helm/www/lambdadelta/basic_2.html

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  10     <title>\lambda\delta home page</title>
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  20       </a>
  21     </div>
  22     <div class="head1">cic:/matita/lambdadelta/basic_2/ (core λδ version 2)</div>
  23     <div class="spacer">
  24       <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
  25     </div>
  26     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
  27       <br />
  28     </div>
  29     <div xmlns:ld="http://lambdadelta.info/" class="text">
  30       <table cellpadding="4" cellspacing="0">
  31         <tbody>
  32           <tr>
  33             <td class="snns capitalize italic sky">
  34               <a href="http://lambdadelta.info/home.html">home</a>
  35             </td>
  36             <td class="snns capitalize italic magenta">
  37               <a href="http://lambdadelta.info/news.html">news</a>
  38             </td>
  39             <td class="snns capitalize italic white">
  40               <a href="http://lambdadelta.info/specification.html">specification</a>
  41             </td>
  42             <td class="snnn capitalize italic white">
  43               <br />
  44             </td>
  45             <td class="snnn capitalize italic white">
  46               <br />
  47             </td>
  48             <td class="snns capitalize italic orange">
  49               <a href="http://lambdadelta.info/documentation.html">documentation</a>
  50             </td>
  51             <td class="snns capitalize italic green">
  52               <a href="http://lambdadelta.info/implementation.html">implementation</a>
  53             </td>
  54             <td class="ssnn capitalize italic green">
  55               <br />
  56             </td>
  57           </tr>
  58           <tr>
  59             <td class="snns capitalize sky">
  60               <a href="http://lambdadelta.info/home.html#foreword">foreword</a>
  61             </td>
  62             <td class="snns capitalize magenta">
  63               <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
  64             </td>
  65             <td class="snns capitalize white">
  66               <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
  67             </td>
  68             <td class="snnn capitalize white">(<a href="http://lambdadelta.info/ground_2.html">background</a> - <a href="http://lambdadelta.info/basic_2.html">core</a> - <a href="http://lambdadelta.info/apps_2.html">applications</a>)</td>
  69             <td class="snnn capitalize white">
  70               <br />
  71             </td>
  72             <td class="snns capitalize orange">
  73               <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
  74             </td>
  75             <td class="snns capitalize green">
  76               <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
  77             </td>
  78             <td class="ssnn capitalize green">
  79               <a href="http://lambdadelta.info/osn/">Open Symbolic Notation (OSN)</a>
  80             </td>
  81           </tr>
  82           <tr>
  83             <td class="snss capitalize sky">
  84               <a href="http://lambdadelta.info/home.html#citations">citations</a>
  85             </td>
  86             <td class="snss capitalize magenta">
  87               <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
  88             </td>
  89             <td class="snss capitalize white">
  90               <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
  91             </td>
  92             <td class="snsn capitalize white">(<a href="http://lambdadelta.info/ground_1.html">background</a> - <a href="http://lambdadelta.info/basic_1.html">core</a>)</td>
  93             <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
  94             <td class="snss capitalize orange">
  95               <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
  96             </td>
  97             <td class="snss capitalize green">
  98               <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
  99             </td>
 100             <td class="sssn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
 101           </tr>
 102         </tbody>
 103       </table>
 104     </div>
 105     <!--
 106    <section>System's Syntax and Behavior</section>
 107    <body>This is a summary of the "block structure"
 108          of the System's syntactic items and reductions.
 109    </body>
 110    <table name="basic_2_blk"/>
 111    <body>* In terms only.
 112          ** In terms and local environments only.
 113          *** In global environments only.
 114          **** Sort level k in terms only.
 115    </body>
 116 -->
 117     <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="summary">Summary of the Specification <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png" />
 118     </div>
 119     <div xmlns:ld="http://lambdadelta.info/" class="text">Here is a numerical account of the specification's contents
 120          and its timeline.
 121    </div>
 122     <div xmlns:ld="http://lambdadelta.info/" class="text">
 123       <table cellpadding="4" cellspacing="0">
 124         <tbody>
 125           <tr>
 126             <td class="snns capitalize italic gray">category</td>
 127             <td class="snns italic gray">units</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 water">sizes</td>
 146             <td class="snns italic water">characters (files)</td>
 147             <td class="snnn right italic water">315581 (309)</td>
 148             <td class="snns italic water">nodes (objects)</td>
 149             <td class="snnn right italic water">1458870 (1431)</td>
 150             <td class="snns italic water">intrinsic loss factor</td>
 151             <td class="ssnn right italic water">4.6</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">92</td>
 157             <td class="snns italic green">lemmas</td>
 158             <td class="snnn right italic green">1085</td>
 159             <td class="snns italic green">total</td>
 160             <td class="ssnn right italic green">1177</td>
 161           </tr>
 162           <tr>
 163             <td class="snss capitalize italic grass">concepts</td>
 164             <td class="snss italic grass">declared</td>
 165             <td class="snsn right italic grass">34</td>
 166             <td class="snss italic grass">defined</td>
 167             <td class="snsn right italic grass">93</td>
 168             <td class="snss italic grass">total</td>
 169             <td class="sssn right italic grass">127</td>
 170           </tr>
 171         </tbody>
 172       </table>
 173     </div>
 174     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="B">Stage "B"</div>
 175     <ul xmlns:ld="http://lambdadelta.info/">
 176       <li>
 177         <span class="emph alpha">Ongoing.</span>
 178          Context-sensitive subject equivalence
 179          for native type assignment.
 180    </li>
 181     </ul>
 182     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A2">Stage "A2": "Extending the Applicability Condition"</div>
 183     <ul xmlns:ld="http://lambdadelta.info/">
 184       <li>
 185         <span class="emph alpha">2017 October 17.</span>
 186          Exclusion binder in local environments.
 187          Syntactic component updated:
 188          syntax, relocation, s_transition, s_computation, static, i_static.
 189    </li>
 190     </ul>
 191     <ul xmlns:ld="http://lambdadelta.info/">
 192       <li>
 193         <span class="emph alpha">2017 April 16.</span>
 194          Strong rt-normalization
 195          for simply typed terms
 196          (anniversary milestone).
 197    </li>
 198     </ul>
 199     <ul xmlns:ld="http://lambdadelta.info/">
 200       <li>
 201         <span class="emph alpha">2017 March 16.</span>
 202          First behavioral component reconstructed:
 203          rt_transition.
 204    </li>
 205     </ul>
 206     <ul xmlns:ld="http://lambdadelta.info/">
 207       <li>
 208         <span class="emph alpha">2017 February 19.</span>
 209          Generic candidates of reducibility.
 210    </li>
 211     </ul>
 212     <ul xmlns:ld="http://lambdadelta.info/">
 213       <li>
 214         <span class="emph alpha">2017 January 17.</span>
 215          Confluence for parallel r-transition on referred entries of local environments.
 216    </li>
 217     </ul>
 218     <ul xmlns:ld="http://lambdadelta.info/">
 219       <li>
 220         <span class="emph alpha">2016 September 15.</span>
 221          Confluence for context-sensitive parallel r-transition on terms.
 222    </li>
 223     </ul>
 224     <ul xmlns:ld="http://lambdadelta.info/">
 225       <li>
 226         <span class="emph alpha">2016 April 16.</span>
 227          Syntactic component reconstructed:
 228          syntax, relocation, s_transition, s_computation, static
 229          (anniversary milestone).
 230    </li>
 231     </ul>
 232     <ul xmlns:ld="http://lambdadelta.info/">
 233       <li>
 234         <span class="emph alpha">2016 March 25.</span>
 235          Relocation with reference transforming maps (rtmap).
 236    </li>
 237     </ul>
 238     <ul xmlns:ld="http://lambdadelta.info/">
 239       <li>
 240         <span class="emph alpha">2015 October 9.</span>
 241          λδ version 2A2 is started.
 242    </li>
 243     </ul>
 244     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
 245     <ul xmlns:ld="http://lambdadelta.info/">
 246       <li>
 247         <span class="emph delta">2015 August 27.</span>
 248          λδ version 2A1 appears too complex and is dismissed.
 249    </li>
 250     </ul>
 251     <ul xmlns:ld="http://lambdadelta.info/">
 252       <li>
 253         <span class="emph gamma">2014 October 28.</span>
 254          λδ version 2A1 is released.
 255    </li>
 256     </ul>
 257     <ul xmlns:ld="http://lambdadelta.info/">
 258       <li>
 259         <span class="emph beta">2014 September 9.</span>
 260          Iterated static type assignment defined (more elegantly)
 261          as a primitive notion.
 262    </li>
 263     </ul>
 264     <ul xmlns:ld="http://lambdadelta.info/">
 265       <li>
 266         <span class="emph beta">2014 June 18.</span>
 267          Preservation of stratified native validity
 268          for context-sensitive computation on terms.
 269    </li>
 270     </ul>
 271     <ul xmlns:ld="http://lambdadelta.info/">
 272       <li>
 273         <span class="emph alpha">2014 June 9.</span>
 274          Strong qrst-normalization
 275          for simply typed terms.
 276    </li>
 277     </ul>
 278     <ul xmlns:ld="http://lambdadelta.info/">
 279       <li>
 280         <span class="emph alpha">2014 April 16.</span>
 281          Lazy equivalence on local environments
 282          added as q-step to rst-computation on closures
 283          (anniversary milestone).
 284    </li>
 285     </ul>
 286     <ul xmlns:ld="http://lambdadelta.info/">
 287       <li>
 288         <span class="emph alpha">2014 January 20.</span>
 289          Parametrized slicing on local environments
 290          comprises both versions of this operation
 291          (one from basic_1, the other used in basic_2 till now).
 292    </li>
 293     </ul>
 294     <ul xmlns:ld="http://lambdadelta.info/">
 295       <li>
 296         <span class="emph alpha">2013 August 7.</span>
 297          Passive support for global environments.
 298    </li>
 299     </ul>
 300     <ul xmlns:ld="http://lambdadelta.info/">
 301       <li>
 302         <span class="emph alpha">2013 July 27.</span>
 303          Reaxiomatized β-reductum as in rt-reduction.
 304    </li>
 305     </ul>
 306     <ul xmlns:ld="http://lambdadelta.info/">
 307       <li>
 308         <span class="emph alpha">2013 July 20.</span>
 309          Context-sensitive strong rt-normalization
 310          for simply typed terms.
 311    </li>
 312     </ul>
 313     <ul xmlns:ld="http://lambdadelta.info/">
 314       <li>
 315         <span class="emph alpha">2013 April 16.</span>
 316          Reaxiomatized substitution and reduction
 317          commute with respect to subclosure
 318          (anniversary milestone).
 319    </li>
 320     </ul>
 321     <ul xmlns:ld="http://lambdadelta.info/">
 322       <li>
 323         <span class="emph alpha">2013 March 16.</span>
 324          Mutual recursive preservation of stratified native validity
 325          for rst-computation on closures.
 326    </li>
 327     </ul>
 328     <ul xmlns:ld="http://lambdadelta.info/">
 329       <li>
 330         <span class="emph alpha">2012 October 16.</span>
 331          Confluence for context-free parallel reduction on closures.
 332    </li>
 333     </ul>
 334     <ul xmlns:ld="http://lambdadelta.info/">
 335       <li>
 336         <span class="emph alpha">2012 July 26.</span>
 337          Term binders polarized to control ζ-reduction (not released).
 338    </li>
 339     </ul>
 340     <ul xmlns:ld="http://lambdadelta.info/">
 341       <li>
 342         <span class="emph alpha">2012 April 16.</span>
 343          Context-sensitive subject equivalence
 344          for atomic arity assignment
 345          (anniversary milestone).
 346    </li>
 347     </ul>
 348     <ul xmlns:ld="http://lambdadelta.info/">
 349       <li>
 350         <span class="emph alpha">2012 March 15.</span>
 351          Context-sensitive strong normalization
 352          for simply typed terms.
 353    </li>
 354     </ul>
 355     <ul xmlns:ld="http://lambdadelta.info/">
 356       <li>
 357         <span class="emph alpha">2012 January 27.</span>
 358          Generic candidates of reducibility.
 359    </li>
 360     </ul>
 361     <ul xmlns:ld="http://lambdadelta.info/">
 362       <li>
 363         <span class="emph alpha">2011 September 21.</span>
 364          Confluence for context-sensitive parallel reduction on terms.
 365    </li>
 366     </ul>
 367     <ul xmlns:ld="http://lambdadelta.info/">
 368       <li>
 369         <span class="emph alpha">2011 September 6.</span>
 370          Confluence for context-free parallel reduction on terms.
 371    </li>
 372     </ul>
 373     <ul xmlns:ld="http://lambdadelta.info/">
 374       <li>
 375         <span class="emph alpha">2011 April 17.</span>
 376          λδ version 2 is started.
 377    </li>
 378     </ul>
 379     <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="structure">Logical Structure of the Specification <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png" />
 380     </div>
 381     <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
 382    </div>
 383     <div xmlns:ld="http://lambdadelta.info/" class="text">
 384       <table cellpadding="4" cellspacing="0">
 385         <tbody>
 386           <tr>
 387             <td class="snns top capitalize italic gray">component</td>
 388             <td class="snns top capitalize italic gray">section</td>
 389             <td class="snns top italic gray">plane</td>
 390             <td class="snns top gray">files</td>
 391             <td class="ssnn top gray">
 392               <br />
 393             </td>
 394           </tr>
 395           <tr>
 396             <td class="snns top capitalize italic blue">rt-conversion</td>
 397             <td class="snns top capitalize italic blue">context-sensitive parallel r-conversion</td>
 398             <td class="snns top italic blue">for terms</td>
 399             <td class="snns top blue">cpc ( ⦃?,?⦄ ⊢ ? ⬌[?] ? )</td>
 400             <td class="ssnn top blue">cpc_cpc</td>
 401           </tr>
 402           <tr>
 403             <td class="snns top capitalize italic sky">rt-computation</td>
 404             <td class="snns top capitalize italic sky">uncounted context-sensitive parallel rt-computation</td>
 405             <td class="snns top italic sky">refinement for lenvs</td>
 406             <td class="snns top sky">lsubsx ( ? ⊢ ? ⊆ⓧ[?,?,?] ? )</td>
 407             <td class="ssnn top sky">lsubsx_lfsx lsubsx_lsubsx</td>
 408           </tr>
 409           <tr>
 410             <td class="nnns top capitalize italic sky">
 411               <br />
 412             </td>
 413             <td class="nnns top capitalize italic sky">
 414               <br />
 415             </td>
 416             <td class="snns top italic sky">strongly normalizing for lenvs on referred entries</td>
 417             <td class="snns top sky">lfsx ( ? ⊢ ⬈*[?,?,?] 𝐒⦃?⦄ )</td>
 418             <td class="ssnn top sky">lfsx_drops lfsx_fqup lfsx_lfpxs lfsx_lfsx</td>
 419           </tr>
 420           <tr>
 421             <td class="nnns top capitalize italic sky">
 422               <br />
 423             </td>
 424             <td class="nnns top capitalize italic sky">
 425               <br />
 426             </td>
 427             <td class="snns top italic sky">strongly normalizing for term vectors</td>
 428             <td class="snns top sky">csx_vector ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )</td>
 429             <td class="ssnn top sky">csx_cnx_vector csx_csx_vector</td>
 430           </tr>
 431           <tr>
 432             <td class="nnns top capitalize italic sky">
 433               <br />
 434             </td>
 435             <td class="nnns top capitalize italic sky">
 436               <br />
 437             </td>
 438             <td class="snns top italic sky">strongly normalizing for terms</td>
 439             <td class="snns top sky">csx ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )</td>
 440             <td class="ssnn top sky">csx_simple csx_simple_theq csx_drops csx_lsubr csx_lfdeq csx_aaa csx_gcp csx_gcr csx_lfpx csx_cnx csx_cpxs csx_lfpxs csx_csx</td>
 441           </tr>
 442           <tr>
 443             <td class="nnns top capitalize italic sky">
 444               <br />
 445             </td>
 446             <td class="nnns top capitalize italic sky">
 447               <br />
 448             </td>
 449             <td class="snns top italic sky">for lenvs on referred entries</td>
 450             <td class="snns top sky">lfpxs ( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )</td>
 451             <td class="ssnn top sky">lfpxs_length lfpxs_drops lfpxs_fqup lfpxs_lfdeq lfpxs_aaa lfpxs_cpxs lfpxs_lpxs lfpxs_lfpxs</td>
 452           </tr>
 453           <tr>
 454             <td class="nnns top capitalize italic sky">
 455               <br />
 456             </td>
 457             <td class="nnns top capitalize italic sky">
 458               <br />
 459             </td>
 460             <td class="snns top italic sky">for lenvs on all entries</td>
 461             <td class="snns top sky">lpxs ( ⦃?,?⦄ ⊢ ⬈*[?] ? )</td>
 462             <td class="ssnn top sky">
 463               <br />
 464             </td>
 465           </tr>
 466           <tr>
 467             <td class="nnns top capitalize italic sky">
 468               <br />
 469             </td>
 470             <td class="nnns top capitalize italic sky">
 471               <br />
 472             </td>
 473             <td class="snns top italic sky">for terms</td>
 474             <td class="snns top sky">cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )</td>
 475             <td class="ssnn top sky">cpxs_tdeq cpxs_theq cpxs_theq_vector cpxs_drops cpxs_fqus cpxs_lsubr cpxs_lfdeq cpxs_aaa cpxs_lpx cpxs_lfpx cpxs_cnx cpxs_cpxs</td>
 476           </tr>
 477           <tr>
 478             <td class="snns top capitalize italic cyan">rt-transition</td>
 479             <td class="snns top capitalize italic cyan">uncounted parallel rst-transition</td>
 480             <td class="snns top italic cyan">for closures</td>
 481             <td class="snns top cyan">fpbq ( ⦃?,?,?⦄ ≽[?] ⦃?,?,?⦄ )</td>
 482             <td class="ssnn top cyan">fpbq_aaa</td>
 483           </tr>
 484           <tr>
 485             <td class="nnns top capitalize italic cyan">
 486               <br />
 487             </td>
 488             <td class="nnns top capitalize italic cyan">
 489               <br />
 490             </td>
 491             <td class="snns top italic cyan">proper for closures</td>
 492             <td class="snns top cyan">fpb ( ⦃?,?,?⦄ ≻[?] ⦃?,?,?⦄ )</td>
 493             <td class="ssnn top cyan">fpb_lfdeq</td>
 494           </tr>
 495           <tr>
 496             <td class="nnns top capitalize italic cyan">
 497               <br />
 498             </td>
 499             <td class="snns top capitalize italic cyan">context-sensitive parallel r-transition</td>
 500             <td class="snns top italic cyan">for lenvs on referred entries</td>
 501             <td class="snns top cyan">lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
 502             <td class="ssnn top cyan">lfpr_length lfpr_drops lfpr_fquq lfpr_fqup lfpr_frees lfpr_aaa lfpr_lfpx lfpr_lfpr</td>
 503           </tr>
 504           <tr>
 505             <td class="nnns top capitalize italic cyan">
 506               <br />
 507             </td>
 508             <td class="nnns top capitalize italic cyan">
 509               <br />
 510             </td>
 511             <td class="snns top italic cyan">for binders</td>
 512             <td class="snns top cyan">cpr_ext ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 513             <td class="ssnn top cyan">
 514               <br />
 515             </td>
 516           </tr>
 517           <tr>
 518             <td class="nnns top capitalize italic cyan">
 519               <br />
 520             </td>
 521             <td class="nnns top capitalize italic cyan">
 522               <br />
 523             </td>
 524             <td class="snns top italic cyan">for terms</td>
 525             <td class="snns top cyan">cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 526             <td class="ssnn top cyan">cpr_drops</td>
 527           </tr>
 528           <tr>
 529             <td class="nnns top capitalize italic cyan">
 530               <br />
 531             </td>
 532             <td class="snns top capitalize italic cyan">t-bound context-sensitive parallel rt-transition</td>
 533             <td class="snns top italic cyan">for terms</td>
 534             <td class="snns top cyan">cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
 535             <td class="ssnn top cyan">cpm_simple cpm_drops cpm_lsubr cpm_lfxs cpm_cpx</td>
 536           </tr>
 537           <tr>
 538             <td class="nnns top capitalize italic cyan">
 539               <br />
 540             </td>
 541             <td class="snns top capitalize italic cyan">uncounted context-sensitive parallel rt-transition</td>
 542             <td class="snns top italic cyan">normal form for terms</td>
 543             <td class="snns top cyan">cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )</td>
 544             <td class="ssnn top cyan">cnx_simple cnx_drops cnx_cnx</td>
 545           </tr>
 546           <tr>
 547             <td class="nnns top capitalize italic cyan">
 548               <br />
 549             </td>
 550             <td class="nnns top capitalize italic cyan">
 551               <br />
 552             </td>
 553             <td class="snns top italic cyan">for lenvs on referred entries</td>
 554             <td class="snns top cyan">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
 555             <td class="ssnn top cyan">lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_lfdeq lfpx_aaa lfpx_cpx lfpx_lfpx</td>
 556           </tr>
 557           <tr>
 558             <td class="nnns top capitalize italic cyan">
 559               <br />
 560             </td>
 561             <td class="nnns top capitalize italic cyan">
 562               <br />
 563             </td>
 564             <td class="snns top italic cyan">for lenvs on all entries</td>
 565             <td class="snns top cyan">lpx ( ⦃?,?⦄ ⊢ ⬈[?] ? )</td>
 566             <td class="ssnn top cyan">
 567               <br />
 568             </td>
 569           </tr>
 570           <tr>
 571             <td class="nnns top capitalize italic cyan">
 572               <br />
 573             </td>
 574             <td class="nnns top capitalize italic cyan">
 575               <br />
 576             </td>
 577             <td class="snns top italic cyan">for binders</td>
 578             <td class="snns top cyan">cpx_ext ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
 579             <td class="ssnn top cyan">
 580               <br />
 581             </td>
 582           </tr>
 583           <tr>
 584             <td class="nnns top capitalize italic cyan">
 585               <br />
 586             </td>
 587             <td class="nnns top capitalize italic cyan">
 588               <br />
 589             </td>
 590             <td class="snns top italic cyan">for terms</td>
 591             <td class="snns top cyan">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
 592             <td class="ssnn top cyan">cpx_simple cpx_drops cpx_fqus cpx_lsubr cpx_lfxs cpx_lfeq</td>
 593           </tr>
 594           <tr>
 595             <td class="nnns top capitalize italic cyan">
 596               <br />
 597             </td>
 598             <td class="snns top capitalize italic cyan">counted context-sensitive parallel rt-transition</td>
 599             <td class="snns top italic cyan">for terms</td>
 600             <td class="snns top cyan">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
 601             <td class="ssnn top cyan">cpg_simple cpg_drops cpg_lsubr</td>
 602           </tr>
 603           <tr>
 604             <td class="snns top capitalize italic water">iterated static typing</td>
 605             <td class="snns top capitalize italic water">iterated generic extension of a context-sensitive relation</td>
 606             <td class="snns top italic water">for lenvs on referred entries</td>
 607             <td class="snns top water">tc_lfxs ( ? ⦻**[?,?] ? )</td>
 608             <td class="ssnn top water">tc_lfxs_length tc_lfxs_lex tc_lfxs_drops tc_lfxs_fqup tc_lfxs_tc_lfxs</td>
 609           </tr>
 610           <tr>
 611             <td class="snns top capitalize italic green">static typing</td>
 612             <td class="snns top capitalize italic green">generic reducibility</td>
 613             <td class="snns top italic green">restricted refinement for lenvs</td>
 614             <td class="snns top green">lsubc ( ? ⊢ ? ⫃[?] ? )</td>
 615             <td class="ssnn top green">lsubc_drops lsubc_lsubr lsubc_lsuba</td>
 616           </tr>
 617           <tr>
 618             <td class="nnns top capitalize italic green">
 619               <br />
 620             </td>
 621             <td class="nnns top capitalize italic green">
 622               <br />
 623             </td>
 624             <td class="snns top italic green">candidates</td>
 625             <td class="snns top green">gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
 626             <td class="ssnn top green">gcp_aaa</td>
 627           </tr>
 628           <tr>
 629             <td class="nnns top capitalize italic green">
 630               <br />
 631             </td>
 632             <td class="nnns top capitalize italic green">
 633               <br />
 634             </td>
 635             <td class="snns top italic green">computation properties</td>
 636             <td class="snns top green">gcp</td>
 637             <td class="ssnn top green">
 638               <br />
 639             </td>
 640           </tr>
 641           <tr>
 642             <td class="nnns top capitalize italic green">
 643               <br />
 644             </td>
 645             <td class="snns top capitalize italic green">atomic arity assignment</td>
 646             <td class="snns top italic green">restricted refinement for lenvs</td>
 647             <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
 648             <td class="ssnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
 649           </tr>
 650           <tr>
 651             <td class="nnns top capitalize italic green">
 652               <br />
 653             </td>
 654             <td class="nnns top capitalize italic green">
 655               <br />
 656             </td>
 657             <td class="snns top italic green">for terms</td>
 658             <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 659             <td class="ssnn top green">aaa_drops aaa_fqus aaa_lfdeq aaa_aaa</td>
 660           </tr>
 661           <tr>
 662             <td class="nnns top capitalize italic green">
 663               <br />
 664             </td>
 665             <td class="snns top capitalize italic green">degree-based equivalence</td>
 666             <td class="snns top italic green">for closures on referred entries</td>
 667             <td class="snns top green">ffdeq ( ⦃?,?,?⦄ ≛[?,?] ⦃?,?,?⦄ )</td>
 668             <td class="ssnn top green">ffdeq_fqup ffdeq_ffdeq</td>
 669           </tr>
 670           <tr>
 671             <td class="nnns top capitalize italic green">
 672               <br />
 673             </td>
 674             <td class="nnns top capitalize italic green">
 675               <br />
 676             </td>
 677             <td class="snns top italic green">for lenvs on referred entries</td>
 678             <td class="snns top green">lfdeq ( ? ≛[?,?,?] ? )</td>
 679             <td class="ssnn top green">lfdeq_length lfdeq_drops lfdeq_fqup lfdeq_fqus lfdeq_lfdeq</td>
 680           </tr>
 681           <tr>
 682             <td class="nnns top capitalize italic green">
 683               <br />
 684             </td>
 685             <td class="snns top capitalize italic green">syntactic equivalence</td>
 686             <td class="snns top italic green">for lenvs on referred entries</td>
 687             <td class="snns top green">lfeq ( ? ≡[?] ? )</td>
 688             <td class="ssnn top green">lfeq_fqup lfeq_lfeq</td>
 689           </tr>
 690           <tr>
 691             <td class="nnns top capitalize italic green">
 692               <br />
 693             </td>
 694             <td class="snns top capitalize italic green">generic extension of a context-sensitive relation</td>
 695             <td class="snns top italic green">for lenvs on referred entries</td>
 696             <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
 697             <td class="ssnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
 698           </tr>
 699           <tr>
 700             <td class="nnns top capitalize italic green">
 701               <br />
 702             </td>
 703             <td class="snns top capitalize italic green">context-sensitive free variables</td>
 704             <td class="snns top italic green">restricted refinement for lenvs</td>
 705             <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
 706             <td class="ssnn top green">lsubf_lsubr lsubf_frees lsubf_lsubf</td>
 707           </tr>
 708           <tr>
 709             <td class="nnns top capitalize italic green">
 710               <br />
 711             </td>
 712             <td class="nnns top capitalize italic green">
 713               <br />
 714             </td>
 715             <td class="snns top italic green">for terms</td>
 716             <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 717             <td class="ssnn top green">frees_drops frees_fqup frees_frees</td>
 718           </tr>
 719           <tr>
 720             <td class="nnns top capitalize italic green">
 721               <br />
 722             </td>
 723             <td class="snns top capitalize italic green">local environments</td>
 724             <td class="snns top italic green">restricted refinement</td>
 725             <td class="snns top green">lsubr ( ? ⫃ ? )</td>
 726             <td class="ssnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
 727           </tr>
 728           <tr>
 729             <td class="snns top capitalize italic grass">s-computation</td>
 730             <td class="snns top capitalize italic grass">iterated structural successor</td>
 731             <td class="snns top italic grass">for closures</td>
 732             <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐*[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
 733             <td class="ssnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
 734           </tr>
 735           <tr>
 736             <td class="nnns top capitalize italic grass">
 737               <br />
 738             </td>
 739             <td class="nnns top capitalize italic grass">
 740               <br />
 741             </td>
 742             <td class="snns top italic grass">proper for closures</td>
 743             <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
 744             <td class="ssnn top grass">fqup_weight fqup_drops fqup_fqup</td>
 745           </tr>
 746           <tr>
 747             <td class="snns top capitalize italic yellow">s-transition</td>
 748             <td class="snns top capitalize italic yellow">structural successor</td>
 749             <td class="snns top italic yellow">for closures</td>
 750             <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
 751             <td class="ssnn top yellow">fquq_length fquq_weight</td>
 752           </tr>
 753           <tr>
 754             <td class="nnns top capitalize italic yellow">
 755               <br />
 756             </td>
 757             <td class="nnns top capitalize italic yellow">
 758               <br />
 759             </td>
 760             <td class="snns top italic yellow">proper for closures</td>
 761             <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
 762             <td class="ssnn top yellow">fqu_length fqu_weight</td>
 763           </tr>
 764           <tr>
 765             <td class="snns top capitalize italic orange">relocation</td>
 766             <td class="snns top capitalize italic orange">generic slicing</td>
 767             <td class="snns top italic orange">for lenvs</td>
 768             <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 769             <td class="ssnn top orange">drops_lstar drops_weight drops_length drops_cext2 drops_lexs drops_lreq drops_drops drops_vector</td>
 770           </tr>
 771           <tr>
 772             <td class="nnns top capitalize italic orange">
 773               <br />
 774             </td>
 775             <td class="snns top capitalize italic orange">generic relocation</td>
 776             <td class="snns top italic orange">for binders</td>
 777             <td class="snns top orange">lifts_bind ( ⬆*[?] ? ≡ ? )</td>
 778             <td class="ssnn top orange">lifts_weight_bind lifts_lifts_bind</td>
 779           </tr>
 780           <tr>
 781             <td class="nnns top capitalize italic orange">
 782               <br />
 783             </td>
 784             <td class="nnns top capitalize italic orange">
 785               <br />
 786             </td>
 787             <td class="snns top italic orange">for term vectors</td>
 788             <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 789             <td class="ssnn top orange">lifts_lifts_vector</td>
 790           </tr>
 791           <tr>
 792             <td class="nnns top capitalize italic orange">
 793               <br />
 794             </td>
 795             <td class="nnns top capitalize italic orange">
 796               <br />
 797             </td>
 798             <td class="snns top italic orange">for terms</td>
 799             <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
 800             <td class="ssnn top orange">lifts_simple lifts_weight lifts_tdeq lifts_lifts</td>
 801           </tr>
 802           <tr>
 803             <td class="nnns top capitalize italic orange">
 804               <br />
 805             </td>
 806             <td class="snns top capitalize italic orange">syntactic equivalence</td>
 807             <td class="snns top italic orange">for lenvs on selected entries</td>
 808             <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
 809             <td class="ssnn top orange">lreq_length lreq_lreq</td>
 810           </tr>
 811           <tr>
 812             <td class="nnns top capitalize italic orange">
 813               <br />
 814             </td>
 815             <td class="snns top capitalize italic orange">generic entrywise extension</td>
 816             <td class="snns top italic orange">for lenvs of one contex-sensitive relation</td>
 817             <td class="snns top orange">lex ( ? ⦻[?] ? )</td>
 818             <td class="ssnn top orange">lex_tc</td>
 819           </tr>
 820           <tr>
 821             <td class="nnns top capitalize italic orange">
 822               <br />
 823             </td>
 824             <td class="nnns top capitalize italic orange">
 825               <br />
 826             </td>
 827             <td class="snns top italic orange">for lenvs of two contex-sensitive relations</td>
 828             <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
 829             <td class="ssnn top orange">lexs_tc lexs_length lexs_lexs</td>
 830           </tr>
 831           <tr>
 832             <td class="snns top capitalize italic red">syntax</td>
 833             <td class="snns top capitalize italic red">append for local environments</td>
 834             <td class="snns top italic red" />
 835             <td class="snns top red">append ( ? @@ ? )</td>
 836             <td class="ssnn top red">append_length</td>
 837           </tr>
 838           <tr>
 839             <td class="nnns top capitalize italic red">
 840               <br />
 841             </td>
 842             <td class="snns top capitalize italic red">head equivalence for terms</td>
 843             <td class="snns top italic red" />
 844             <td class="snns top red">theq ( ? ⩳[?,?] ? )</td>
 845             <td class="ssnn top red">theq_simple theq_tdeq theq_theq theq_simple_vector</td>
 846           </tr>
 847           <tr>
 848             <td class="nnns top capitalize italic red">
 849               <br />
 850             </td>
 851             <td class="snns top capitalize italic red">degree-based equivalence</td>
 852             <td class="snns top italic red" />
 853             <td class="snns top red">tdeq_ext ( ? ≛[?,?] ? ) ( ? ⊢ ? ≛[?,?] ? )</td>
 854             <td class="ssnn top red">
 855               <br />
 856             </td>
 857           </tr>
 858           <tr>
 859             <td class="nnns top capitalize italic red">
 860               <br />
 861             </td>
 862             <td class="nnns top capitalize italic red">
 863               <br />
 864             </td>
 865             <td class="snns top italic red" />
 866             <td class="snns top red">tdeq ( ? ≛[?,?] ? )</td>
 867             <td class="ssnn top red">tdeq_tdeq</td>
 868           </tr>
 869           <tr>
 870             <td class="nnns top capitalize italic red">
 871               <br />
 872             </td>
 873             <td class="snns top capitalize italic red">closures</td>
 874             <td class="snns top italic red" />
 875             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 876             <td class="ssnn top red">
 877               <br />
 878             </td>
 879           </tr>
 880           <tr>
 881             <td class="nnns top capitalize italic red">
 882               <br />
 883             </td>
 884             <td class="nnns top capitalize italic red">
 885               <br />
 886             </td>
 887             <td class="snns top italic red" />
 888             <td class="snns top red">cl_restricted_weight ( ♯{?,?} )</td>
 889             <td class="ssnn top red">
 890               <br />
 891             </td>
 892           </tr>
 893           <tr>
 894             <td class="nnns top capitalize italic red">
 895               <br />
 896             </td>
 897             <td class="snns top capitalize italic red">global environments</td>
 898             <td class="snns top italic red" />
 899             <td class="snns top red">genv</td>
 900             <td class="ssnn top red">
 901               <br />
 902             </td>
 903           </tr>
 904           <tr>
 905             <td class="nnns top capitalize italic red">
 906               <br />
 907             </td>
 908             <td class="snns top capitalize italic red">local environments</td>
 909             <td class="snns top italic red" />
 910             <td class="snns top red">ceq_ext</td>
 911             <td class="ssnn top red">ceq_ext_ceq_ext</td>
 912           </tr>
 913           <tr>
 914             <td class="nnns top capitalize italic red">
 915               <br />
 916             </td>
 917             <td class="nnns top capitalize italic red">
 918               <br />
 919             </td>
 920             <td class="snns top italic red" />
 921             <td class="snns top red">cext2</td>
 922             <td class="ssnn top red">
 923               <br />
 924             </td>
 925           </tr>
 926           <tr>
 927             <td class="nnns top capitalize italic red">
 928               <br />
 929             </td>
 930             <td class="nnns top capitalize italic red">
 931               <br />
 932             </td>
 933             <td class="snns top italic red" />
 934             <td class="snns top red">lenv_length ( |?| )</td>
 935             <td class="ssnn top red">
 936               <br />
 937             </td>
 938           </tr>
 939           <tr>
 940             <td class="nnns top capitalize italic red">
 941               <br />
 942             </td>
 943             <td class="nnns top capitalize italic red">
 944               <br />
 945             </td>
 946             <td class="snns top italic red" />
 947             <td class="snns top red">lenv_weight ( ♯{?} )</td>
 948             <td class="ssnn top red">
 949               <br />
 950             </td>
 951           </tr>
 952           <tr>
 953             <td class="nnns top capitalize italic red">
 954               <br />
 955             </td>
 956             <td class="nnns top capitalize italic red">
 957               <br />
 958             </td>
 959             <td class="snns top italic red" />
 960             <td class="snns top red">lenv</td>
 961             <td class="ssnn top red">
 962               <br />
 963             </td>
 964           </tr>
 965           <tr>
 966             <td class="nnns top capitalize italic red">
 967               <br />
 968             </td>
 969             <td class="snns top capitalize italic red">binders for local environments</td>
 970             <td class="snns top italic red" />
 971             <td class="snns top red">ext2</td>
 972             <td class="ssnn top red">ext2_tc ext2_ext2</td>
 973           </tr>
 974           <tr>
 975             <td class="nnns top capitalize italic red">
 976               <br />
 977             </td>
 978             <td class="nnns top capitalize italic red">
 979               <br />
 980             </td>
 981             <td class="snns top italic red" />
 982             <td class="snns top red">bind</td>
 983             <td class="ssnn top red">bind_weight</td>
 984           </tr>
 985           <tr>
 986             <td class="nnns top capitalize italic red">
 987               <br />
 988             </td>
 989             <td class="snns top capitalize italic red">terms</td>
 990             <td class="snns top italic red" />
 991             <td class="snns top red">term_vector ( Ⓐ?.? )</td>
 992             <td class="ssnn top red">
 993               <br />
 994             </td>
 995           </tr>
 996           <tr>
 997             <td class="nnns top capitalize italic red">
 998               <br />
 999             </td>
1000             <td class="nnns top capitalize italic red">
1001               <br />
1002             </td>
1003             <td class="snns top italic red" />
1004             <td class="snns top red">term_simple ( 𝐒⦃?⦄ )</td>
1005             <td class="ssnn top red">
1006               <br />
1007             </td>
1008           </tr>
1009           <tr>
1010             <td class="nnns top capitalize italic red">
1011               <br />
1012             </td>
1013             <td class="nnns top capitalize italic red">
1014               <br />
1015             </td>
1016             <td class="snns top italic red" />
1017             <td class="snns top red">term_weight ( ♯{?} )</td>
1018             <td class="ssnn top red">
1019               <br />
1020             </td>
1021           </tr>
1022           <tr>
1023             <td class="nnns top capitalize italic red">
1024               <br />
1025             </td>
1026             <td class="nnns top capitalize italic red">
1027               <br />
1028             </td>
1029             <td class="snns top italic red" />
1030             <td class="snns top red">term</td>
1031             <td class="ssnn top red">
1032               <br />
1033             </td>
1034           </tr>
1035           <tr>
1036             <td class="nnns top capitalize italic red">
1037               <br />
1038             </td>
1039             <td class="snns top capitalize italic red">items</td>
1040             <td class="snns top italic red" />
1041             <td class="snns top red">item_sd</td>
1042             <td class="ssnn top red">
1043               <br />
1044             </td>
1045           </tr>
1046           <tr>
1047             <td class="nnns top capitalize italic red">
1048               <br />
1049             </td>
1050             <td class="nnns top capitalize italic red">
1051               <br />
1052             </td>
1053             <td class="snns top italic red" />
1054             <td class="snns top red">item_sh</td>
1055             <td class="ssnn top red">
1056               <br />
1057             </td>
1058           </tr>
1059           <tr>
1060             <td class="nnns top capitalize italic red">
1061               <br />
1062             </td>
1063             <td class="nnns top capitalize italic red">
1064               <br />
1065             </td>
1066             <td class="snns top italic red" />
1067             <td class="snns top red">item</td>
1068             <td class="ssnn top red">
1069               <br />
1070             </td>
1071           </tr>
1072           <tr>
1073             <td class="nnss top capitalize italic red">
1074               <br />
1075             </td>
1076             <td class="snss top capitalize italic red">atomic arities</td>
1077             <td class="snss top italic red" />
1078             <td class="snss top red">aarity</td>
1079             <td class="sssn top red">
1080               <br />
1081             </td>
1082           </tr>
1083         </tbody>
1084       </table>
1085     </div>
1086     <div class="spacer">
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