483             <td class="snns top cyan">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
 484             <td class="ssnn top cyan">cpx_simple cpx_drops cpx_fqus cpx_lsubr cpx_lfxs</td>
 485           </tr>
 486           <tr>
 487             <td class="nnns top capitalize italic cyan">
 488               <br />
 489             </td>
 490             <td class="snns top italic cyan">counted context-sensitive rt-transition</td>
 491             <td class="snns top cyan">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
 492             <td class="ssnn top cyan">cpg_simple cpg_drops cpg_lsubr</td>
 493           </tr>
 494           <tr>
 495             <td class="snns top capitalize italic water">iterated static typing</td>
 496             <td class="snns top italic water">iterated extension on referred entries</td>
 497             <td class="snns top water">tc_lfxs ( ? ⦻**[?,?] ? )</td>
 498             <td class="ssnn top water">
 499               <br />
 500             </td>
 501           </tr>
 502           <tr>
 503             <td class="snns top capitalize italic green">static typing</td>
 504             <td class="snns top italic green">generic reducibility</td>
 505             <td class="snns top green">lsubc ( ? ⊢ ? ⫃[?] ? )</td>
 506             <td class="ssnn top green">lsubc_drops lsubc_lsubr lsubc_lsuba</td>
 507           </tr>
 508           <tr>
 509             <td class="nnns top capitalize italic green">
 510               <br />
 511             </td>
 512             <td class="nnns top italic green">
 513               <br />
 514             </td>
 515             <td class="snns top green">gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
 516             <td class="ssnn top green">gcp_aaa</td>
 517           </tr>
 518           <tr>
 519             <td class="nnns top capitalize italic green">
 520               <br />
 521             </td>
 522             <td class="nnns top italic green">
 523               <br />
 524             </td>
 525             <td class="snns top green">gcp</td>
 526             <td class="ssnn top green">
 527               <br />
 528             </td>
 529           </tr>
 530           <tr>
 531             <td class="nnns top capitalize italic green">
 532               <br />
 533             </td>
 534             <td class="snns top italic green">atomic arity assignment</td>
 535             <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
 536             <td class="ssnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
 537           </tr>
 538           <tr>
 539             <td class="nnns top capitalize italic green">
 540               <br />
 541             </td>
 542             <td class="nnns top italic green">
 543               <br />
 544             </td>
 545             <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 546             <td class="ssnn top green">aaa_drops aaa_fqus aaa_lfdeq aaa_aaa</td>
 547           </tr>
 548           <tr>
 549             <td class="nnns top capitalize italic green">
 550               <br />
 551             </td>
 552             <td class="snns top italic green">degree-based equivalence on referred entries</td>
 553             <td class="snns top green">ffdeq ( ⦃?,?,?⦄ ≡[?,?] ⦃?,?,?⦄ )</td>
 554             <td class="ssnn top green">ffdeq_fqup ffdeq_ffdeq</td>
 555           </tr>
 556           <tr>
 557             <td class="nnns top capitalize italic green">
 558               <br />
 559             </td>
 560             <td class="nnns top italic green">
 561               <br />
 562             </td>
 563             <td class="snns top green">lfdeq ( ? ≡[?,?,?] ? )</td>
 564             <td class="ssnn top green">lfdeq_length lfdeq_drops lfdeq_fqup lfdeq_fqus lfdeq_lfdeq</td>
 565           </tr>
 566           <tr>
 567             <td class="nnns top capitalize italic green">
 568               <br />
 569             </td>
 570             <td class="snns top italic green">generic extension on referred entries</td>
 571             <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
 572             <td class="ssnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
 573           </tr>
 574           <tr>
 575             <td class="nnns top capitalize italic green">
 576               <br />
 577             </td>
 578             <td class="snns top italic green">context-sensitive free variables</td>
 579             <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
 580             <td class="ssnn top green">lsubf_frees</td>
 581           </tr>
 582           <tr>
 583             <td class="nnns top capitalize italic green">
 584               <br />
 585             </td>
 586             <td class="nnns top italic green">
 587               <br />
 588             </td>
 589             <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 590             <td class="ssnn top green">frees_drops frees_fqup frees_frees</td>
 591           </tr>
 592           <tr>
 593             <td class="nnns top capitalize italic green">
 594               <br />
 595             </td>
 596             <td class="snns top italic green">restricted ref. for local env.</td>
 597             <td class="snns top green">lsubr ( ? ⫃ ? )</td>
 598             <td class="ssnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
 599           </tr>
 600           <tr>
 601             <td class="snns top capitalize italic grass">s-computation</td>
 602             <td class="snns top italic grass">iterated structural successor for closures</td>
 603             <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
 604             <td class="ssnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
 605           </tr>
 606           <tr>
 607             <td class="nnns top capitalize italic grass">
 608               <br />
 609             </td>
 610             <td class="nnns top italic grass">
 611               <br />
 612             </td>
 613             <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
 614             <td class="ssnn top grass">fqup_weight fqup_drops fqup_fqup</td>
 615           </tr>
 616           <tr>
 617             <td class="snns top capitalize italic yellow">s-transition</td>
 618             <td class="snns top italic yellow">structural successor for closures</td>
 619             <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
 620             <td class="ssnn top yellow">fquq_length fquq_weight</td>
 621           </tr>
 622           <tr>
 623             <td class="nnns top capitalize italic yellow">
 624               <br />
 625             </td>
 626             <td class="nnns top italic yellow">
 627               <br />
 628             </td>
 629             <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
 630             <td class="ssnn top yellow">fqu_length fqu_weight</td>
 631           </tr>
 632           <tr>
 633             <td class="snns top capitalize italic orange">relocation</td>
 634             <td class="snns top italic orange">generic slicing for local environments</td>
 635             <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 636             <td class="ssnn top orange">
 637               <br />
 638             </td>
 639           </tr>
 640           <tr>
 641             <td class="nnns top capitalize italic orange">
 642               <br />
 643             </td>
 644             <td class="nnns top italic orange">
 645               <br />
 646             </td>
 647             <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 648             <td class="ssnn top orange">drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops</td>
 649           </tr>
 650           <tr>
 651             <td class="nnns top capitalize italic orange">
 652               <br />
 653             </td>
 654             <td class="snns top italic orange">generic relocation for terms</td>
 655             <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 656             <td class="ssnn top orange">lifts_lifts_vector</td>
 657           </tr>
 658           <tr>
 659             <td class="nnns top capitalize italic orange">
 660               <br />
 661             </td>
 662             <td class="nnns top italic orange">
 663               <br />
 664             </td>
 665             <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
 666             <td class="ssnn top orange">lifts_simple lifts_weight lifts_tdeq lifts_lifts</td>
 667           </tr>
 668           <tr>
 669             <td class="nnns top capitalize italic orange">
 670               <br />
 671             </td>
 672             <td class="snns top italic orange">ranged equivalence for local environments</td>
 673             <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
 674             <td class="ssnn top orange">lreq_length lreq_lreq</td>
 675           </tr>
 676           <tr>
 677             <td class="nnns top capitalize italic orange">
 678               <br />
 679             </td>
 680             <td class="snns top italic orange">generic entrywise extension</td>
 681             <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
 682             <td class="ssnn top orange">lexs_length lexs_lexs</td>
 683           </tr>
 684           <tr>
 685             <td class="snns top capitalize italic red">syntax</td>
 686             <td class="snns top italic red">append for local environments</td>
 687             <td class="snns top red">append ( ? @@ ? )</td>
 688             <td class="ssnn top red">append_length</td>
 689           </tr>
 690           <tr>
 691             <td class="nnns top capitalize italic red">
 692               <br />
 693             </td>
 694             <td class="snns top italic red">head equivalence for terms</td>
 695             <td class="snns top red">theq ( ? ⩳[?,?] ? )</td>
 696             <td class="ssnn top red">theq_simple theq_tdeq theq_theq theq_simple_vector</td>
 697           </tr>
 698           <tr>
 699             <td class="nnns top capitalize italic red">
 700               <br />
 701             </td>
 702             <td class="snns top italic red">degree-based equivalence for terms</td>
 703             <td class="snns top red">deq ( ? ≡[?,?] ? ) </td>
 704             <td class="ssnn top red">deq_deq</td>
 705           </tr>
 706           <tr>
 707             <td class="nnns top capitalize italic red">
 708               <br />
 709             </td>
 710             <td class="snns top italic red">closures</td>
 711             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 712             <td class="ssnn top red">
 713               <br />
 714             </td>
 715           </tr>
 716           <tr>
 717             <td class="nnns top capitalize italic red">
 718               <br />
 719             </td>
 720             <td class="nnns top italic red">
 721               <br />
 722             </td>
 723             <td class="snns top red">cl_restricted_weight ( ♯{?,?} )</td>
 724             <td class="ssnn top red">
 725               <br />
 726             </td>
 727           </tr>
 728           <tr>
 729             <td class="nnns top capitalize italic red">
 730               <br />
 731             </td>
 732             <td class="snns top italic red">global environments</td>
 733             <td class="snns top red">genv</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="snns top italic red">local environments</td>
 743             <td class="snns top red">lenv_length ( |?| )</td>
 744             <td class="ssnn top red">
 745               <br />
 746             </td>
 747           </tr>
 748           <tr>
 749             <td class="nnns top capitalize italic red">
 750               <br />
 751             </td>
 752             <td class="nnns top italic red">
 753               <br />
 754             </td>
 755             <td class="snns top red">lenv_weight ( ♯{?} )</td>
 756             <td class="ssnn top red">
 757               <br />
 758             </td>
 759           </tr>
 760           <tr>
 761             <td class="nnns top capitalize italic red">
 762               <br />
 763             </td>
 764             <td class="nnns top italic red">
 765               <br />
 766             </td>
 767             <td class="snns top red">lenv</td>
 768             <td class="ssnn top red">
 769               <br />
 770             </td>
 771           </tr>
 772           <tr>
 773             <td class="nnns top capitalize italic red">
 774               <br />
 775             </td>
 776             <td class="snns top italic red">terms</td>
 777             <td class="snns top red">term_vector ( Ⓐ?.? )</td>
 778             <td class="ssnn top red">
 779               <br />
 780             </td>
 781           </tr>
 782           <tr>
 783             <td class="nnns top capitalize italic red">
 784               <br />
 785             </td>
 786             <td class="nnns top italic red">
 787               <br />
 788             </td>
 789             <td class="snns top red">term_simple ( 𝐒⦃?⦄ )</td>
 790             <td class="ssnn top red">
 791               <br />
 792             </td>
 793           </tr>
 794           <tr>
 795             <td class="nnns top capitalize italic red">
 796               <br />
 797             </td>
 798             <td class="nnns top italic red">
 799               <br />
 800             </td>
 801             <td class="snns top red">term_weight ( ♯{?} )</td>
 802             <td class="ssnn top red">
 803               <br />
 804             </td>
 805           </tr>
 806           <tr>
 807             <td class="nnns top capitalize italic red">
 808               <br />
 809             </td>
 810             <td class="nnns top italic red">
 811               <br />
 812             </td>
 813             <td class="snns top red">term</td>
 814             <td class="ssnn top red">
 815               <br />
 816             </td>
 817           </tr>
 818           <tr>
 819             <td class="nnns top capitalize italic red">
 820               <br />
 821             </td>
 822             <td class="snns top italic red">items</td>
 823             <td class="snns top red">item_sd</td>
 824             <td class="ssnn top red">
 825               <br />
 826             </td>
 827           </tr>
 828           <tr>
 829             <td class="nnns top capitalize italic red">
 830               <br />
 831             </td>
 832             <td class="nnns top italic red">
 833               <br />
 834             </td>
 835             <td class="snns top red">item_sh</td>
 836             <td class="ssnn top red">
 837               <br />
 838             </td>
 839           </tr>
 840           <tr>
 841             <td class="nnns top capitalize italic red">
 842               <br />
 843             </td>
 844             <td class="nnns top italic red">
 845               <br />
 846             </td>
 847             <td class="snns top red">item</td>
 848             <td class="ssnn top red">
 849               <br />
 850             </td>
 851           </tr>
 852           <tr>
 853             <td class="nnss top capitalize italic red">
 854               <br />
 855             </td>
 856             <td class="snss top italic red">atomic arities</td>
 857             <td class="snss top red">aarity</td>
 858             <td class="sssn top red">
 859               <br />
 860             </td>
 861           </tr>
 862         </tbody>
 863       </table>
 864     </div>
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