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    </div>
 137    <div xmlns:ld="http://lambdadelta.info/" class="text">
 138       <table cellpadding="4" cellspacing="0">
 139         <tbody>
 140           <tr>
 141             <td class="snns component grey">category</td>
 142             <td class="snns plane grey">objects</td>
 143             <td class="snnn number grey">
 144               <br />
 145             </td>
 146             <td class="snnn plane grey">
 147               <br />
 148             </td>
 149             <td class="snnn number grey">
 150               <br />
 151             </td>
 152             <td class="snnn plane grey">
 153               <br />
 154             </td>
 155             <td class="ssnn number grey">
 156               <br />
 157             </td>
 158           </tr>
 159           <tr>
 160             <td class="snns component cyan">sizes</td>
 161             <td class="snns plane cyan">files</td>
 162             <td class="snnn number cyan">213  </td>
 163             <td class="snns plane cyan">characters</td>
 164             <td class="snnn number cyan">392008</td>
 165             <td class="snns plane cyan">nodes</td>
 166             <td class="ssnn number cyan">1052979</td>
 167           </tr>
 168           <tr>
 169             <td class="snns component green">propositions</td>
 170             <td class="snns plane green">theorems</td>
 171             <td class="snnn number green">79</td>
 172             <td class="snns plane green">lemmas</td>
 173             <td class="snnn number green">875</td>
 174             <td class="snns plane green">total</td>
 175             <td class="ssnn number green">954</td>
 176           </tr>
 177           <tr>
 178             <td class="snss component yellow">concepts</td>
 179             <td class="snss plane yellow">declared</td>
 180             <td class="snsn number yellow">45</td>
 181             <td class="snss plane yellow">defined</td>
 182             <td class="snsn number yellow">75</td>
 183             <td class="snss plane yellow">total</td>
 184             <td class="sssn number yellow">120</td>
 185           </tr>
 186         </tbody>
 187       </table>
 188     </div>
 189    <ul xmlns:ld="http://lambdadelta.info/">
 190       <li>
 191         <span class="date">In progress.</span>
 192          Context-sensitive subject equivalence
 193          for native type assignment.
 194    </li>
 195     </ul>
 196    <ul xmlns:ld="http://lambdadelta.info/">
 197       <li>
 198         <span class="date">In progress.</span>
 199          Closure of extended context-sensitive computation
 200          for native validity.
 201    </li>
 202     </ul>
 203    <ul xmlns:ld="http://lambdadelta.info/">
 204       <li>
 205         <span class="date">In progress.</span>
 206          Extended context-sensitive strong normalization
 207          for simply typed terms.
 208    </li>
 209     </ul>
 210    <ul xmlns:ld="http://lambdadelta.info/">
 211       <li>
 212         <span class="date">2013 April 16.</span>
 213          Reaxiomatized substitution and reduction
 214          commute with respect to subclosure
 215          (anniversary milestone).
 216    </li>
 217     </ul>
 218    <ul xmlns:ld="http://lambdadelta.info/">
 219       <li>
 220         <span class="date">2013 March 16.</span>
 221          Mutual recursive preservation of stratified native validity
 222          for hyper computation on closures.
 223    </li>
 224     </ul>
 225    <ul xmlns:ld="http://lambdadelta.info/">
 226       <li>
 227         <span class="date">2012 October 16.</span>
 228          Confluence for context-free parallel reduction on closures.
 229    </li>
 230     </ul>
 231    <ul xmlns:ld="http://lambdadelta.info/">
 232       <li>
 233         <span class="date">2012 July 26.</span>
 234          Term binders polarized to control ζ reduction.
 235    </li>
 236     </ul>
 237    <ul xmlns:ld="http://lambdadelta.info/">
 238       <li>
 239         <span class="date">2012 April 16.</span>
 240          Context-sensitive subject equivalence
 241          for atomic arity assignment
 242          (anniversary milestone).
 243    </li>
 244     </ul>
 245    <ul xmlns:ld="http://lambdadelta.info/">
 246       <li>
 247         <span class="date">2012 March 15.</span>
 248          Context-sensitive strong normalization
 249          for simply typed terms.
 250    </li>
 251     </ul>
 252    <ul xmlns:ld="http://lambdadelta.info/">
 253       <li>
 254         <span class="date">2012 January 27.</span>
 255          Support for abstract candidates of reducibility.
 256    </li>
 257     </ul>
 258    <ul xmlns:ld="http://lambdadelta.info/">
 259       <li>
 260         <span class="date">2011 September 21.</span>
 261          Confluence for context-sensitive parallel reduction on terms.
 262    </li>
 263     </ul>
 264    <ul xmlns:ld="http://lambdadelta.info/">
 265       <li>
 266         <span class="date">2011 September 6.</span>
 267          Confluence for context-free parallel reduction on terms.
 268    </li>
 269     </ul>
 270    <ul xmlns:ld="http://lambdadelta.info/">
 271       <li>
 272         <span class="date">2011 April 17.</span>
 273          Specification starts.
 274    </li>
 275     </ul>
 276
 277    <div xmlns:ld="http://lambdadelta.info/" class="head2">Logical Structure of the Specification</div>
 278    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in planes and components
 279          according to the following table.
 280          A notation file covering the whole specification is provided.
 281          The notation for the relations or functions introduced in each file
 282          is shown in parentheses (? are placeholders).
 283    </div>
 284    <div xmlns:ld="http://lambdadelta.info/" class="text">
 285       <table cellpadding="4" cellspacing="0">
 286         <tbody>
 287           <tr>
 288             <td class="snns component grey">component</td>
 289             <td class="snns plane grey">plane</td>
 290             <td class="snns file grey">files</td>
 291             <td class="snnn file grey">
 292               <br />
 293             </td>
 294             <td class="snnn file grey">
 295               <br />
 296             </td>
 297             <td class="snnn file grey">
 298               <br />
 299             </td>
 300             <td class="ssnn file grey">
 301               <br />
 302             </td>
 303           </tr>
 304           <tr>
 305             <td class="snns component prune">dynamic typing</td>
 306             <td class="snns plane prune">"big tree" parallel computation</td>
 307             <td class="snns file prune">yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )</td>
 308             <td class="snnn file prune">yprs_yprs</td>
 309             <td class="snnn file prune">ygt ( ? ⊢ ⦃?,?⦄ &gt;[g] ⦃?,?⦄ )</td>
 310             <td class="snnn file prune">ygt_ygt</td>
 311             <td class="ssnn file prune">
 312               <br />
 313             </td>
 314           </tr>
 315           <tr>
 316             <td class="nnns component prune">
 317               <br />
 318             </td>
 319             <td class="snns plane prune">"big tree" parallel reduction</td>
 320             <td class="snns file prune">ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )</td>
 321             <td class="snnn file prune">ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )</td>
 322             <td class="snnn file prune">
 323               <br />
 324             </td>
 325             <td class="snnn file prune">
 326               <br />
 327             </td>
 328             <td class="ssnn file prune">
 329               <br />
 330             </td>
 331           </tr>
 332           <tr>
 333             <td class="nnns component prune">
 334               <br />
 335             </td>
 336             <td class="snns plane prune">local env. ref. for stratified native validity</td>
 337             <td class="snns file prune">lsubsv ( ? ⊢ ? ¡⊑[?] ? )</td>
 338             <td class="snnn file prune">lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv</td>
 339             <td class="snnn file prune">
 340               <br />
 341             </td>
 342             <td class="snnn file prune">
 343               <br />
 344             </td>
 345             <td class="ssnn file prune">
 346               <br />
 347             </td>
 348           </tr>
 349           <tr>
 350             <td class="nnns component prune">
 351               <br />
 352             </td>
 353             <td class="snns plane prune">stratified native validity</td>
 354             <td class="snns file prune">snv ( ⦃?,?⦄ ⊢ ? ¡[?] )</td>
 355             <td class="snnn file prune">snv_lift snv_ltpss_dx snv_ltpss_sn snv_aaa snv_ssta snv_sstas snv_ssta_ltpr snv_ltpr snv_cpcs</td>
 356             <td class="snnn file prune">
 357               <br />
 358             </td>
 359             <td class="snnn file prune">
 360               <br />
 361             </td>
 362             <td class="ssnn file prune">
 363               <br />
 364             </td>
 365           </tr>
 366           <tr>
 367             <td class="snns component blue">equivalence</td>
 368             <td class="snns plane blue">focalized equivalence</td>
 369             <td class="snns file blue">lfpcs ( ⦃?⦄ ⬌* ⦃?⦄ )</td>
 370             <td class="snnn file blue">lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs</td>
 371             <td class="snnn file blue">
 372               <br />
 373             </td>
 374             <td class="snnn file blue">
 375               <br />
 376             </td>
 377             <td class="ssnn file blue">
 378               <br />
 379             </td>
 380           </tr>
 381           <tr>
 382             <td class="nnns component blue">
 383               <br />
 384             </td>
 385             <td class="nnns plane blue">
 386               <br />
 387             </td>
 388             <td class="snns file blue">fpcs ( ⦃?,?⦄ ⬌* ⦃?,?⦄ )</td>
 389             <td class="snnn file blue">fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs</td>
 390             <td class="snnn file blue">
 391               <br />
 392             </td>
 393             <td class="snnn file blue">
 394               <br />
 395             </td>
 396             <td class="ssnn file blue">
 397               <br />
 398             </td>
 399           </tr>
 400           <tr>
 401             <td class="nnns component blue">
 402               <br />
 403             </td>
 404             <td class="snns plane blue">local env. ref. for stratified static type assignment</td>
 405             <td class="snns file blue">lsubss ( ? •⊑[?] ? )</td>
 406             <td class="snnn file blue">lsubss_ldrop lsubss_ssta lsubss_cpcs</td>
 407             <td class="snnn file blue">
 408               <br />
 409             </td>
 410             <td class="snnn file blue">
 411               <br />
 412             </td>
 413             <td class="ssnn file blue">
 414               <br />
 415             </td>
 416           </tr>
 417           <tr>
 418             <td class="nnns component blue">
 419               <br />
 420             </td>
 421             <td class="snns plane blue">context-sensitive equivalence</td>
 422             <td class="snns file blue">cpcs ( ? ⊢ ? ⬌* ? )</td>
 423             <td class="snnn file blue">cpcs_ltpss_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs</td>
 424             <td class="snnn file blue">
 425               <br />
 426             </td>
 427             <td class="snnn file blue">
 428               <br />
 429             </td>
 430             <td class="ssnn file blue">
 431               <br />
 432             </td>
 433           </tr>
 434           <tr>
 435             <td class="snns component sky">conversion</td>
 436             <td class="snns plane sky">focalized conversion</td>
 437             <td class="snns file sky">lfpc ( ⦃?⦄ ⬌ ⦃?⦄ )</td>
 438             <td class="snnn file sky">lfpc_lfpc</td>
 439             <td class="snnn file sky">
 440               <br />
 441             </td>
 442             <td class="snnn file sky">
 443               <br />
 444             </td>
 445             <td class="ssnn file sky">
 446               <br />
 447             </td>
 448           </tr>
 449           <tr>
 450             <td class="nnns component sky">
 451               <br />
 452             </td>
 453             <td class="nnns plane sky">
 454               <br />
 455             </td>
 456             <td class="snns file sky">fpc ( ⦃?,?⦄ ⬌ ⦃?,?⦄ )</td>
 457             <td class="snnn file sky">fpc_fpc</td>
 458             <td class="snnn file sky">
 459               <br />
 460             </td>
 461             <td class="snnn file sky">
 462               <br />
 463             </td>
 464             <td class="ssnn file sky">
 465               <br />
 466             </td>
 467           </tr>
 468           <tr>
 469             <td class="nnns component sky">
 470               <br />
 471             </td>
 472             <td class="snns plane sky">context-sensitive conversion</td>
 473             <td class="snns file sky">cpc ( ? ⊢ ? ⬌ ? )</td>
 474             <td class="snnn file sky">cpc_cpc</td>
 475             <td class="snnn file sky">
 476               <br />
 477             </td>
 478             <td class="snnn file sky">
 479               <br />
 480             </td>
 481             <td class="ssnn file sky">
 482               <br />
 483             </td>
 484           </tr>
 485           <tr>
 486             <td class="snns component cyan">computation</td>
 487             <td class="snns plane cyan">focalized computation</td>
 488             <td class="snns file cyan">lfprs ( ⦃?⦄ ➡* ⦃?⦄ )</td>
 489             <td class="snnn file cyan">lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs</td>
 490             <td class="snnn file cyan">
 491               <br />
 492             </td>
 493             <td class="snnn file cyan">
 494               <br />
 495             </td>
 496             <td class="ssnn file cyan">
 497               <br />
 498             </td>
 499           </tr>
 500           <tr>
 501             <td class="nnns component cyan">
 502               <br />
 503             </td>
 504             <td class="nnns plane cyan">
 505               <br />
 506             </td>
 507             <td class="snns file cyan">fprs ( ⦃?,?⦄ ➡* ⦃?,?⦄ )</td>
 508             <td class="snnn file cyan">fprs_aaa fprs_fprs</td>
 509             <td class="snnn file cyan">
 510               <br />
 511             </td>
 512             <td class="snnn file cyan">
 513               <br />
 514             </td>
 515             <td class="ssnn file cyan">
 516               <br />
 517             </td>
 518           </tr>
 519           <tr>
 520             <td class="nnns component cyan">
 521               <br />
 522             </td>
 523             <td class="snns plane cyan">decomposed extended computation</td>
 524             <td class="snns file cyan">dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )</td>
 525             <td class="snnn file cyan">dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn dxprs_aaa dxprs_dxprs</td>
 526             <td class="snnn file cyan">
 527               <br />
 528             </td>
 529             <td class="snnn file cyan">
 530               <br />
 531             </td>
 532             <td class="ssnn file cyan">
 533               <br />
 534             </td>
 535           </tr>
 536           <tr>
 537             <td class="nnns component cyan">
 538               <br />
 539             </td>
 540             <td class="snns plane cyan">weakly normalizing computation</td>
 541             <td class="snns file cyan">cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
 542             <td class="snnn file cyan">cpe_cpe</td>
 543             <td class="snnn file cyan">
 544               <br />
 545             </td>
 546             <td class="snnn file cyan">
 547               <br />
 548             </td>
 549             <td class="ssnn file cyan">
 550               <br />
 551             </td>
 552           </tr>
 553           <tr>
 554             <td class="nnns component cyan">
 555               <br />
 556             </td>
 557             <td class="snns plane cyan">strongly normalizing computation</td>
 558             <td class="snns file cyan">csn_vector ( ? ⊢ ⬊* ? )</td>
 559             <td class="snnn file cyan">csn_cpr_vector csn_tstc_vector csn_aaa</td>
 560             <td class="snnn file cyan">
 561               <br />
 562             </td>
 563             <td class="snnn file cyan">
 564               <br />
 565             </td>
 566             <td class="ssnn file cyan">
 567               <br />
 568             </td>
 569           </tr>
 570           <tr>
 571             <td class="nnns component cyan">
 572               <br />
 573             </td>
 574             <td class="nnns plane cyan">
 575               <br />
 576             </td>
 577             <td class="snns file cyan">csn ( ? ⊢ ⬊* ? )</td>
 578             <td class="snnn file cyan">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
 579             <td class="snnn file cyan">csn_lift csn_cpr csn_lfpr</td>
 580             <td class="snnn file cyan">
 581               <br />
 582             </td>
 583             <td class="ssnn file cyan">
 584               <br />
 585             </td>
 586           </tr>
 587           <tr>
 588             <td class="nnns component cyan">
 589               <br />
 590             </td>
 591             <td class="snns plane cyan">context-sensitive computation</td>
 592             <td class="snns file cyan">cprs (? ⊢ ? ➡* ?)</td>
 593             <td class="snnn file cyan">cprs_lift cprs_tpss cprs_ltpss_dx cprs_ltpss_sn cprs_delift cprs_aaa cprs_ltpr cprs_lfpr cprs_cprs cprs_lfprs cprs_tstc cprs_tstc_vector</td>
 594             <td class="snnn file cyan">
 595               <br />
 596             </td>
 597             <td class="snnn file cyan">
 598               <br />
 599             </td>
 600             <td class="ssnn file cyan">
 601               <br />
 602             </td>
 603           </tr>
 604           <tr>
 605             <td class="nnns component cyan">
 606               <br />
 607             </td>
 608             <td class="snns plane cyan">context-free computation</td>
 609             <td class="snns file cyan">ltprs ( ? ➡* ? )</td>
 610             <td class="snnn file cyan">ltprs_alt ( ? ➡➡* ? )</td>
 611             <td class="snnn file cyan">ltprs_ldrop ltprs_ltprs</td>
 612             <td class="snnn file cyan">
 613               <br />
 614             </td>
 615             <td class="ssnn file cyan">
 616               <br />
 617             </td>
 618           </tr>
 619           <tr>
 620             <td class="nnns component cyan">
 621               <br />
 622             </td>
 623             <td class="nnns plane cyan">
 624               <br />
 625             </td>
 626             <td class="snns file cyan">tprs ( ? ➡* ?)</td>
 627             <td class="snnn file cyan">tprs_lift tprs_tprs</td>
 628             <td class="snnn file cyan">
 629               <br />
 630             </td>
 631             <td class="snnn file cyan">
 632               <br />
 633             </td>
 634             <td class="ssnn file cyan">
 635               <br />
 636             </td>
 637           </tr>
 638           <tr>
 639             <td class="nnns component cyan">
 640               <br />
 641             </td>
 642             <td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</td>
 643             <td class="snns file cyan">lsubc ( ? ⊑[?] ? )</td>
 644             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
 645             <td class="snnn file cyan">
 646               <br />
 647             </td>
 648             <td class="snnn file cyan">
 649               <br />
 650             </td>
 651             <td class="ssnn file cyan">
 652               <br />
 653             </td>
 654           </tr>
 655           <tr>
 656             <td class="nnns component cyan">
 657               <br />
 658             </td>
 659             <td class="snns plane cyan">support for abstract computation properties</td>
 660             <td class="snns file cyan">acp</td>
 661             <td class="snnn file cyan">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
 662             <td class="snnn file cyan">acp_aaa</td>
 663             <td class="snnn file cyan">
 664               <br />
 665             </td>
 666             <td class="ssnn file cyan">
 667               <br />
 668             </td>
 669           </tr>
 670           <tr>
 671             <td class="snns component water">reduction</td>
 672             <td class="snns plane water">context-sensitive normal forms</td>
 673             <td class="snns file water">cnf ( ? ⊢ 𝐍⦃?⦄ )</td>
 674             <td class="snnn file water">cnf_liftt cnf_crf cnf_cif</td>
 675             <td class="snnn file water">
 676               <br />
 677             </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="nnns plane water">
 690               <br />
 691             </td>
 692             <td class="snns file water">chnf ( ? ⊢ 𝐇𝐍⦃?⦄ )</td>
 693             <td class="snnn file water">
 694               <br />
 695             </td>
 696             <td class="snnn file water">
 697               <br />
 698             </td>
 699             <td class="snnn file water">
 700               <br />
 701             </td>
 702             <td class="ssnn file water">
 703               <br />
 704             </td>
 705           </tr>
 706           <tr>
 707             <td class="nnns component water">
 708               <br />
 709             </td>
 710             <td class="snns plane water">context-sensitive reduction</td>
 711             <td class="snns file water">lpr ( ? ⊢ ➡ ? )</td>
 712             <td class="snnn file water">lpr_ldrop lpr_cpss lpr_lpss lpr_aaa lpr_cpr lpr_lpr</td>
 713             <td class="snnn file water">
 714               <br />
 715             </td>
 716             <td class="snnn file water">
 717               <br />
 718             </td>
 719             <td class="ssnn file water">
 720               <br />
 721             </td>
 722           </tr>
 723           <tr>
 724             <td class="nnns component water">
 725               <br />
 726             </td>
 727             <td class="nnns plane water">
 728               <br />
 729             </td>
 730             <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
 731             <td class="snnn file water">lpr_tshf cpr_lift cpr_cif</td>
 732             <td class="snnn file water">
 733               <br />
 734             </td>
 735             <td class="snnn file water">
 736               <br />
 737             </td>
 738             <td class="ssnn file water">
 739               <br />
 740             </td>
 741           </tr>
 742           <tr>
 743             <td class="nnns component water">
 744               <br />
 745             </td>
 746             <td class="snns plane water">context-sensitive reducible forms</td>
 747             <td class="snns file water">crf ( ? ⊢ 𝐑⦃?⦄ )</td>
 748             <td class="snnn file water">crf_append</td>
 749             <td class="snnn file water">cif ( ? ⊢ 𝐈⦃?⦄ )</td>
 750             <td class="snnn file water">cif_append</td>
 751             <td class="ssnn file water">
 752               <br />
 753             </td>
 754           </tr>
 755           <tr>
 756             <td class="snns component green">unfold</td>
 757             <td class="snns plane green">restricted parallel computation</td>
 758             <td class="snns file green">lpqs ( ? ⊢ ➤* ? )</td>
 759             <td class="snnn file green">lpqs_ldrop lpqs_cpqs lpqs_lpqs</td>
 760             <td class="snnn file green">
 761               <br />
 762             </td>
 763             <td class="snnn file green">
 764               <br />
 765             </td>
 766             <td class="ssnn file green">
 767               <br />
 768             </td>
 769           </tr>
 770           <tr>
 771             <td class="nnns component green">
 772               <br />
 773             </td>
 774             <td class="nnns plane green">
 775               <br />
 776             </td>
 777             <td class="snns file green">cpqs ( ? ⊢ ? ➤* ? )</td>
 778             <td class="snnn file green">cpqs_lift</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">unfold</td>
 794             <td class="snns file green">unfold ( ? ⊢ ? ⧫* ? )</td>
 795             <td class="snnn file green">
 796               <br />
 797             </td>
 798             <td class="snnn file green">
 799               <br />
 800             </td>
 801             <td class="snnn file green">
 802               <br />
 803             </td>
 804             <td class="ssnn file green">
 805               <br />
 806             </td>
 807           </tr>
 808           <tr>
 809             <td class="nnns component green">
 810               <br />
 811             </td>
 812             <td class="snns plane green">iterated stratified static type assignment</td>
 813             <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
 814             <td class="snnn file green">sstas_lift sstas_lpss sstas_aaa sstas_sstas</td>
 815             <td class="snnn file green">
 816               <br />
 817             </td>
 818             <td class="snnn file green">
 819               <br />
 820             </td>
 821             <td class="ssnn file green">
 822               <br />
 823             </td>
 824           </tr>
 825           <tr>
 826             <td class="snns component grass">static typing</td>
 827             <td class="snns plane grass">stratified static type assignment</td>
 828             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 829             <td class="snnn file grass">ssta_lift ssta_lpss ssta_aaa ssta_ssta</td>
 830             <td class="snnn file grass">
 831               <br />
 832             </td>
 833             <td class="snnn file grass">
 834               <br />
 835             </td>
 836             <td class="ssnn file grass">
 837               <br />
 838             </td>
 839           </tr>
 840           <tr>
 841             <td class="nnns component grass">
 842               <br />
 843             </td>
 844             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
 845             <td class="snns file grass">lsuba ( ? ⁝⊑ ? )</td>
 846             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
 847             <td class="snnn file grass">
 848               <br />
 849             </td>
 850             <td class="snnn file grass">
 851               <br />
 852             </td>
 853             <td class="ssnn file grass">
 854               <br />
 855             </td>
 856           </tr>
 857           <tr>
 858             <td class="nnns component grass">
 859               <br />
 860             </td>
 861             <td class="snns plane grass">atomic arity assignment</td>
 862             <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
 863             <td class="snnn file grass">aaa_lift aaa_lifts aaa_lpss aaa_aaa</td>
 864             <td class="snnn file grass">
 865               <br />
 866             </td>
 867             <td class="snnn file grass">
 868               <br />
 869             </td>
 870             <td class="ssnn file grass">
 871               <br />
 872             </td>
 873           </tr>
 874           <tr>
 875             <td class="nnns component grass">
 876               <br />
 877             </td>
 878             <td class="snns plane grass">parameters</td>
 879             <td class="snns file grass">sh</td>
 880             <td class="snnn file grass">sd</td>
 881             <td class="snnn file grass">
 882               <br />
 883             </td>
 884             <td class="snnn file grass">
 885               <br />
 886             </td>
 887             <td class="ssnn file grass">
 888               <br />
 889             </td>
 890           </tr>
 891           <tr>
 892             <td class="snns component yellow">substitution</td>
 893             <td class="snns plane yellow">parallel substitution</td>
 894             <td class="snns file yellow">lpss ( ? ⊢ ▶* ? )</td>
 895             <td class="snnn file yellow">lpss_ldrop lpss_cpss lpss_lpss</td>
 896             <td class="snnn file yellow">
 897               <br />
 898             </td>
 899             <td class="snnn file yellow">
 900               <br />
 901             </td>
 902             <td class="ssnn file yellow">
 903               <br />
 904             </td>
 905           </tr>
 906           <tr>
 907             <td class="nnns component yellow">
 908               <br />
 909             </td>
 910             <td class="nnns plane yellow">
 911               <br />
 912             </td>
 913             <td class="snns file yellow">cpss ( ? ⊢ ? ▶* ? )</td>
 914             <td class="snnn file yellow">cpss_lift</td>
 915             <td class="snnn file yellow">
 916               <br />
 917             </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">iterated structural successor for closures</td>
 930             <td class="snns file yellow">fsups ( ⦃?,?⦄ ⊃* ⦃?,?⦄ )</td>
 931             <td class="snnn file yellow">fsups_fsups</td>
 932             <td class="snnn file yellow">
 933               <br />
 934             </td>
 935             <td class="snnn file yellow">
 936               <br />
 937             </td>
 938             <td class="ssnn file yellow">
 939               <br />
 940             </td>
 941           </tr>
 942           <tr>
 943             <td class="nnns component yellow">
 944               <br />
 945             </td>
 946             <td class="nnns plane yellow">
 947               <br />
 948             </td>
 949             <td class="snns file yellow">fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )</td>
 950             <td class="snnn file yellow">fsupp_fsupp</td>
 951             <td class="snnn file yellow">
 952               <br />
 953             </td>
 954             <td class="snnn file yellow">
 955               <br />
 956             </td>
 957             <td class="ssnn file yellow">
 958               <br />
 959             </td>
 960           </tr>
 961           <tr>
 962             <td class="nnns component yellow">
 963               <br />
 964             </td>
 965             <td class="snns plane yellow">generic local env. slicing</td>
 966             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
 967             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
 968             <td class="snnn file yellow">
 969               <br />
 970             </td>
 971             <td class="snnn file yellow">
 972               <br />
 973             </td>
 974             <td class="ssnn file yellow">
 975               <br />
 976             </td>
 977           </tr>
 978           <tr>
 979             <td class="nnns component yellow">
 980               <br />
 981             </td>
 982             <td class="snns plane yellow">generic term relocation</td>
 983             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
 984             <td class="snnn file yellow">lifts_lift_vector</td>
 985             <td class="snnn file yellow">
 986               <br />
 987             </td>
 988             <td class="snnn file yellow">
 989               <br />
 990             </td>
 991             <td class="ssnn file yellow">
 992               <br />
 993             </td>
 994           </tr>
 995           <tr>
 996             <td class="nnns component yellow">
 997               <br />
 998             </td>
 999             <td class="nnns plane yellow">
1000               <br />
1001             </td>
1002             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
1003             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
1004             <td class="snnn file yellow">
1005               <br />
1006             </td>
1007             <td class="snnn file yellow">
1008               <br />
1009             </td>
1010             <td class="ssnn file yellow">
1011               <br />
1012             </td>
1013           </tr>
1014           <tr>
1015             <td class="nnns component yellow">
1016               <br />
1017             </td>
1018             <td class="snns plane yellow">support for generic relocation</td>
1019             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
1020             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
1021             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
1022             <td class="snnn file yellow">gr2_gr2</td>
1023             <td class="ssnn file yellow">
1024               <br />
1025             </td>
1026           </tr>
1027           <tr>
1028             <td class="snns component orange">relocation</td>
1029             <td class="snns plane orange">structural successor for closures</td>
1030             <td class="snns file orange">fsup ( ⦃?,?⦄ ⊃ ⦃?,?⦄ )</td>
1031             <td class="snnn file orange">
1032               <br />
1033             </td>
1034             <td class="snnn file orange">
1035               <br />
1036             </td>
1037             <td class="snnn file orange">
1038               <br />
1039             </td>
1040             <td class="ssnn file orange">
1041               <br />
1042             </td>
1043           </tr>
1044           <tr>
1045             <td class="nnns component orange">
1046               <br />
1047             </td>
1048             <td class="snns plane orange">global env. slicing</td>
1049             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
1050             <td class="snnn file orange">gdrop_gdrop</td>
1051             <td class="snnn file orange">
1052               <br />
1053             </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="snns plane orange">basic local env. slicing</td>
1066             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
1067             <td class="snnn file orange">ldrop_append ldrop_lpx ldrop_lpx_sn ldrop_lbotr ldrop_ldrop</td>
1068             <td class="snnn file orange">
1069               <br />
1070             </td>
1071             <td class="snnn file orange">
1072               <br />
1073             </td>
1074             <td class="ssnn file orange">
1075               <br />
1076             </td>
1077           </tr>
1078           <tr>
1079             <td class="nnns component orange">
1080               <br />
1081             </td>
1082             <td class="snns plane orange">local env. ref. for substitution</td>
1083             <td class="snns file orange">lsubr ( ? ⊑[?,?] ? )</td>
1084             <td class="snnn file orange">(lsubr_lsubr)</td>
1085             <td class="snnn file orange">lsubr_lbotr ( ⊒[?,?] ? )</td>
1086             <td class="snnn file orange">
1087               <br />
1088             </td>
1089             <td class="ssnn file orange">
1090               <br />
1091             </td>
1092           </tr>
1093           <tr>
1094             <td class="nnns component orange">
1095               <br />
1096             </td>
1097             <td class="snns plane orange">basic term relocation</td>
1098             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
1099             <td class="snnn file orange">lift_lift_vector</td>
1100             <td class="snnn file orange">
1101               <br />
1102             </td>
1103             <td class="snnn file orange">
1104               <br />
1105             </td>
1106             <td class="ssnn file orange">
1107               <br />
1108             </td>
1109           </tr>
1110           <tr>
1111             <td class="nnns component orange">
1112               <br />
1113             </td>
1114             <td class="nnns plane orange">
1115               <br />
1116             </td>
1117             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
1118             <td class="snnn file orange">lift_lift</td>
1119             <td class="snnn file orange">
1120               <br />
1121             </td>
1122             <td class="snnn file orange">
1123               <br />
1124             </td>
1125             <td class="ssnn file orange">
1126               <br />
1127             </td>
1128           </tr>
1129           <tr>
1130             <td class="snns component red">grammar</td>
1131             <td class="snns plane red">same head term form</td>
1132             <td class="snns file red">tshf ( ? ≈ ? )</td>
1133             <td class="snnn file red">(tshf_tshf)</td>
1134             <td class="snnn file red">
1135               <br />
1136             </td>
1137             <td class="snnn file red">
1138               <br />
1139             </td>
1140             <td class="ssnn file red">
1141               <br />
1142             </td>
1143           </tr>
1144           <tr>
1145             <td class="nnns component red">
1146               <br />
1147             </td>
1148             <td class="snns plane red">same top term constructor</td>
1149             <td class="snns file red">tstc ( ? ≃ ? )</td>
1150             <td class="snnn file red">tstc_tstc tstc_vector</td>
1151             <td class="snnn file red">
1152               <br />
1153             </td>
1154             <td class="snnn file red">
1155               <br />
1156             </td>
1157             <td class="ssnn file red">
1158               <br />
1159             </td>
1160           </tr>
1161           <tr>
1162             <td class="nnns component red">
1163               <br />
1164             </td>
1165             <td class="snns plane red">closures</td>
1166             <td class="snns file red">cl_shift ( ? @@ ? )</td>
1167             <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
1168             <td class="snnn file red">
1169               <br />
1170             </td>
1171             <td class="snnn file red">
1172               <br />
1173             </td>
1174             <td class="ssnn file red">
1175               <br />
1176             </td>
1177           </tr>
1178           <tr>
1179             <td class="nnns component red">
1180               <br />
1181             </td>
1182             <td class="snns plane red">internal syntax</td>
1183             <td class="snns file red">genv</td>
1184             <td class="snnn file red">
1185               <br />
1186             </td>
1187             <td class="snnn file red">
1188               <br />
1189             </td>
1190             <td class="snnn file red">
1191               <br />
1192             </td>
1193             <td class="ssnn file red">
1194               <br />
1195             </td>
1196           </tr>
1197           <tr>
1198             <td class="nnns component red">
1199               <br />
1200             </td>
1201             <td class="nnns plane red">
1202               <br />
1203             </td>
1204             <td class="snns file red">lenv</td>
1205             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
1206             <td class="snnn file red">lenv_length ( |?| )</td>
1207             <td class="snnn file red">lenv_append ( ? @@ ? )</td>
1208             <td class="ssnn file red">lenv_px lenv_px_sn lenv_px_bi</td>
1209           </tr>
1210           <tr>
1211             <td class="nnns component red">
1212               <br />
1213             </td>
1214             <td class="nnns plane red">
1215               <br />
1216             </td>
1217             <td class="snns file red">term</td>
1218             <td class="snnn file red">term_weight ( ♯{?} )</td>
1219             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
1220             <td class="snnn file red">term_vector</td>
1221             <td class="ssnn file red">
1222               <br />
1223             </td>
1224           </tr>
1225           <tr>
1226             <td class="nnns component red">
1227               <br />
1228             </td>
1229             <td class="nnns plane red">
1230               <br />
1231             </td>
1232             <td class="snns file red">item</td>
1233             <td class="snnn file red">
1234               <br />
1235             </td>
1236             <td class="snnn file red">
1237               <br />
1238             </td>
1239             <td class="snnn file red">
1240               <br />
1241             </td>
1242             <td class="ssnn file red">
1243               <br />
1244             </td>
1245           </tr>
1246           <tr>
1247             <td class="nnss component red">
1248               <br />
1249             </td>
1250             <td class="snss plane red">external syntax</td>
1251             <td class="snss file red">aarity</td>
1252             <td class="snsn file red">
1253               <br />
1254             </td>
1255             <td class="snsn file red">
1256               <br />
1257             </td>
1258             <td class="snsn file red">
1259               <br />
1260             </td>
1261             <td class="sssn file red">
1262               <br />
1263             </td>
1264           </tr>
1265         </tbody>
1266       </table>
1267     </div>
1268
1269    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1270    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1271          one for each component.
1272    </div>
1273    <div class="spacer">
1274       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
1275     </div>
1276     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1277       <br />
1278     </div>
1279     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1280       <a href="http://validator.w3.org/check?uri=referer">
1281         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
1282       </a>
1283       <a href="http://jigsaw.w3.org/css-validator/check/referer">
1284         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
1285       </a>
1286       <a href="http://www.w3.org/XML/">
1287         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
1288       </a>
1289       <a href="http://www.w3.org/Graphics/PNG/">
1290         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
1291       </a>
1292       <a href="http://www.anybrowser.org/campaign/">
1293         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
1294       </a>
1295     </div>
1296     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1297       <br />
1298     </div>
1299     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sun, 21 Apr 2013 17:53:32 +0200</div>
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