helm/www/lambdadelta/basic_2.html

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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">293  </td>
 167             <td class="snns plane cyan">characters</td>
 168             <td class="snnn number cyan">441375</td>
 169             <td class="snns plane cyan">nodes</td>
 170             <td class="ssnn number cyan">1286916</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">888</td>
 178             <td class="snns plane green">total</td>
 179             <td class="ssnn number green">979</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">49</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">134</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 "big tree" 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_fleq 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">parallel computation for "big tree" normal forms</td>
 454             <td class="snns file cyan">fpns ( ⦃?,?,?⦄ ⊢ ⋕➡*[?,?] ⦃?,?,?⦄ )</td>
 455             <td class="snnn file cyan">fpns_fpns</td>
 456             <td class="snnn file cyan">
 457               <br />
 458             </td>
 459             <td class="ssnn file cyan">
 460               <br />
 461             </td>
 462           </tr>
 463           <tr>
 464             <td class="nnns component cyan">
 465               <br />
 466             </td>
 467             <td class="snns plane cyan">"big tree" parallel computation</td>
 468             <td class="snns file cyan">fpbr ( ⦃?,?,?⦄ ⊃≥[?,?] ⦃?,?,?⦄ )</td>
 469             <td class="snnn file cyan">fpbr_fpbr</td>
 470             <td class="snnn file cyan">
 471               <br />
 472             </td>
 473             <td class="ssnn file cyan">
 474               <br />
 475             </td>
 476           </tr>
 477           <tr>
 478             <td class="nnns component cyan">
 479               <br />
 480             </td>
 481             <td class="nnns plane cyan">
 482               <br />
 483             </td>
 484             <td class="snns file cyan">fpbg ( ⦃?,?,?⦄ &gt;[?,?] ⦃?,?,?⦄ )</td>
 485             <td class="snnn file cyan">fpbg_lift fpbg_fpbg</td>
 486             <td class="snnn file cyan">
 487               <br />
 488             </td>
 489             <td class="ssnn file cyan">
 490               <br />
 491             </td>
 492           </tr>
 493           <tr>
 494             <td class="nnns component cyan">
 495               <br />
 496             </td>
 497             <td class="nnns plane cyan">
 498               <br />
 499             </td>
 500             <td class="snns file cyan">fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )</td>
 501             <td class="snnn file cyan">fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )</td>
 502             <td class="snnn file cyan">fpbs_lift fpbs_fleq fpbs_fpbs</td>
 503             <td class="ssnn file cyan">
 504               <br />
 505             </td>
 506           </tr>
 507           <tr>
 508             <td class="nnns component cyan">
 509               <br />
 510             </td>
 511             <td class="snns plane cyan">decomposed extended computation</td>
 512             <td class="snns file cyan">cpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?] ? )</td>
 513             <td class="snnn file cyan">cpds_lift cpds_aaa cpds_cpds</td>
 514             <td class="snnn file cyan">
 515               <br />
 516             </td>
 517             <td class="ssnn file cyan">
 518               <br />
 519             </td>
 520           </tr>
 521           <tr>
 522             <td class="nnns component cyan">
 523               <br />
 524             </td>
 525             <td class="snns plane cyan">context-sensitive extended computation</td>
 526             <td class="snns file cyan">lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )</td>
 527             <td class="snnn file cyan">lpxs_alt ( ⦃?,?⦄ ⊢ ➡➡*[?,?] ? )</td>
 528             <td class="snnn file cyan">lpxs_ldrop lpxs_aaa lpxs_cpxs lpxs_lpxs</td>
 529             <td class="ssnn file cyan">
 530               <br />
 531             </td>
 532           </tr>
 533           <tr>
 534             <td class="nnns component cyan">
 535               <br />
 536             </td>
 537             <td class="nnns plane cyan">
 538               <br />
 539             </td>
 540             <td class="snns file cyan">cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )</td>
 541             <td class="snnn file cyan">cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_aaa cpxs_cpxs</td>
 542             <td class="snnn file cyan">
 543               <br />
 544             </td>
 545             <td class="ssnn file cyan">
 546               <br />
 547             </td>
 548           </tr>
 549           <tr>
 550             <td class="nnns component cyan">
 551               <br />
 552             </td>
 553             <td class="snns plane cyan">context-sensitive computation</td>
 554             <td class="snns file cyan">lprs ( ⦃?,?⦄ ⊢ ➡* ? )</td>
 555             <td class="snnn file cyan">lprs_alt ( ⦃?,?⦄ ⊢ ➡➡* ? )</td>
 556             <td class="snnn file cyan">lprs_ldrop lprs_cprs lprs_lprs</td>
 557             <td class="ssnn file cyan">
 558               <br />
 559             </td>
 560           </tr>
 561           <tr>
 562             <td class="nnns component cyan">
 563               <br />
 564             </td>
 565             <td class="nnns plane cyan">
 566               <br />
 567             </td>
 568             <td class="snns file cyan">cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)</td>
 569             <td class="snnn file cyan">cprs_lift cprs_cprs</td>
 570             <td class="snnn file cyan">
 571               <br />
 572             </td>
 573             <td class="ssnn file cyan">
 574               <br />
 575             </td>
 576           </tr>
 577           <tr>
 578             <td class="nnns component cyan">
 579               <br />
 580             </td>
 581             <td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</td>
 582             <td class="snns file cyan">lsubc ( ? ⊢ ? ⊑[?] ? )</td>
 583             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
 584             <td class="snnn file cyan">
 585               <br />
 586             </td>
 587             <td class="ssnn file cyan">
 588               <br />
 589             </td>
 590           </tr>
 591           <tr>
 592             <td class="nnns component cyan">
 593               <br />
 594             </td>
 595             <td class="snns plane cyan">support for abstract computation properties</td>
 596             <td class="snns file cyan">acp</td>
 597             <td class="snnn file cyan">acp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
 598             <td class="snnn file cyan">acp_aaa</td>
 599             <td class="ssnn file cyan">
 600               <br />
 601             </td>
 602           </tr>
 603           <tr>
 604             <td class="snns component water">reduction</td>
 605             <td class="snns plane water">"big tree" parallel reduction</td>
 606             <td class="snns file water">fpbc ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )</td>
 607             <td class="snnn file water">fpbc_lift</td>
 608             <td class="snnn file water">
 609               <br />
 610             </td>
 611             <td class="ssnn file water">
 612               <br />
 613             </td>
 614           </tr>
 615           <tr>
 616             <td class="nnns component water">
 617               <br />
 618             </td>
 619             <td class="nnns plane water">
 620               <br />
 621             </td>
 622             <td class="snns file water">fpb ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )</td>
 623             <td class="snnn file water">fpb_lift</td>
 624             <td class="snnn file water">
 625               <br />
 626             </td>
 627             <td class="ssnn file water">
 628               <br />
 629             </td>
 630           </tr>
 631           <tr>
 632             <td class="nnns component water">
 633               <br />
 634             </td>
 635             <td class="snns plane water">context-sensitive extended normal forms</td>
 636             <td class="snns file water">cnx ( ⦃?,?⦄ ⊢ 𝐍[?,?]⦃?⦄ )</td>
 637             <td class="snnn file water">cnx_lift cnx_crx cnx_cix</td>
 638             <td class="snnn file water">
 639               <br />
 640             </td>
 641             <td class="ssnn file water">
 642               <br />
 643             </td>
 644           </tr>
 645           <tr>
 646             <td class="nnns component water">
 647               <br />
 648             </td>
 649             <td class="snns plane water">context-sensitive extended reduction</td>
 650             <td class="snns file water">lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
 651             <td class="snnn file water">lpx_ldrop lpx_aaa lpx_lpx</td>
 652             <td class="snnn file water">
 653               <br />
 654             </td>
 655             <td class="ssnn file water">
 656               <br />
 657             </td>
 658           </tr>
 659           <tr>
 660             <td class="nnns component water">
 661               <br />
 662             </td>
 663             <td class="nnns plane water">
 664               <br />
 665             </td>
 666             <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
 667             <td class="snnn file water">cpx_lift cpx_cix cpx_cpx</td>
 668             <td class="snnn file water">
 669               <br />
 670             </td>
 671             <td class="ssnn file water">
 672               <br />
 673             </td>
 674           </tr>
 675           <tr>
 676             <td class="nnns component water">
 677               <br />
 678             </td>
 679             <td class="snns plane water">context-sensitive extended irreducible forms</td>
 680             <td class="snns file water">cix ( ⦃?,?⦄ ⊢ 𝐈[?,?]⦃?⦄ )</td>
 681             <td class="snnn file water">cix_append cix_lift</td>
 682             <td class="snnn file water">
 683               <br />
 684             </td>
 685             <td class="ssnn file water">
 686               <br />
 687             </td>
 688           </tr>
 689           <tr>
 690             <td class="nnns component water">
 691               <br />
 692             </td>
 693             <td class="snns plane water">context-sensitive extended reducible forms</td>
 694             <td class="snns file water">crx ( ⦃?,?⦄ ⊢ 𝐑[?,?]⦃?⦄ )</td>
 695             <td class="snnn file water">crx_append crx_lift</td>
 696             <td class="snnn file water">
 697               <br />
 698             </td>
 699             <td class="ssnn file water">
 700               <br />
 701             </td>
 702           </tr>
 703           <tr>
 704             <td class="nnns component water">
 705               <br />
 706             </td>
 707             <td class="snns plane water">context-sensitive normal forms</td>
 708             <td class="snns file water">cnr ( ⦃?,?⦄ ⊢ 𝐍⦃?⦄ )</td>
 709             <td class="snnn file water">cnr_lift cnr_crr cnr_cir</td>
 710             <td class="snnn file water">
 711               <br />
 712             </td>
 713             <td class="ssnn file water">
 714               <br />
 715             </td>
 716           </tr>
 717           <tr>
 718             <td class="nnns component water">
 719               <br />
 720             </td>
 721             <td class="snns plane water">context-sensitive reduction</td>
 722             <td class="snns file water">lpr ( ⦃?,?⦄ ⊢ ➡ ? )</td>
 723             <td class="snnn file water">lpr_ldrop lpr_lpr</td>
 724             <td class="snnn file water">
 725               <br />
 726             </td>
 727             <td class="ssnn file water">
 728               <br />
 729             </td>
 730           </tr>
 731           <tr>
 732             <td class="nnns component water">
 733               <br />
 734             </td>
 735             <td class="nnns plane water">
 736               <br />
 737             </td>
 738             <td class="snns file water">cpr ( ⦃?,?⦄ ⊢ ? ➡ ? )</td>
 739             <td class="snnn file water">cpr_lift cpr_cir</td>
 740             <td class="snnn file water">
 741               <br />
 742             </td>
 743             <td class="ssnn file water">
 744               <br />
 745             </td>
 746           </tr>
 747           <tr>
 748             <td class="nnns component water">
 749               <br />
 750             </td>
 751             <td class="snns plane water">context-sensitive irreducible forms</td>
 752             <td class="snns file water">cir ( ⦃?,?⦄ ⊢ 𝐈⦃?⦄ )</td>
 753             <td class="snnn file water">cir_append cir_lift</td>
 754             <td class="snnn file water">
 755               <br />
 756             </td>
 757             <td class="ssnn file water">
 758               <br />
 759             </td>
 760           </tr>
 761           <tr>
 762             <td class="nnns component water">
 763               <br />
 764             </td>
 765             <td class="snns plane water">context-sensitive reducible forms</td>
 766             <td class="snns file water">crr ( ⦃?,?⦄ ⊢ 𝐑⦃?⦄ )</td>
 767             <td class="snnn file water">crr_append crr_lift</td>
 768             <td class="snnn file water">
 769               <br />
 770             </td>
 771             <td class="ssnn file water">
 772               <br />
 773             </td>
 774           </tr>
 775           <tr>
 776             <td class="snns component green">unfold</td>
 777             <td class="snns plane green">unfold</td>
 778             <td class="snns file green">unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )</td>
 779             <td class="snnn file green">
 780               <br />
 781             </td>
 782             <td class="snnn file green">
 783               <br />
 784             </td>
 785             <td class="ssnn file green">
 786               <br />
 787             </td>
 788           </tr>
 789           <tr>
 790             <td class="nnns component green">
 791               <br />
 792             </td>
 793             <td class="snns plane green">iterated static type assignment</td>
 794             <td class="snns file green">lsstas ( ⦃?,?⦄ ⊢ ? •*[?,?,?] ? )</td>
 795             <td class="snnn file green">lsstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?,?] ? )</td>
 796             <td class="snnn file green">lsstas_lift lsstas_aaa lsstas_lsstas</td>
 797             <td class="ssnn file green">
 798               <br />
 799             </td>
 800           </tr>
 801           <tr>
 802             <td class="snns component grass">static typing</td>
 803             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
 804             <td class="snns file grass">lsuba ( ? ⊢ ? ⁝⊑ ? )</td>
 805             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
 806             <td class="snnn file grass">
 807               <br />
 808             </td>
 809             <td class="ssnn file grass">
 810               <br />
 811             </td>
 812           </tr>
 813           <tr>
 814             <td class="nnns component grass">
 815               <br />
 816             </td>
 817             <td class="snns plane grass">atomic arity assignment</td>
 818             <td class="snns file grass">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 819             <td class="snnn file grass">aaa_lift aaa_lifts aaa_da aaa_ssta aaa_aaa</td>
 820             <td class="snnn file grass">
 821               <br />
 822             </td>
 823             <td class="ssnn file grass">
 824               <br />
 825             </td>
 826           </tr>
 827           <tr>
 828             <td class="nnns component grass">
 829               <br />
 830             </td>
 831             <td class="snns plane grass">stratified static type assignment</td>
 832             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 833             <td class="snnn file grass">ssta_lift ssta_ssta</td>
 834             <td class="snnn file grass">
 835               <br />
 836             </td>
 837             <td class="ssnn file grass">
 838               <br />
 839             </td>
 840           </tr>
 841           <tr>
 842             <td class="nnns component grass">
 843               <br />
 844             </td>
 845             <td class="snns plane grass">local env. ref. for degree assignment</td>
 846             <td class="snns file grass">lsubd ( ? ⊢ ? ▪⊑ ? )</td>
 847             <td class="snnn file grass">lsubd_da lsubd_lsubd</td>
 848             <td class="snnn file grass">
 849               <br />
 850             </td>
 851             <td class="ssnn file grass">
 852               <br />
 853             </td>
 854           </tr>
 855           <tr>
 856             <td class="nnns component grass">
 857               <br />
 858             </td>
 859             <td class="snns plane grass">degree assignment</td>
 860             <td class="snns file grass">da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )</td>
 861             <td class="snnn file grass">da_lift da_da</td>
 862             <td class="snnn file grass">
 863               <br />
 864             </td>
 865             <td class="ssnn file grass">
 866               <br />
 867             </td>
 868           </tr>
 869           <tr>
 870             <td class="nnns component grass">
 871               <br />
 872             </td>
 873             <td class="snns plane grass">parameters</td>
 874             <td class="snns file grass">sh</td>
 875             <td class="snnn file grass">sd</td>
 876             <td class="snnn file grass">
 877               <br />
 878             </td>
 879             <td class="ssnn file grass">
 880               <br />
 881             </td>
 882           </tr>
 883           <tr>
 884             <td class="snns component yellow">substitution</td>
 885             <td class="snns plane yellow">restricted local env. ref.</td>
 886             <td class="snns file yellow">lsubr ( ? ⊑ ? )</td>
 887             <td class="snnn file yellow">lsubr_lsubr</td>
 888             <td class="snnn file yellow">
 889               <br />
 890             </td>
 891             <td class="ssnn file yellow">
 892               <br />
 893             </td>
 894           </tr>
 895           <tr>
 896             <td class="nnns component yellow">
 897               <br />
 898             </td>
 899             <td class="snns plane yellow">iterated structural successor for closures</td>
 900             <td class="snns file yellow">fqus ( ⦃?,?,?⦄ ⊃* ⦃?,?,?⦄ )</td>
 901             <td class="snnn file yellow">fqus_alt fqus_fqus</td>
 902             <td class="snnn file yellow">
 903               <br />
 904             </td>
 905             <td class="ssnn file yellow">
 906               <br />
 907             </td>
 908           </tr>
 909           <tr>
 910             <td class="nnns component yellow">
 911               <br />
 912             </td>
 913             <td class="nnns plane yellow">
 914               <br />
 915             </td>
 916             <td class="snns file yellow">fqup ( ⦃?,?,?⦄ ⊃+ ⦃?,?,?⦄ )</td>
 917             <td class="snnn file yellow">fqup_fqup</td>
 918             <td class="snnn file yellow">
 919               <br />
 920             </td>
 921             <td class="ssnn file yellow">
 922               <br />
 923             </td>
 924           </tr>
 925           <tr>
 926             <td class="nnns component yellow">
 927               <br />
 928             </td>
 929             <td class="snns plane yellow">generic local env. slicing</td>
 930             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
 931             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
 932             <td class="snnn file yellow">
 933               <br />
 934             </td>
 935             <td class="ssnn file yellow">
 936               <br />
 937             </td>
 938           </tr>
 939           <tr>
 940             <td class="nnns component yellow">
 941               <br />
 942             </td>
 943             <td class="snns plane yellow">generic term relocation</td>
 944             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
 945             <td class="snnn file yellow">lifts_lift_vector</td>
 946             <td class="snnn file yellow">
 947               <br />
 948             </td>
 949             <td class="ssnn file yellow">
 950               <br />
 951             </td>
 952           </tr>
 953           <tr>
 954             <td class="nnns component yellow">
 955               <br />
 956             </td>
 957             <td class="nnns plane yellow">
 958               <br />
 959             </td>
 960             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
 961             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
 962             <td class="snnn file yellow">
 963               <br />
 964             </td>
 965             <td class="ssnn file yellow">
 966               <br />
 967             </td>
 968           </tr>
 969           <tr>
 970             <td class="nnns component yellow">
 971               <br />
 972             </td>
 973             <td class="snns plane yellow">support for generic relocation</td>
 974             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
 975             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
 976             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
 977             <td class="ssnn file yellow">gr2_gr2</td>
 978           </tr>
 979           <tr>
 980             <td class="snns component orange">relocation</td>
 981             <td class="snns plane orange">structural successor for closures</td>
 982             <td class="snns file orange">fquq ( ⦃?,?,?⦄ ⊃⸮ ⦃?,?,?⦄ )</td>
 983             <td class="snnn file orange">fquq_alt ( ⦃?,?,?⦄ ⊃⊃⸮ ⦃?,?,?⦄ )</td>
 984             <td class="snnn file orange">fquq_fquq</td>
 985             <td class="ssnn file orange">
 986               <br />
 987             </td>
 988           </tr>
 989           <tr>
 990             <td class="nnns component orange">
 991               <br />
 992             </td>
 993             <td class="nnns plane orange">
 994               <br />
 995             </td>
 996             <td class="snns file orange">fqu ( ⦃?,?,?⦄ ⊃ ⦃?,?,?⦄ )</td>
 997             <td class="snnn file orange">fqu_fqu</td>
 998             <td class="snnn file orange">
 999               <br />
1000             </td>
1001             <td class="ssnn file orange">
1002               <br />
1003             </td>
1004           </tr>
1005           <tr>
1006             <td class="nnns component orange">
1007               <br />
1008             </td>
1009             <td class="snns plane orange">lazy equivalence for local environments</td>
1010             <td class="snns file orange">lleq ( ? ⋕[?] ? )</td>
1011             <td class="snnn file orange">lleq_fleq</td>
1012             <td class="snnn file orange">
1013               <br />
1014             </td>
1015             <td class="ssnn file orange">
1016               <br />
1017             </td>
1018           </tr>
1019           <tr>
1020             <td class="nnns component orange">
1021               <br />
1022             </td>
1023             <td class="snns plane orange">global env. slicing</td>
1024             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
1025             <td class="snnn file orange">gdrop_gdrop</td>
1026             <td class="snnn file orange">
1027               <br />
1028             </td>
1029             <td class="ssnn file orange">
1030               <br />
1031             </td>
1032           </tr>
1033           <tr>
1034             <td class="nnns component orange">
1035               <br />
1036             </td>
1037             <td class="snns plane orange">basic local env. slicing</td>
1038             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
1039             <td class="snnn file orange">ldrop_append ldrop_lpx_sn ldrop_ldrop</td>
1040             <td class="snnn file orange">
1041               <br />
1042             </td>
1043             <td class="ssnn file orange">
1044               <br />
1045             </td>
1046           </tr>
1047           <tr>
1048             <td class="nnns component orange">
1049               <br />
1050             </td>
1051             <td class="snns plane orange">basic term relocation</td>
1052             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
1053             <td class="snnn file orange">lift_lift_vector</td>
1054             <td class="snnn file orange">
1055               <br />
1056             </td>
1057             <td class="ssnn file orange">
1058               <br />
1059             </td>
1060           </tr>
1061           <tr>
1062             <td class="nnns component orange">
1063               <br />
1064             </td>
1065             <td class="nnns plane orange">
1066               <br />
1067             </td>
1068             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
1069             <td class="snnn file orange">lift_lift</td>
1070             <td class="snnn file orange">
1071               <br />
1072             </td>
1073             <td class="ssnn file orange">
1074               <br />
1075             </td>
1076           </tr>
1077           <tr>
1078             <td class="snns component red">grammar</td>
1079             <td class="snns plane red">pointwise extension of a relation</td>
1080             <td class="snns file red">lpx_sn</td>
1081             <td class="snnn file red">lpx_sn_tc lpx_sn_lpx_sn</td>
1082             <td class="snnn file red">
1083               <br />
1084             </td>
1085             <td class="ssnn file red">
1086               <br />
1087             </td>
1088           </tr>
1089           <tr>
1090             <td class="nnns component red">
1091               <br />
1092             </td>
1093             <td class="snns plane red">same top term constructor</td>
1094             <td class="snns file red">tstc ( ? ≃ ? )</td>
1095             <td class="snnn file red">tstc_tstc tstc_vector</td>
1096             <td class="snnn file red">
1097               <br />
1098             </td>
1099             <td class="ssnn file red">
1100               <br />
1101             </td>
1102           </tr>
1103           <tr>
1104             <td class="nnns component red">
1105               <br />
1106             </td>
1107             <td class="snns plane red">closures</td>
1108             <td class="snns file red">cl_shift ( ? @@ ? )</td>
1109             <td class="snnn file red">cl_weight ( ♯{?,?,?} )</td>
1110             <td class="snnn file red">
1111               <br />
1112             </td>
1113             <td class="ssnn file red">
1114               <br />
1115             </td>
1116           </tr>
1117           <tr>
1118             <td class="nnns component red">
1119               <br />
1120             </td>
1121             <td class="snns plane red">internal syntax</td>
1122             <td class="snns file red">genv</td>
1123             <td class="snnn file red">
1124               <br />
1125             </td>
1126             <td class="snnn file red">
1127               <br />
1128             </td>
1129             <td class="ssnn file red">
1130               <br />
1131             </td>
1132           </tr>
1133           <tr>
1134             <td class="nnns component red">
1135               <br />
1136             </td>
1137             <td class="nnns plane red">
1138               <br />
1139             </td>
1140             <td class="snns file red">lenv</td>
1141             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
1142             <td class="snnn file red">lenv_length ( |?| )</td>
1143             <td class="ssnn file red">lenv_append ( ? @@ ? )</td>
1144           </tr>
1145           <tr>
1146             <td class="nnns component red">
1147               <br />
1148             </td>
1149             <td class="nnns plane red">
1150               <br />
1151             </td>
1152             <td class="snns file red">term</td>
1153             <td class="snnn file red">term_weight ( ♯{?} )</td>
1154             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
1155             <td class="ssnn file red">term_vector</td>
1156           </tr>
1157           <tr>
1158             <td class="nnns component red">
1159               <br />
1160             </td>
1161             <td class="nnns plane red">
1162               <br />
1163             </td>
1164             <td class="snns file red">item</td>
1165             <td class="snnn file red">
1166               <br />
1167             </td>
1168             <td class="snnn file red">
1169               <br />
1170             </td>
1171             <td class="ssnn file red">
1172               <br />
1173             </td>
1174           </tr>
1175           <tr>
1176             <td class="nnss component red">
1177               <br />
1178             </td>
1179             <td class="snss plane red">external syntax</td>
1180             <td class="snss file red">aarity</td>
1181             <td class="snsn file red">
1182               <br />
1183             </td>
1184             <td class="snsn file red">
1185               <br />
1186             </td>
1187             <td class="sssn file red">
1188               <br />
1189             </td>
1190           </tr>
1191         </tbody>
1192       </table>
1193     </div>
1194
1195    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1196    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1197          one for each component.
1198    </div>
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1224     </div>
1225     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Mon, 25 Nov 2013 15:44:49 +0100</div>
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