helm/www/lambdadelta/basic_2.html

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  10     <title>lambdadelta version 2</title>
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  22     <div class="head1">cic:/matita/lambdadelta/basic_2/ (λδ version 2)</div>
  23     <div class="spacer">
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  25     </div>
  26    <div xmlns:ld="http://lambdadelta.info/" class="head2">System's Syntax and Behavior</div>
  27    <div xmlns:ld="http://lambdadelta.info/" class="text">This is a summary of the "block structure"
  28          of the System's syntactic items and reductions.
  29    </div>
  30    <div xmlns:ld="http://lambdadelta.info/" class="text">
  31       <table cellpadding="4" cellspacing="0">
  32         <tbody>
  33           <tr>
  34             <td class="snns text grey">domain</td>
  35             <td class="snns plane grey">block</td>
  36             <td class="snns text grey">leader</td>
  37             <td class="snns text grey">applicator (with →θ)*</td>
  38             <td class="snns text grey">reduction</td>
  39             <td class="snns text grey">→ζ *</td>
  40             <td class="ssns text grey">reference *</td>
  41           </tr>
  42           <tr>
  43             <td class="snns text">{X | Γ ⊢ X : W}</td>
  44             <td class="snns plane wine">local typed abstraction *</td>
  45             <td class="snns text wine">Γ ⊢ +λW</td>
  46             <td class="snns text wine">ⓐV</td>
  47             <td class="snns text wine">→β</td>
  48             <td class="snns text wine">no</td>
  49             <td class="ssns text wine">#i</td>
  50           </tr>
  51           <tr>
  52             <td class="nnns text">
  53               <br />
  54             </td>
  55             <td class="snns plane magenta">local typed declaration **</td>
  56             <td class="snns text magenta">Γ ⊢ -λW</td>
  57             <td class="snns text magenta">ⓐV</td>
  58             <td class="snns text magenta">→β</td>
  59             <td class="snns text magenta">no</td>
  60             <td class="ssns text magenta">#i</td>
  61           </tr>
  62           <tr>
  63             <td class="nnns text">
  64               <br />
  65             </td>
  66             <td class="snns plane prune">global typed declaration ***</td>
  67             <td class="snns text prune">Γ ⊢ pλW</td>
  68             <td class="snns text prune">no</td>
  69             <td class="snns text prune">no</td>
  70             <td class="snns text prune">no</td>
  71             <td class="ssns text prune">$p</td>
  72           </tr>
  73           <tr>
  74             <td class="nnns text">
  75               <br />
  76             </td>
  77             <td class="snns plane blue">native type annotation *</td>
  78             <td class="snns text blue">Γ ⊢ ⓝW</td>
  79             <td class="snns text blue">no</td>
  80             <td class="snns text blue">no</td>
  81             <td class="snns text blue">yes</td>
  82             <td class="ssns text blue">no</td>
  83           </tr>
  84           <tr>
  85             <td class="snns text">{X | Γ ⊢ X = V}</td>
  86             <td class="snns plane sky">local abbreviation *</td>
  87             <td class="snns text sky">Γ ⊢ +δV</td>
  88             <td class="snns text sky">no</td>
  89             <td class="snns text sky">local →δ</td>
  90             <td class="snns text sky">yes</td>
  91             <td class="ssns text sky">#i</td>
  92           </tr>
  93           <tr>
  94             <td class="nnns text">
  95               <br />
  96             </td>
  97             <td class="snns plane cyan">local definition **</td>
  98             <td class="snns text cyan">Γ ⊢ -δV</td>
  99             <td class="snns text cyan">no</td>
 100             <td class="snns text cyan">local →δ</td>
 101             <td class="snns text cyan">no</td>
 102             <td class="ssns text cyan">#i</td>
 103           </tr>
 104           <tr>
 105             <td class="nnns text">
 106               <br />
 107             </td>
 108             <td class="snns plane water">global definition ***</td>
 109             <td class="snns text water">Γ ⊢ pδV</td>
 110             <td class="snns text water">no</td>
 111             <td class="snns text water">global →δ</td>
 112             <td class="snns text water">no</td>
 113             <td class="ssns text water">$p</td>
 114           </tr>
 115           <tr>
 116             <td class="snss text">no</td>
 117             <td class="snss plane green">sort ****</td>
 118             <td class="snss text green">Γ ⊢ ⋆k</td>
 119             <td class="snss text green">no</td>
 120             <td class="snss text green">no</td>
 121             <td class="snss text green">no</td>
 122             <td class="ssss text green">no</td>
 123           </tr>
 124         </tbody>
 125       </table>
 126     </div>
 127    <div xmlns:ld="http://lambdadelta.info/" class="text">* In terms only.
 128          ** In terms and local environments only.
 129          *** In global environments only.
 130          **** Sort level k in terms only.
 131    </div>
 132
 133    <div xmlns:ld="http://lambdadelta.info/" class="head2">Summary of the Specification</div>
 134    <div xmlns:ld="http://lambdadelta.info/" class="text">Here is a numerical acount of the specification's contents
 135          and its timeline.
 136          Nodes are counted according to the "intrinsinc complexity measure"
 137          [F. Guidi: "Procedural Representation of CIC Proof Terms"
 138          Journal of Automated Reasoning 44(1-2), Springer (February 2010),
 139          pp. 53-78].
 140    </div>
 141    <div xmlns:ld="http://lambdadelta.info/" class="text">
 142       <table cellpadding="4" cellspacing="0">
 143         <tbody>
 144           <tr>
 145             <td class="snns component grey">category</td>
 146             <td class="snns plane grey">objects</td>
 147             <td class="snnn number grey">
 148               <br />
 149             </td>
 150             <td class="snnn plane grey">
 151               <br />
 152             </td>
 153             <td class="snnn number grey">
 154               <br />
 155             </td>
 156             <td class="snnn plane grey">
 157               <br />
 158             </td>
 159             <td class="ssnn number grey">
 160               <br />
 161             </td>
 162           </tr>
 163           <tr>
 164             <td class="snns component cyan">sizes</td>
 165             <td class="snns plane cyan">files</td>
 166             <td class="snnn number cyan">282  </td>
 167             <td class="snns plane cyan">characters</td>
 168             <td class="snnn number cyan">424295</td>
 169             <td class="snns plane cyan">nodes</td>
 170             <td class="ssnn number cyan">1238363</td>
 171           </tr>
 172           <tr>
 173             <td class="snns component green">propositions</td>
 174             <td class="snns plane green">theorems</td>
 175             <td class="snnn number green">91</td>
 176             <td class="snns plane green">lemmas</td>
 177             <td class="snnn number green">863</td>
 178             <td class="snns plane green">total</td>
 179             <td class="ssnn number green">954</td>
 180           </tr>
 181           <tr>
 182             <td class="snss component yellow">concepts</td>
 183             <td class="snss plane yellow">declared</td>
 184             <td class="snsn number yellow">47</td>
 185             <td class="snss plane yellow">defined</td>
 186             <td class="snsn number yellow">85</td>
 187             <td class="snss plane yellow">total</td>
 188             <td class="sssn number yellow">132</td>
 189           </tr>
 190         </tbody>
 191       </table>
 192     </div>
 193    <ul xmlns:ld="http://lambdadelta.info/">
 194       <li>
 195         <span class="date">In progress.</span>
 196          Context-sensitive subject equivalence
 197          for native type assignment.
 198    </li>
 199     </ul>
 200    <ul xmlns:ld="http://lambdadelta.info/">
 201       <li>
 202         <span class="date">In progress.</span>
 203          Closure of context-sensitive extended computation
 204          for native validity.
 205    </li>
 206     </ul>
 207    <ul xmlns:ld="http://lambdadelta.info/">
 208       <li>
 209         <span class="date">2013 August 7.</span>
 210          Passive support for global environments.
 211    </li>
 212     </ul>
 213    <ul xmlns:ld="http://lambdadelta.info/">
 214       <li>
 215         <span class="date">2013 July 27.</span>
 216          Reaxiomatized β-reductum as in extended β-reduction
 217    </li>
 218     </ul>
 219    <ul xmlns:ld="http://lambdadelta.info/">
 220       <li>
 221         <span class="date">2013 July 20.</span>
 222          Context-sensitive extended strong normalization
 223          for simply typed terms.
 224    </li>
 225     </ul>
 226    <ul xmlns:ld="http://lambdadelta.info/">
 227       <li>
 228         <span class="date">2013 April 16.</span>
 229          Reaxiomatized substitution and reduction
 230          commute with respect to subclosure
 231          (anniversary milestone).
 232    </li>
 233     </ul>
 234    <ul xmlns:ld="http://lambdadelta.info/">
 235       <li>
 236         <span class="date">2013 March 16.</span>
 237          Mutual recursive preservation of stratified native validity
 238          for hyper computation on closures.
 239    </li>
 240     </ul>
 241    <ul xmlns:ld="http://lambdadelta.info/">
 242       <li>
 243         <span class="date">2012 October 16.</span>
 244          Confluence for context-free parallel reduction on closures.
 245    </li>
 246     </ul>
 247    <ul xmlns:ld="http://lambdadelta.info/">
 248       <li>
 249         <span class="date">2012 July 26.</span>
 250          Term binders polarized to control ζ-reduction.
 251    </li>
 252     </ul>
 253    <ul xmlns:ld="http://lambdadelta.info/">
 254       <li>
 255         <span class="date">2012 April 16.</span>
 256          Context-sensitive subject equivalence
 257          for atomic arity assignment
 258          (anniversary milestone).
 259    </li>
 260     </ul>
 261    <ul xmlns:ld="http://lambdadelta.info/">
 262       <li>
 263         <span class="date">2012 March 15.</span>
 264          Context-sensitive strong normalization
 265          for simply typed terms.
 266    </li>
 267     </ul>
 268    <ul xmlns:ld="http://lambdadelta.info/">
 269       <li>
 270         <span class="date">2012 January 27.</span>
 271          Support for abstract candidates of reducibility.
 272    </li>
 273     </ul>
 274    <ul xmlns:ld="http://lambdadelta.info/">
 275       <li>
 276         <span class="date">2011 September 21.</span>
 277          Confluence for context-sensitive parallel reduction on terms.
 278    </li>
 279     </ul>
 280    <ul xmlns:ld="http://lambdadelta.info/">
 281       <li>
 282         <span class="date">2011 September 6.</span>
 283          Confluence for context-free parallel reduction on terms.
 284    </li>
 285     </ul>
 286    <ul xmlns:ld="http://lambdadelta.info/">
 287       <li>
 288         <span class="date">2011 April 17.</span>
 289          Specification starts.
 290    </li>
 291     </ul>
 292
 293    <div xmlns:ld="http://lambdadelta.info/" class="head2">Logical Structure of the Specification</div>
 294    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in planes and components
 295          according to the following table.
 296          A notation file covering the whole specification is provided.
 297          The notation for the relations or functions introduced in each file
 298          is shown in parentheses (? are placeholders).
 299    </div>
 300    <div xmlns:ld="http://lambdadelta.info/" class="text">
 301       <table cellpadding="4" cellspacing="0">
 302         <tbody>
 303           <tr>
 304             <td class="snns component grey">component</td>
 305             <td class="snns plane grey">plane</td>
 306             <td class="snns file grey">files</td>
 307             <td class="snnn file grey">
 308               <br />
 309             </td>
 310             <td class="snnn file grey">
 311               <br />
 312             </td>
 313             <td class="ssnn file grey">
 314               <br />
 315             </td>
 316           </tr>
 317           <tr>
 318             <td class="snns component prune">dynamic typing</td>
 319             <td class="snns plane prune">local env. ref. for stratified native validity</td>
 320             <td class="snns file prune">lsubsv ( ? ⊢ ? ¡⊑[?,?] ? )</td>
 321             <td class="snnn file prune">lsubsv_ldrop lsubsv_lsubd lsubsv_lsuba lsubsv_lsstas lsubsv_cpds lsubsv_cpcs lsubsv_snv</td>
 322             <td class="snnn file prune">
 323               <br />
 324             </td>
 325             <td class="ssnn file prune">
 326               <br />
 327             </td>
 328           </tr>
 329           <tr>
 330             <td class="nnns component prune">
 331               <br />
 332             </td>
 333             <td class="snns plane prune">stratified native validity</td>
 334             <td class="snns file prune">snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )</td>
 335             <td class="snnn file prune">snv_lift snv_da_lpr snv_aaa snv_lsstas snv_lsstas_lpr snv_lpr snv_cpcs</td>
 336             <td class="snnn file prune">
 337               <br />
 338             </td>
 339             <td class="ssnn file prune">
 340               <br />
 341             </td>
 342           </tr>
 343           <tr>
 344             <td class="snns component blue">equivalence</td>
 345             <td class="snns plane blue">decomposed extended equivalence</td>
 346             <td class="snns file blue">cpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?] ? )</td>
 347             <td class="snnn file blue">cpes_cpds</td>
 348             <td class="snnn file blue">
 349               <br />
 350             </td>
 351             <td class="ssnn file blue">
 352               <br />
 353             </td>
 354           </tr>
 355           <tr>
 356             <td class="nnns component blue">
 357               <br />
 358             </td>
 359             <td class="snns plane blue">context-sensitive equivalence</td>
 360             <td class="snns file blue">cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )</td>
 361             <td class="snnn file blue">cpcs_aaa cpcs_cprs cpcs_cpcs</td>
 362             <td class="snnn file blue">
 363               <br />
 364             </td>
 365             <td class="ssnn file blue">
 366               <br />
 367             </td>
 368           </tr>
 369           <tr>
 370             <td class="snns component sky">conversion</td>
 371             <td class="snns plane sky">context-sensitive conversion</td>
 372             <td class="snns file sky">cpc ( ⦃?,?⦄ ⊢ ? ⬌ ? )</td>
 373             <td class="snnn file sky">cpc_cpc</td>
 374             <td class="snnn file sky">
 375               <br />
 376             </td>
 377             <td class="ssnn file sky">
 378               <br />
 379             </td>
 380           </tr>
 381           <tr>
 382             <td class="snns component cyan">computation</td>
 383             <td class="snns plane cyan">context-sensitive extended evaluation</td>
 384             <td class="snns file cyan">cpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ )</td>
 385             <td class="snnn file cyan">
 386               <br />
 387             </td>
 388             <td class="snnn file cyan">
 389               <br />
 390             </td>
 391             <td class="ssnn file cyan">
 392               <br />
 393             </td>
 394           </tr>
 395           <tr>
 396             <td class="nnns component cyan">
 397               <br />
 398             </td>
 399             <td class="snns plane cyan">context-sensitive evaluation</td>
 400             <td class="snns file cyan">cpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )</td>
 401             <td class="snnn file cyan">cpre_cpre</td>
 402             <td class="snnn file cyan">
 403               <br />
 404             </td>
 405             <td class="ssnn file cyan">
 406               <br />
 407             </td>
 408           </tr>
 409           <tr>
 410             <td class="nnns component cyan">
 411               <br />
 412             </td>
 413             <td class="snns plane cyan">strongly normalizing "big tree" computation</td>
 414             <td class="snns file cyan">fsb ( ⦃?,?⦄ ⊢ ⦥[?,?] ? )</td>
 415             <td class="snnn file cyan">fsb_alt ( ⦃?,?⦄ ⊢ ⦥⦥[?,?] ? )</td>
 416             <td class="snnn file cyan">fsb_csx</td>
 417             <td class="ssnn file cyan">
 418               <br />
 419             </td>
 420           </tr>
 421           <tr>
 422             <td class="nnns component cyan">
 423               <br />
 424             </td>
 425             <td class="snns plane cyan">strongly normalizing extended computation</td>
 426             <td class="snns file cyan">csx_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )</td>
 427             <td class="snnn file cyan">csx_tstc_vector csx_aaa</td>
 428             <td class="snnn file cyan">
 429               <br />
 430             </td>
 431             <td class="ssnn file cyan">
 432               <br />
 433             </td>
 434           </tr>
 435           <tr>
 436             <td class="nnns component cyan">
 437               <br />
 438             </td>
 439             <td class="nnns plane cyan">
 440               <br />
 441             </td>
 442             <td class="snns file cyan">csx ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )</td>
 443             <td class="snnn file cyan">csx_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )</td>
 444             <td class="snnn file cyan">csx_lift csx_lpx</td>
 445             <td class="ssnn file cyan">
 446               <br />
 447             </td>
 448           </tr>
 449           <tr>
 450             <td class="nnns component cyan">
 451               <br />
 452             </td>
 453             <td class="snns plane cyan">"big tree" parallel computation</td>
 454             <td class="snns file cyan">fpbg ( ⦃?,?,?⦄ &gt;[?,?] ⦃?,?,?⦄ )</td>
 455             <td class="snnn file cyan">fpbg_alt</td>
 456             <td class="snnn file cyan">fpbg_lift fpbg_fpbg</td>
 457             <td class="ssnn file cyan">
 458               <br />
 459             </td>
 460           </tr>
 461           <tr>
 462             <td class="nnns component cyan">
 463               <br />
 464             </td>
 465             <td class="nnns plane cyan">
 466               <br />
 467             </td>
 468             <td class="snns file cyan">fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )</td>
 469             <td class="snnn file cyan">fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )</td>
 470             <td class="snnn file cyan">fpbs_lift fpbs_fpbs</td>
 471             <td class="ssnn file cyan">
 472               <br />
 473             </td>
 474           </tr>
 475           <tr>
 476             <td class="nnns component cyan">
 477               <br />
 478             </td>
 479             <td class="snns plane cyan">decomposed extended computation</td>
 480             <td class="snns file cyan">cpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?] ? )</td>
 481             <td class="snnn file cyan">cpds_lift cpds_aaa cpds_cpds</td>
 482             <td class="snnn file cyan">
 483               <br />
 484             </td>
 485             <td class="ssnn file cyan">
 486               <br />
 487             </td>
 488           </tr>
 489           <tr>
 490             <td class="nnns component cyan">
 491               <br />
 492             </td>
 493             <td class="snns plane cyan">context-sensitive extended computation</td>
 494             <td class="snns file cyan">lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )</td>
 495             <td class="snnn file cyan">lpxs_alt ( ⦃?,?⦄ ⊢ ➡➡*[?,?] ? )</td>
 496             <td class="snnn file cyan">lpxs_ldrop lpxs_aaa lpxs_cpxs lpxs_lpxs</td>
 497             <td class="ssnn file cyan">
 498               <br />
 499             </td>
 500           </tr>
 501           <tr>
 502             <td class="nnns component cyan">
 503               <br />
 504             </td>
 505             <td class="nnns plane cyan">
 506               <br />
 507             </td>
 508             <td class="snns file cyan">cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )</td>
 509             <td class="snnn file cyan">cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_aaa cpxs_cpxs</td>
 510             <td class="snnn file cyan">
 511               <br />
 512             </td>
 513             <td class="ssnn file cyan">
 514               <br />
 515             </td>
 516           </tr>
 517           <tr>
 518             <td class="nnns component cyan">
 519               <br />
 520             </td>
 521             <td class="snns plane cyan">context-sensitive computation</td>
 522             <td class="snns file cyan">lprs ( ⦃?,?⦄ ⊢ ➡* ? )</td>
 523             <td class="snnn file cyan">lprs_alt ( ⦃?,?⦄ ⊢ ➡➡* ? )</td>
 524             <td class="snnn file cyan">lprs_ldrop lprs_cprs lprs_lprs</td>
 525             <td class="ssnn file cyan">
 526               <br />
 527             </td>
 528           </tr>
 529           <tr>
 530             <td class="nnns component cyan">
 531               <br />
 532             </td>
 533             <td class="nnns plane cyan">
 534               <br />
 535             </td>
 536             <td class="snns file cyan">cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)</td>
 537             <td class="snnn file cyan">cprs_lift cprs_cprs</td>
 538             <td class="snnn file cyan">
 539               <br />
 540             </td>
 541             <td class="ssnn file cyan">
 542               <br />
 543             </td>
 544           </tr>
 545           <tr>
 546             <td class="nnns component cyan">
 547               <br />
 548             </td>
 549             <td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</td>
 550             <td class="snns file cyan">lsubc ( ? ⊢ ? ⊑[?] ? )</td>
 551             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
 552             <td class="snnn file cyan">
 553               <br />
 554             </td>
 555             <td class="ssnn file cyan">
 556               <br />
 557             </td>
 558           </tr>
 559           <tr>
 560             <td class="nnns component cyan">
 561               <br />
 562             </td>
 563             <td class="snns plane cyan">support for abstract computation properties</td>
 564             <td class="snns file cyan">acp</td>
 565             <td class="snnn file cyan">acp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
 566             <td class="snnn file cyan">acp_aaa</td>
 567             <td class="ssnn file cyan">
 568               <br />
 569             </td>
 570           </tr>
 571           <tr>
 572             <td class="snns component water">reduction</td>
 573             <td class="snns plane water">"big tree" parallel reduction</td>
 574             <td class="snns file water">fpbc ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )</td>
 575             <td class="snnn file water">fpbc_lift</td>
 576             <td class="snnn file water">
 577               <br />
 578             </td>
 579             <td class="ssnn file water">
 580               <br />
 581             </td>
 582           </tr>
 583           <tr>
 584             <td class="nnns component water">
 585               <br />
 586             </td>
 587             <td class="nnns plane water">
 588               <br />
 589             </td>
 590             <td class="snns file water">fpb ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )</td>
 591             <td class="snnn file water">fpb_lift</td>
 592             <td class="snnn file water">
 593               <br />
 594             </td>
 595             <td class="ssnn file water">
 596               <br />
 597             </td>
 598           </tr>
 599           <tr>
 600             <td class="nnns component water">
 601               <br />
 602             </td>
 603             <td class="snns plane water">context-sensitive extended normal forms</td>
 604             <td class="snns file water">cnx ( ⦃?,?⦄ ⊢ 𝐍[?,?]⦃?⦄ )</td>
 605             <td class="snnn file water">cnx_lift cnx_crx cnx_cix</td>
 606             <td class="snnn file water">
 607               <br />
 608             </td>
 609             <td class="ssnn file water">
 610               <br />
 611             </td>
 612           </tr>
 613           <tr>
 614             <td class="nnns component water">
 615               <br />
 616             </td>
 617             <td class="snns plane water">context-sensitive extended reduction</td>
 618             <td class="snns file water">lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
 619             <td class="snnn file water">lpx_ldrop lpx_aaa</td>
 620             <td class="snnn file water">
 621               <br />
 622             </td>
 623             <td class="ssnn file water">
 624               <br />
 625             </td>
 626           </tr>
 627           <tr>
 628             <td class="nnns component water">
 629               <br />
 630             </td>
 631             <td class="nnns plane water">
 632               <br />
 633             </td>
 634             <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
 635             <td class="snnn file water">cpx_lift cpx_cix</td>
 636             <td class="snnn file water">
 637               <br />
 638             </td>
 639             <td class="ssnn file water">
 640               <br />
 641             </td>
 642           </tr>
 643           <tr>
 644             <td class="nnns component water">
 645               <br />
 646             </td>
 647             <td class="snns plane water">context-sensitive extended irreducible forms</td>
 648             <td class="snns file water">cix ( ⦃?,?⦄ ⊢ 𝐈[?,?]⦃?⦄ )</td>
 649             <td class="snnn file water">cix_append cix_lift</td>
 650             <td class="snnn file water">
 651               <br />
 652             </td>
 653             <td class="ssnn file water">
 654               <br />
 655             </td>
 656           </tr>
 657           <tr>
 658             <td class="nnns component water">
 659               <br />
 660             </td>
 661             <td class="snns plane water">context-sensitive extended reducible forms</td>
 662             <td class="snns file water">crx ( ⦃?,?⦄ ⊢ 𝐑[?,?]⦃?⦄ )</td>
 663             <td class="snnn file water">crx_append crx_lift</td>
 664             <td class="snnn file water">
 665               <br />
 666             </td>
 667             <td class="ssnn file water">
 668               <br />
 669             </td>
 670           </tr>
 671           <tr>
 672             <td class="nnns component water">
 673               <br />
 674             </td>
 675             <td class="snns plane water">context-sensitive normal forms</td>
 676             <td class="snns file water">cnr ( ⦃?,?⦄ ⊢ 𝐍⦃?⦄ )</td>
 677             <td class="snnn file water">cnr_lift cnr_crr cnr_cir</td>
 678             <td class="snnn file water">
 679               <br />
 680             </td>
 681             <td class="ssnn file water">
 682               <br />
 683             </td>
 684           </tr>
 685           <tr>
 686             <td class="nnns component water">
 687               <br />
 688             </td>
 689             <td class="snns plane water">context-sensitive reduction</td>
 690             <td class="snns file water">lpr ( ⦃?,?⦄ ⊢ ➡ ? )</td>
 691             <td class="snnn file water">lpr_ldrop lpr_lpr</td>
 692             <td class="snnn file water">
 693               <br />
 694             </td>
 695             <td class="ssnn file water">
 696               <br />
 697             </td>
 698           </tr>
 699           <tr>
 700             <td class="nnns component water">
 701               <br />
 702             </td>
 703             <td class="nnns plane water">
 704               <br />
 705             </td>
 706             <td class="snns file water">cpr ( ⦃?,?⦄ ⊢ ? ➡ ? )</td>
 707             <td class="snnn file water">cpr_lift cpr_cir</td>
 708             <td class="snnn file water">
 709               <br />
 710             </td>
 711             <td class="ssnn file water">
 712               <br />
 713             </td>
 714           </tr>
 715           <tr>
 716             <td class="nnns component water">
 717               <br />
 718             </td>
 719             <td class="snns plane water">context-sensitive irreducible forms</td>
 720             <td class="snns file water">cir ( ⦃?,?⦄ ⊢ 𝐈⦃?⦄ )</td>
 721             <td class="snnn file water">cir_append cir_lift</td>
 722             <td class="snnn file water">
 723               <br />
 724             </td>
 725             <td class="ssnn file water">
 726               <br />
 727             </td>
 728           </tr>
 729           <tr>
 730             <td class="nnns component water">
 731               <br />
 732             </td>
 733             <td class="snns plane water">context-sensitive reducible forms</td>
 734             <td class="snns file water">crr ( ⦃?,?⦄ ⊢ 𝐑⦃?⦄ )</td>
 735             <td class="snnn file water">crr_append crr_lift</td>
 736             <td class="snnn file water">
 737               <br />
 738             </td>
 739             <td class="ssnn file water">
 740               <br />
 741             </td>
 742           </tr>
 743           <tr>
 744             <td class="snns component green">unfold</td>
 745             <td class="snns plane green">unfold</td>
 746             <td class="snns file green">unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )</td>
 747             <td class="snnn file green">
 748               <br />
 749             </td>
 750             <td class="snnn file green">
 751               <br />
 752             </td>
 753             <td class="ssnn file green">
 754               <br />
 755             </td>
 756           </tr>
 757           <tr>
 758             <td class="nnns component green">
 759               <br />
 760             </td>
 761             <td class="snns plane green">iterated static type assignment</td>
 762             <td class="snns file green">lsstas ( ⦃?,?⦄ ⊢ ? •*[?,?,?] ? )</td>
 763             <td class="snnn file green">lsstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?,?] ? )</td>
 764             <td class="snnn file green">lsstas_lift lsstas_aaa lsstas_lsstas</td>
 765             <td class="ssnn file green">
 766               <br />
 767             </td>
 768           </tr>
 769           <tr>
 770             <td class="snns component grass">static typing</td>
 771             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
 772             <td class="snns file grass">lsuba ( ? ⊢ ? ⁝⊑ ? )</td>
 773             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
 774             <td class="snnn file grass">
 775               <br />
 776             </td>
 777             <td class="ssnn file grass">
 778               <br />
 779             </td>
 780           </tr>
 781           <tr>
 782             <td class="nnns component grass">
 783               <br />
 784             </td>
 785             <td class="snns plane grass">atomic arity assignment</td>
 786             <td class="snns file grass">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 787             <td class="snnn file grass">aaa_lift aaa_lifts aaa_da aaa_ssta aaa_aaa</td>
 788             <td class="snnn file grass">
 789               <br />
 790             </td>
 791             <td class="ssnn file grass">
 792               <br />
 793             </td>
 794           </tr>
 795           <tr>
 796             <td class="nnns component grass">
 797               <br />
 798             </td>
 799             <td class="snns plane grass">stratified static type assignment</td>
 800             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 801             <td class="snnn file grass">ssta_lift ssta_ssta</td>
 802             <td class="snnn file grass">
 803               <br />
 804             </td>
 805             <td class="ssnn file grass">
 806               <br />
 807             </td>
 808           </tr>
 809           <tr>
 810             <td class="nnns component grass">
 811               <br />
 812             </td>
 813             <td class="snns plane grass">local env. ref. for degree assignment</td>
 814             <td class="snns file grass">lsubd ( ? ⊢ ? ▪⊑ ? )</td>
 815             <td class="snnn file grass">lsubd_da lsubd_lsubd</td>
 816             <td class="snnn file grass">
 817               <br />
 818             </td>
 819             <td class="ssnn file grass">
 820               <br />
 821             </td>
 822           </tr>
 823           <tr>
 824             <td class="nnns component grass">
 825               <br />
 826             </td>
 827             <td class="snns plane grass">degree assignment</td>
 828             <td class="snns file grass">da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )</td>
 829             <td class="snnn file grass">da_lift da_da</td>
 830             <td class="snnn file grass">
 831               <br />
 832             </td>
 833             <td class="ssnn file grass">
 834               <br />
 835             </td>
 836           </tr>
 837           <tr>
 838             <td class="nnns component grass">
 839               <br />
 840             </td>
 841             <td class="snns plane grass">parameters</td>
 842             <td class="snns file grass">sh</td>
 843             <td class="snnn file grass">sd</td>
 844             <td class="snnn file grass">
 845               <br />
 846             </td>
 847             <td class="ssnn file grass">
 848               <br />
 849             </td>
 850           </tr>
 851           <tr>
 852             <td class="snns component yellow">substitution</td>
 853             <td class="snns plane yellow">restricted local env. ref.</td>
 854             <td class="snns file yellow">lsubr ( ? ⊑ ? )</td>
 855             <td class="snnn file yellow">lsubr_lsubr</td>
 856             <td class="snnn file yellow">
 857               <br />
 858             </td>
 859             <td class="ssnn file yellow">
 860               <br />
 861             </td>
 862           </tr>
 863           <tr>
 864             <td class="nnns component yellow">
 865               <br />
 866             </td>
 867             <td class="snns plane yellow">iterated structural successor for closures</td>
 868             <td class="snns file yellow">fqus ( ⦃?,?,?⦄ ⊃* ⦃?,?,?⦄ )</td>
 869             <td class="snnn file yellow">fqus_alt</td>
 870             <td class="snnn file yellow">fqus_fqus</td>
 871             <td class="ssnn file yellow">
 872               <br />
 873             </td>
 874           </tr>
 875           <tr>
 876             <td class="nnns component yellow">
 877               <br />
 878             </td>
 879             <td class="nnns plane yellow">
 880               <br />
 881             </td>
 882             <td class="snns file yellow">fqup ( ⦃?,?,?⦄ ⊃+ ⦃?,?,?⦄ )</td>
 883             <td class="snnn file yellow">fqup_fqup</td>
 884             <td class="snnn file yellow">
 885               <br />
 886             </td>
 887             <td class="ssnn file yellow">
 888               <br />
 889             </td>
 890           </tr>
 891           <tr>
 892             <td class="nnns component yellow">
 893               <br />
 894             </td>
 895             <td class="snns plane yellow">generic local env. slicing</td>
 896             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
 897             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
 898             <td class="snnn file yellow">
 899               <br />
 900             </td>
 901             <td class="ssnn file yellow">
 902               <br />
 903             </td>
 904           </tr>
 905           <tr>
 906             <td class="nnns component yellow">
 907               <br />
 908             </td>
 909             <td class="snns plane yellow">generic term relocation</td>
 910             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
 911             <td class="snnn file yellow">lifts_lift_vector</td>
 912             <td class="snnn file yellow">
 913               <br />
 914             </td>
 915             <td class="ssnn file yellow">
 916               <br />
 917             </td>
 918           </tr>
 919           <tr>
 920             <td class="nnns component yellow">
 921               <br />
 922             </td>
 923             <td class="nnns plane yellow">
 924               <br />
 925             </td>
 926             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
 927             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
 928             <td class="snnn file yellow">
 929               <br />
 930             </td>
 931             <td class="ssnn file yellow">
 932               <br />
 933             </td>
 934           </tr>
 935           <tr>
 936             <td class="nnns component yellow">
 937               <br />
 938             </td>
 939             <td class="snns plane yellow">support for generic relocation</td>
 940             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
 941             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
 942             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
 943             <td class="ssnn file yellow">gr2_gr2</td>
 944           </tr>
 945           <tr>
 946             <td class="snns component orange">relocation</td>
 947             <td class="snns plane orange">structural successor for closures</td>
 948             <td class="snns file orange">fqu ( ⦃?,?,?⦄ ⊃ ⦃?,?,?⦄ )</td>
 949             <td class="snnn file orange">fquq ( ⦃?,?,?⦄ ⊃⸮ ⦃?,?,?⦄ )</td>
 950             <td class="snnn file orange">fquq_alt ( ⦃?,?,?⦄ ⊃⊃⸮ ⦃?,?,?⦄ )</td>
 951             <td class="ssnn file orange">
 952               <br />
 953             </td>
 954           </tr>
 955           <tr>
 956             <td class="nnns component orange">
 957               <br />
 958             </td>
 959             <td class="snns plane orange">global env. slicing</td>
 960             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
 961             <td class="snnn file orange">gdrop_gdrop</td>
 962             <td class="snnn file orange">
 963               <br />
 964             </td>
 965             <td class="ssnn file orange">
 966               <br />
 967             </td>
 968           </tr>
 969           <tr>
 970             <td class="nnns component orange">
 971               <br />
 972             </td>
 973             <td class="snns plane orange">basic local env. slicing</td>
 974             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
 975             <td class="snnn file orange">ldrop_append ldrop_lpx_sn ldrop_ldrop</td>
 976             <td class="snnn file orange">
 977               <br />
 978             </td>
 979             <td class="ssnn file orange">
 980               <br />
 981             </td>
 982           </tr>
 983           <tr>
 984             <td class="nnns component orange">
 985               <br />
 986             </td>
 987             <td class="snns plane orange">basic term relocation</td>
 988             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
 989             <td class="snnn file orange">lift_lift_vector</td>
 990             <td class="snnn file orange">
 991               <br />
 992             </td>
 993             <td class="ssnn file orange">
 994               <br />
 995             </td>
 996           </tr>
 997           <tr>
 998             <td class="nnns component orange">
 999               <br />
1000             </td>
1001             <td class="nnns plane orange">
1002               <br />
1003             </td>
1004             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
1005             <td class="snnn file orange">lift_lift</td>
1006             <td class="snnn file orange">
1007               <br />
1008             </td>
1009             <td class="ssnn file orange">
1010               <br />
1011             </td>
1012           </tr>
1013           <tr>
1014             <td class="snns component red">grammar</td>
1015             <td class="snns plane red">pointwise extension of a relation</td>
1016             <td class="snns file red">lpx_sn</td>
1017             <td class="snnn file red">lpx_sn_tc lpx_sn_lpx_sn</td>
1018             <td class="snnn file red">
1019               <br />
1020             </td>
1021             <td class="ssnn file red">
1022               <br />
1023             </td>
1024           </tr>
1025           <tr>
1026             <td class="nnns component red">
1027               <br />
1028             </td>
1029             <td class="snns plane red">same top term constructor</td>
1030             <td class="snns file red">tstc ( ? ≃ ? )</td>
1031             <td class="snnn file red">tstc_tstc tstc_vector</td>
1032             <td class="snnn file red">
1033               <br />
1034             </td>
1035             <td class="ssnn file red">
1036               <br />
1037             </td>
1038           </tr>
1039           <tr>
1040             <td class="nnns component red">
1041               <br />
1042             </td>
1043             <td class="snns plane red">closures</td>
1044             <td class="snns file red">cl_shift ( ? @@ ? )</td>
1045             <td class="snnn file red">cl_weight ( ♯{?,?,?} )</td>
1046             <td class="snnn file red">
1047               <br />
1048             </td>
1049             <td class="ssnn file red">
1050               <br />
1051             </td>
1052           </tr>
1053           <tr>
1054             <td class="nnns component red">
1055               <br />
1056             </td>
1057             <td class="snns plane red">internal syntax</td>
1058             <td class="snns file red">genv</td>
1059             <td class="snnn file red">
1060               <br />
1061             </td>
1062             <td class="snnn file red">
1063               <br />
1064             </td>
1065             <td class="ssnn file red">
1066               <br />
1067             </td>
1068           </tr>
1069           <tr>
1070             <td class="nnns component red">
1071               <br />
1072             </td>
1073             <td class="nnns plane red">
1074               <br />
1075             </td>
1076             <td class="snns file red">lenv</td>
1077             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
1078             <td class="snnn file red">lenv_length ( |?| )</td>
1079             <td class="ssnn file red">lenv_append ( ? @@ ? )</td>
1080           </tr>
1081           <tr>
1082             <td class="nnns component red">
1083               <br />
1084             </td>
1085             <td class="nnns plane red">
1086               <br />
1087             </td>
1088             <td class="snns file red">term</td>
1089             <td class="snnn file red">term_weight ( ♯{?} )</td>
1090             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
1091             <td class="ssnn file red">term_vector</td>
1092           </tr>
1093           <tr>
1094             <td class="nnns component red">
1095               <br />
1096             </td>
1097             <td class="nnns plane red">
1098               <br />
1099             </td>
1100             <td class="snns file red">item</td>
1101             <td class="snnn file red">
1102               <br />
1103             </td>
1104             <td class="snnn file red">
1105               <br />
1106             </td>
1107             <td class="ssnn file red">
1108               <br />
1109             </td>
1110           </tr>
1111           <tr>
1112             <td class="nnss component red">
1113               <br />
1114             </td>
1115             <td class="snss plane red">external syntax</td>
1116             <td class="snss file red">aarity</td>
1117             <td class="snsn file red">
1118               <br />
1119             </td>
1120             <td class="snsn file red">
1121               <br />
1122             </td>
1123             <td class="sssn file red">
1124               <br />
1125             </td>
1126           </tr>
1127         </tbody>
1128       </table>
1129     </div>
1130
1131    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1132    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1133          one for each component.
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1160     </div>
1161     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Thu, 24 Oct 2013 23:58:51 +0200</div>
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