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">252</td>
 163             <td class="snns plane cyan">characters</td>
 164             <td class="snnn number cyan">483453</td>
 165             <td class="snns plane cyan">nodes</td>
 166             <td class="ssnn number cyan" />
 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">85</td>
 172             <td class="snns plane green">lemmas</td>
 173             <td class="snnn number green">1119</td>
 174             <td class="snns plane green">total</td>
 175             <td class="ssnn number green">1204</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">46</td>
 181             <td class="snss plane yellow">defined</td>
 182             <td class="snsn number yellow">82</td>
 183             <td class="snss plane yellow">total</td>
 184             <td class="sssn number yellow">128</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">2012 October 16.</span>
 213          Confluence for context-free parallel reduction on closures.
 214    </li>
 215     </ul>
 216    <ul xmlns:ld="http://lambdadelta.info/">
 217       <li>
 218         <span class="date">2012 July 26.</span>
 219          Term binders polarized to control ζ reduction.
 220    </li>
 221     </ul>
 222    <ul xmlns:ld="http://lambdadelta.info/">
 223       <li>
 224         <span class="date">2012 April 16.</span>
 225          Context-sensitive subject equivalence
 226          for atomic arity assignment
 227          (anniversary milestone).
 228    </li>
 229     </ul>
 230    <ul xmlns:ld="http://lambdadelta.info/">
 231       <li>
 232         <span class="date">2012 March 15.</span>
 233          Context-sensitive strong normalization
 234          for simply typed terms.
 235    </li>
 236     </ul>
 237    <ul xmlns:ld="http://lambdadelta.info/">
 238       <li>
 239         <span class="date">2012 January 27.</span>
 240          Support for abstract candidates of reducibility.
 241    </li>
 242     </ul>
 243    <ul xmlns:ld="http://lambdadelta.info/">
 244       <li>
 245         <span class="date">2011 September 21.</span>
 246          Confluence for context-sensitive parallel reduction on terms.
 247    </li>
 248     </ul>
 249    <ul xmlns:ld="http://lambdadelta.info/">
 250       <li>
 251         <span class="date">2011 September 6.</span>
 252          Confluence for context-free parallel reduction on terms.
 253    </li>
 254     </ul>
 255    <ul xmlns:ld="http://lambdadelta.info/">
 256       <li>
 257         <span class="date">2011 April 17.</span>
 258          Specification starts.
 259    </li>
 260     </ul>
 261
 262    <div xmlns:ld="http://lambdadelta.info/" class="head2">Logical Structure of the Specification</div>
 263    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in planes and components
 264          according to the following table.
 265          A notation file covering the whole specification is provided.
 266          The notation for the relations or functions introduced in each file
 267          is shown in parentheses (? are placeholders).
 268    </div>
 269    <div xmlns:ld="http://lambdadelta.info/" class="text">
 270       <table cellpadding="4" cellspacing="0">
 271         <tbody>
 272           <tr>
 273             <td class="snns component grey">component</td>
 274             <td class="snns plane grey">plane</td>
 275             <td class="snns file grey">files</td>
 276             <td class="snnn file grey">
 277               <br />
 278             </td>
 279             <td class="snnn file grey">
 280               <br />
 281             </td>
 282             <td class="snnn file grey">
 283               <br />
 284             </td>
 285             <td class="ssnn file grey">
 286               <br />
 287             </td>
 288           </tr>
 289           <tr>
 290             <td class="snns component prune">dynamic typing</td>
 291             <td class="snns plane prune">local env. ref. for stratified native validity</td>
 292             <td class="snns file prune">lsubsv ( ? ⊢ ? ⊩:⊑[?] ? )</td>
 293             <td class="snnn file prune">lsubsv_ldrop</td>
 294             <td class="snnn file prune">lsubsv_snv</td>
 295             <td class="snnn file prune">
 296               <br />
 297             </td>
 298             <td class="ssnn file prune">
 299               <br />
 300             </td>
 301           </tr>
 302           <tr>
 303             <td class="nnns component prune">
 304               <br />
 305             </td>
 306             <td class="snns plane prune">stratified native validity</td>
 307             <td class="snns file prune">snv ( ⦃?,?⦄ ⊩ ? :[?] )</td>
 308             <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>
 309             <td class="snnn file prune">
 310               <br />
 311             </td>
 312             <td class="snnn file prune">
 313               <br />
 314             </td>
 315             <td class="ssnn file prune">
 316               <br />
 317             </td>
 318           </tr>
 319           <tr>
 320             <td class="snns component blue">equivalence</td>
 321             <td class="snns plane blue">focalized equivalence</td>
 322             <td class="snns file blue">lfpcs ( ⦃?⦄ ⬌* ⦃?⦄ )</td>
 323             <td class="snnn file blue">lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs</td>
 324             <td class="snnn file blue">
 325               <br />
 326             </td>
 327             <td class="snnn file blue">
 328               <br />
 329             </td>
 330             <td class="ssnn file blue">
 331               <br />
 332             </td>
 333           </tr>
 334           <tr>
 335             <td class="nnns component blue">
 336               <br />
 337             </td>
 338             <td class="nnns plane blue">
 339               <br />
 340             </td>
 341             <td class="snns file blue">fpcs ( ⦃?,?⦄ ⬌* ⦃?,?⦄ )</td>
 342             <td class="snnn file blue">fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs</td>
 343             <td class="snnn file blue">
 344               <br />
 345             </td>
 346             <td class="snnn file blue">
 347               <br />
 348             </td>
 349             <td class="ssnn file blue">
 350               <br />
 351             </td>
 352           </tr>
 353           <tr>
 354             <td class="nnns component blue">
 355               <br />
 356             </td>
 357             <td class="snns plane blue">local env. ref. for context-sensitive equivalence</td>
 358             <td class="snns file blue">lsubse ( ? ⊢•⊑[?] ? )</td>
 359             <td class="snnn file blue">lsubse_ldrop lsubse_ssta lsubse_cpcs</td>
 360             <td class="snnn file blue">
 361               <br />
 362             </td>
 363             <td class="snnn file blue">
 364               <br />
 365             </td>
 366             <td class="ssnn file blue">
 367               <br />
 368             </td>
 369           </tr>
 370           <tr>
 371             <td class="nnns component blue">
 372               <br />
 373             </td>
 374             <td class="snns plane blue">context-sensitive equivalence</td>
 375             <td class="snns file blue">cpcs ( ? ⊢ ? ⬌* ? )</td>
 376             <td class="snnn file blue">cpcs_ltpss_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs</td>
 377             <td class="snnn file blue">
 378               <br />
 379             </td>
 380             <td class="snnn file blue">
 381               <br />
 382             </td>
 383             <td class="ssnn file blue">
 384               <br />
 385             </td>
 386           </tr>
 387           <tr>
 388             <td class="snns component sky">conversion</td>
 389             <td class="snns plane sky">focalized conversion</td>
 390             <td class="snns file sky">lfpc ( ⦃?⦄ ⬌ ⦃?⦄ )</td>
 391             <td class="snnn file sky">lfpc_lfpc</td>
 392             <td class="snnn file sky">
 393               <br />
 394             </td>
 395             <td class="snnn file sky">
 396               <br />
 397             </td>
 398             <td class="ssnn file sky">
 399               <br />
 400             </td>
 401           </tr>
 402           <tr>
 403             <td class="nnns component sky">
 404               <br />
 405             </td>
 406             <td class="nnns plane sky">
 407               <br />
 408             </td>
 409             <td class="snns file sky">fpc ( ⦃?,?⦄ ⬌ ⦃?,?⦄ )</td>
 410             <td class="snnn file sky">fpc_fpc</td>
 411             <td class="snnn file sky">
 412               <br />
 413             </td>
 414             <td class="snnn file sky">
 415               <br />
 416             </td>
 417             <td class="ssnn file sky">
 418               <br />
 419             </td>
 420           </tr>
 421           <tr>
 422             <td class="nnns component sky">
 423               <br />
 424             </td>
 425             <td class="snns plane sky">context-sensitive conversion</td>
 426             <td class="snns file sky">cpc ( ? ⊢ ? ⬌ ? )</td>
 427             <td class="snnn file sky">cpc_cpc</td>
 428             <td class="snnn file sky">
 429               <br />
 430             </td>
 431             <td class="snnn file sky">
 432               <br />
 433             </td>
 434             <td class="ssnn file sky">
 435               <br />
 436             </td>
 437           </tr>
 438           <tr>
 439             <td class="snns component cyan">computation</td>
 440             <td class="snns plane cyan">focalized computation</td>
 441             <td class="snns file cyan">lfprs ( ⦃?⦄ ➡* ⦃?⦄ )</td>
 442             <td class="snnn file cyan">lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs</td>
 443             <td class="snnn file cyan">
 444               <br />
 445             </td>
 446             <td class="snnn file cyan">
 447               <br />
 448             </td>
 449             <td class="ssnn file cyan">
 450               <br />
 451             </td>
 452           </tr>
 453           <tr>
 454             <td class="nnns component cyan">
 455               <br />
 456             </td>
 457             <td class="nnns plane cyan">
 458               <br />
 459             </td>
 460             <td class="snns file cyan">fprs ( ⦃?,?⦄ ➡* ⦃?,?⦄ )</td>
 461             <td class="snnn file cyan">fprs_aaa fprs_fprs</td>
 462             <td class="snnn file cyan">
 463               <br />
 464             </td>
 465             <td class="snnn file cyan">
 466               <br />
 467             </td>
 468             <td class="ssnn file cyan">
 469               <br />
 470             </td>
 471           </tr>
 472           <tr>
 473             <td class="nnns component cyan">
 474               <br />
 475             </td>
 476             <td class="snns plane cyan">"big tree" parallel computation</td>
 477             <td class="snns file cyan">yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )</td>
 478             <td class="snnn file cyan">yprs_yprs</td>
 479             <td class="snnn file cyan">ygt ( ? ⊢ ⦃?,?⦄ &gt;[g] ⦃?,?⦄ )</td>
 480             <td class="snnn file cyan">ygt_ygt</td>
 481             <td class="ssnn file cyan">
 482               <br />
 483             </td>
 484           </tr>
 485           <tr>
 486             <td class="nnns component cyan">
 487               <br />
 488             </td>
 489             <td class="snns plane cyan">decomposed extended computation</td>
 490             <td class="snns file cyan">dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )</td>
 491             <td class="snnn file cyan">dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn dxprs_aaa dxpr_lsubss dxprs_dxprs</td>
 492             <td class="snnn file cyan">
 493               <br />
 494             </td>
 495             <td class="snnn file cyan">
 496               <br />
 497             </td>
 498             <td class="ssnn file cyan">
 499               <br />
 500             </td>
 501           </tr>
 502           <tr>
 503             <td class="nnns component cyan">
 504               <br />
 505             </td>
 506             <td class="snns plane cyan">weakly normalizing computation</td>
 507             <td class="snns file cyan">cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
 508             <td class="snnn file cyan">cpe_cpe</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">strongly normalizing computation</td>
 524             <td class="snns file cyan">csn_vector ( ? ⊢ ⬊* ? )</td>
 525             <td class="snnn file cyan">csn_cpr_vector csn_tstc_vector csn_aaa</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="nnns plane cyan">
 541               <br />
 542             </td>
 543             <td class="snns file cyan">csn ( ? ⊢ ⬊* ? )</td>
 544             <td class="snnn file cyan">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
 545             <td class="snnn file cyan">csn_lift csn_cpr csn_lfpr</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">context-sensitive computation</td>
 558             <td class="snns file cyan">cprs (? ⊢ ? ➡* ?)</td>
 559             <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>
 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="snns plane cyan">context-free computation</td>
 575             <td class="snns file cyan">ltprs ( ? ➡* ? )</td>
 576             <td class="snnn file cyan">ltprs_alt ( ? ➡➡* ? )</td>
 577             <td class="snnn file cyan">ltprs_ldrop ltprs_ltprs</td>
 578             <td class="snnn file cyan">
 579               <br />
 580             </td>
 581             <td class="ssnn file cyan">
 582               <br />
 583             </td>
 584           </tr>
 585           <tr>
 586             <td class="nnns component cyan">
 587               <br />
 588             </td>
 589             <td class="nnns plane cyan">
 590               <br />
 591             </td>
 592             <td class="snns file cyan">tprs ( ? ➡* ?)</td>
 593             <td class="snnn file cyan">tprs_lift tprs_tprs</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">local env. ref. for abstract candidates of reducibility</td>
 609             <td class="snns file cyan">lsubc ( ? ⊑[?] ? )</td>
 610             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
 611             <td class="snnn file cyan">
 612               <br />
 613             </td>
 614             <td class="snnn file cyan">
 615               <br />
 616             </td>
 617             <td class="ssnn file cyan">
 618               <br />
 619             </td>
 620           </tr>
 621           <tr>
 622             <td class="nnns component cyan">
 623               <br />
 624             </td>
 625             <td class="snns plane cyan">support for abstract computation properties</td>
 626             <td class="snns file cyan">acp</td>
 627             <td class="snnn file cyan">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
 628             <td class="snnn file cyan">acp_aaa</td>
 629             <td class="snnn file cyan">
 630               <br />
 631             </td>
 632             <td class="ssnn file cyan">
 633               <br />
 634             </td>
 635           </tr>
 636           <tr>
 637             <td class="snns component water">reducibility</td>
 638             <td class="snns plane water">context-sensitive focalized reduction</td>
 639             <td class="snns file water">cfpr ( ? ⊢ ⦃?,?⦄ ➡ ⦃?,?⦄ )</td>
 640             <td class="snnn file water">cnfpr_ltpss cfpr_aaa cfpr_cpr cfpr_cfpr</td>
 641             <td class="snnn file water">
 642               <br />
 643             </td>
 644             <td class="snnn file water">
 645               <br />
 646             </td>
 647             <td class="ssnn file water">
 648               <br />
 649             </td>
 650           </tr>
 651           <tr>
 652             <td class="nnns component water">
 653               <br />
 654             </td>
 655             <td class="snns plane water">context-free focalized reduction</td>
 656             <td class="snns file water">lfpr ( ⦃?⦄ ➡ ⦃?⦄ )</td>
 657             <td class="snnn file water">lfpr_alt ( ⦃?⦄ ➡➡ ⦃?⦄ )</td>
 658             <td class="snnn file water">lfpr_aaa lfpr_cpr lfpr_fpr lfpr_lfpr</td>
 659             <td class="snnn file water">
 660               <br />
 661             </td>
 662             <td class="ssnn file water">
 663               <br />
 664             </td>
 665           </tr>
 666           <tr>
 667             <td class="nnns component water">
 668               <br />
 669             </td>
 670             <td class="nnns plane water">
 671               <br />
 672             </td>
 673             <td class="snns file water">fpr ( ⦃?,?⦄ ➡ ⦃?,?⦄ )</td>
 674             <td class="snnn file water">fpr_cpr fpr_fpr</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="snns plane water">"big tree" parallel reduction</td>
 690             <td class="snns file water">ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )</td>
 691             <td class="snnn file water">ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )</td>
 692             <td class="snnn file water">
 693               <br />
 694             </td>
 695             <td class="snnn file water">
 696               <br />
 697             </td>
 698             <td class="ssnn file water">
 699               <br />
 700             </td>
 701           </tr>
 702           <tr>
 703             <td class="nnns component water">
 704               <br />
 705             </td>
 706             <td class="snns plane water">context-sensitive normal forms</td>
 707             <td class="snns file water">cnf ( ? ⊢ 𝐍⦃?⦄ )</td>
 708             <td class="snnn file water">cnf_lift cnf_cif</td>
 709             <td class="snnn file water">
 710               <br />
 711             </td>
 712             <td class="snnn file water">
 713               <br />
 714             </td>
 715             <td class="ssnn file water">
 716               <br />
 717             </td>
 718           </tr>
 719           <tr>
 720             <td class="nnns component water">
 721               <br />
 722             </td>
 723             <td class="snns plane water">context-sensitive reduction</td>
 724             <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
 725             <td class="snnn file water">cpr_lift cpr_tpss cpr_ltpss_dx cpr_ltpss_sn cpr_delift cpr_aaa cpr_ltpr cpr_cpr</td>
 726             <td class="snnn file water">
 727               <br />
 728             </td>
 729             <td class="snnn file water">
 730               <br />
 731             </td>
 732             <td class="ssnn file water">
 733               <br />
 734             </td>
 735           </tr>
 736           <tr>
 737             <td class="nnns component water">
 738               <br />
 739             </td>
 740             <td class="snns plane water">context-sensitive reducible forms</td>
 741             <td class="snns file water">crf ( ? ⊢ 𝐑⦃?⦄ )</td>
 742             <td class="snnn file water">crf_append</td>
 743             <td class="snnn file water">cif ( ? ⊢ 𝐈⦃?⦄ )</td>
 744             <td class="snnn file water">cif_append</td>
 745             <td class="ssnn file water">
 746               <br />
 747             </td>
 748           </tr>
 749           <tr>
 750             <td class="nnns component water">
 751               <br />
 752             </td>
 753             <td class="snns plane water">context-free normal forms</td>
 754             <td class="snns file water">thnf ( 𝐇𝐍⦃?⦄ )</td>
 755             <td class="snnn file water">
 756               <br />
 757             </td>
 758             <td class="snnn file water">
 759               <br />
 760             </td>
 761             <td class="snnn file water">
 762               <br />
 763             </td>
 764             <td class="ssnn file water">
 765               <br />
 766             </td>
 767           </tr>
 768           <tr>
 769             <td class="nnns component water">
 770               <br />
 771             </td>
 772             <td class="snns plane water">context-free reduction</td>
 773             <td class="snns file water">ltpr ( ? ➡ ? )</td>
 774             <td class="snnn file water">ltpr_ldrop ltpr_tps ltpr_ltpss_dx ltpr_ltpss_sn ltpr_aaa ltpr_ltpr</td>
 775             <td class="snnn file water">
 776               <br />
 777             </td>
 778             <td class="snnn file water">
 779               <br />
 780             </td>
 781             <td class="ssnn file water">
 782               <br />
 783             </td>
 784           </tr>
 785           <tr>
 786             <td class="nnns component water">
 787               <br />
 788             </td>
 789             <td class="nnns plane water">
 790               <br />
 791             </td>
 792             <td class="snns file water">tpr ( ? ➡ ? )</td>
 793             <td class="snnn file water">tpr_lift tpr_tps tpr_tpss tpr_delift tpr_tpr</td>
 794             <td class="snnn file water">
 795               <br />
 796             </td>
 797             <td class="snnn file water">
 798               <br />
 799             </td>
 800             <td class="ssnn file water">
 801               <br />
 802             </td>
 803           </tr>
 804           <tr>
 805             <td class="snns component green">unwind</td>
 806             <td class="snns plane green">iterated stratified static type assignment</td>
 807             <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
 808             <td class="snnn file green">sstas_lift sstas_ltpss_dx sstas_ltpss_sn sstas_aaa sstas_lsubss sstas_sstas</td>
 809             <td class="snnn file green">
 810               <br />
 811             </td>
 812             <td class="snnn file green">
 813               <br />
 814             </td>
 815             <td class="ssnn file green">
 816               <br />
 817             </td>
 818           </tr>
 819           <tr>
 820             <td class="snns component grass">static typing</td>
 821             <td class="snns plane grass">local env. ref. for stratified static type assignment</td>
 822             <td class="snns file grass">lsubss ( ? •⊑[?] ? )</td>
 823             <td class="snnn file grass">lsubss_ldrop lsubss_ssta lsubss_lsubss</td>
 824             <td class="snnn file grass">
 825               <br />
 826             </td>
 827             <td class="snnn file grass">
 828               <br />
 829             </td>
 830             <td class="ssnn file grass">
 831               <br />
 832             </td>
 833           </tr>
 834           <tr>
 835             <td class="nnns component grass">
 836               <br />
 837             </td>
 838             <td class="snns plane grass">stratified static type assignment</td>
 839             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 840             <td class="snnn file grass">ssta_lift ssta_ltpss_dx ssta_ltpss_sn ssta_aaa ssta_ssta</td>
 841             <td class="snnn file grass">
 842               <br />
 843             </td>
 844             <td class="snnn file grass">
 845               <br />
 846             </td>
 847             <td class="ssnn file grass">
 848               <br />
 849             </td>
 850           </tr>
 851           <tr>
 852             <td class="nnns component grass">
 853               <br />
 854             </td>
 855             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
 856             <td class="snns file grass">lsuba ( ? ⁝⊑ ? )</td>
 857             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
 858             <td class="snnn file grass">
 859               <br />
 860             </td>
 861             <td class="snnn file grass">
 862               <br />
 863             </td>
 864             <td class="ssnn file grass">
 865               <br />
 866             </td>
 867           </tr>
 868           <tr>
 869             <td class="nnns component grass">
 870               <br />
 871             </td>
 872             <td class="snns plane grass">atomic arity assignment</td>
 873             <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
 874             <td class="snnn file grass">aaa_lift aaa_lifts aaa_ltpss_dx aaa_ltpss_sn aaa_aaa</td>
 875             <td class="snnn file grass">
 876               <br />
 877             </td>
 878             <td class="snnn file grass">
 879               <br />
 880             </td>
 881             <td class="ssnn file grass">
 882               <br />
 883             </td>
 884           </tr>
 885           <tr>
 886             <td class="nnns component grass">
 887               <br />
 888             </td>
 889             <td class="snns plane grass">parameters</td>
 890             <td class="snns file grass">sh</td>
 891             <td class="snnn file grass">sd</td>
 892             <td class="snnn file grass">
 893               <br />
 894             </td>
 895             <td class="snnn file grass">
 896               <br />
 897             </td>
 898             <td class="ssnn file grass">
 899               <br />
 900             </td>
 901           </tr>
 902           <tr>
 903             <td class="snns component yellow">unfold</td>
 904             <td class="snns plane yellow">basic local env. thinning</td>
 905             <td class="snns file yellow">thin ( ? ▼*[?,?] ≡ ? )</td>
 906             <td class="snnn file yellow">thin_ldrop thin_delift</td>
 907             <td class="snnn file yellow">
 908               <br />
 909             </td>
 910             <td class="snnn file yellow">
 911               <br />
 912             </td>
 913             <td class="ssnn file yellow">
 914               <br />
 915             </td>
 916           </tr>
 917           <tr>
 918             <td class="nnns component yellow">
 919               <br />
 920             </td>
 921             <td class="snns plane yellow">inverse basic term relocation</td>
 922             <td class="snns file yellow">delift ( ? ⊢ ? ▼*[?,?] ≡ ? )</td>
 923             <td class="snnn file yellow">delift_alt ( ? ⊢ ? ▼▼*[?,?] ≡ ? )</td>
 924             <td class="snnn file yellow">delift_lift delift_tpss delift_ltpss delift_delift</td>
 925             <td class="snnn file yellow">
 926               <br />
 927             </td>
 928             <td class="ssnn file yellow">
 929               <br />
 930             </td>
 931           </tr>
 932           <tr>
 933             <td class="nnns component yellow">
 934               <br />
 935             </td>
 936             <td class="snns plane yellow">partial unfold</td>
 937             <td class="snns file yellow">ltpss_sn ( ? ⊢ ▶*[?,?] ? )</td>
 938             <td class="snnn file yellow">ltpss_sn_alt ( ? ⊢ ▶▶*[?,?] ? )</td>
 939             <td class="snnn file yellow">ltpss_sn_ldrop ltpss_sn_tps ltpss_sn_tpss ltpss_sn_ltpss_sn</td>
 940             <td class="snnn file yellow">
 941               <br />
 942             </td>
 943             <td class="ssnn file yellow">
 944               <br />
 945             </td>
 946           </tr>
 947           <tr>
 948             <td class="nnns component yellow">
 949               <br />
 950             </td>
 951             <td class="nnns plane yellow">
 952               <br />
 953             </td>
 954             <td class="snns file yellow">ltpss_dx ( ? ▶*[?,?] ? )</td>
 955             <td class="snnn file yellow">ltpss_dx_ldrop ltpss_dx_tps ltpss_dx_tpss ltpss_dx_ltpss_dx</td>
 956             <td class="snnn file yellow">
 957               <br />
 958             </td>
 959             <td class="snnn file yellow">
 960               <br />
 961             </td>
 962             <td class="ssnn file yellow">
 963               <br />
 964             </td>
 965           </tr>
 966           <tr>
 967             <td class="nnns component yellow">
 968               <br />
 969             </td>
 970             <td class="nnns plane yellow">
 971               <br />
 972             </td>
 973             <td class="snns file yellow">tpss ( ? ⊢ ? ▶*[?,?] ? )</td>
 974             <td class="snnn file yellow">tpss_alt ( ? ⊢ ? ▶▶*[?,?] ? )</td>
 975             <td class="snnn file yellow">tpss_lift</td>
 976             <td class="snnn file yellow">tpss_tpss</td>
 977             <td class="ssnn file yellow">
 978               <br />
 979             </td>
 980           </tr>
 981           <tr>
 982             <td class="nnns component yellow">
 983               <br />
 984             </td>
 985             <td class="snns plane yellow">generic local env. slicing</td>
 986             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
 987             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
 988             <td class="snnn file yellow">
 989               <br />
 990             </td>
 991             <td class="snnn file yellow">
 992               <br />
 993             </td>
 994             <td class="ssnn file yellow">
 995               <br />
 996             </td>
 997           </tr>
 998           <tr>
 999             <td class="nnns component yellow">
1000               <br />
1001             </td>
1002             <td class="snns plane yellow">iterated restricted structural predecessor for closures</td>
1003             <td class="snns file yellow">frsups ( ⦃?,?⦄ ⧁* ⦃?,?⦄ )</td>
1004             <td class="snnn file yellow">frsups_frsups</td>
1005             <td class="snnn file yellow">
1006               <br />
1007             </td>
1008             <td class="snnn file yellow">
1009               <br />
1010             </td>
1011             <td class="ssnn file yellow">
1012               <br />
1013             </td>
1014           </tr>
1015           <tr>
1016             <td class="nnns component yellow">
1017               <br />
1018             </td>
1019             <td class="nnns plane yellow">
1020               <br />
1021             </td>
1022             <td class="snns file yellow">frsupp ( ⦃?,?⦄ ⧁+ ⦃?,?⦄ )</td>
1023             <td class="snnn file yellow">frsupp_frsupp</td>
1024             <td class="snnn file yellow">
1025               <br />
1026             </td>
1027             <td class="snnn file yellow">
1028               <br />
1029             </td>
1030             <td class="ssnn file yellow">
1031               <br />
1032             </td>
1033           </tr>
1034           <tr>
1035             <td class="nnns component yellow">
1036               <br />
1037             </td>
1038             <td class="snns plane yellow">generic term relocation</td>
1039             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
1040             <td class="snnn file yellow">lifts_lift_vector</td>
1041             <td class="snnn file yellow">
1042               <br />
1043             </td>
1044             <td class="snnn file yellow">
1045               <br />
1046             </td>
1047             <td class="ssnn file yellow">
1048               <br />
1049             </td>
1050           </tr>
1051           <tr>
1052             <td class="nnns component yellow">
1053               <br />
1054             </td>
1055             <td class="nnns plane yellow">
1056               <br />
1057             </td>
1058             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
1059             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
1060             <td class="snnn file yellow">
1061               <br />
1062             </td>
1063             <td class="snnn file yellow">
1064               <br />
1065             </td>
1066             <td class="ssnn file yellow">
1067               <br />
1068             </td>
1069           </tr>
1070           <tr>
1071             <td class="nnns component yellow">
1072               <br />
1073             </td>
1074             <td class="snns plane yellow">support for generic relocation</td>
1075             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
1076             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
1077             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
1078             <td class="snnn file yellow">gr2_gr2</td>
1079             <td class="ssnn file yellow">
1080               <br />
1081             </td>
1082           </tr>
1083           <tr>
1084             <td class="snns component orange">substitution</td>
1085             <td class="snns plane orange">parallel substitution</td>
1086             <td class="snns file orange">tps ( ? ⊢ ? ▶[?,?] ? )</td>
1087             <td class="snnn file orange">tps_lift tps_tps</td>
1088             <td class="snnn file orange">
1089               <br />
1090             </td>
1091             <td class="snnn file orange">
1092               <br />
1093             </td>
1094             <td class="ssnn file orange">
1095               <br />
1096             </td>
1097           </tr>
1098           <tr>
1099             <td class="nnns component orange">
1100               <br />
1101             </td>
1102             <td class="snns plane orange">global env. slicing</td>
1103             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
1104             <td class="snnn file orange">gdrop_gdrop</td>
1105             <td class="snnn file orange">
1106               <br />
1107             </td>
1108             <td class="snnn file orange">
1109               <br />
1110             </td>
1111             <td class="ssnn file orange">
1112               <br />
1113             </td>
1114           </tr>
1115           <tr>
1116             <td class="nnns component orange">
1117               <br />
1118             </td>
1119             <td class="snns plane orange">basic local env. slicing</td>
1120             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
1121             <td class="snnn file orange">ldrop_append ldrop_lpx ldrop_sfr ldrop_ldrop</td>
1122             <td class="snnn file orange">
1123               <br />
1124             </td>
1125             <td class="snnn file orange">
1126               <br />
1127             </td>
1128             <td class="ssnn file orange">
1129               <br />
1130             </td>
1131           </tr>
1132           <tr>
1133             <td class="nnns component orange">
1134               <br />
1135             </td>
1136             <td class="snns plane orange">local env. ref. for substitution</td>
1137             <td class="snns file orange">lsubs ( ? ≼[?,?] ? )</td>
1138             <td class="snnn file orange">(lsubs_lsubs)</td>
1139             <td class="snnn file orange">lsubs_sfr ( ≽[?,?] ? )</td>
1140             <td class="snnn file orange">
1141               <br />
1142             </td>
1143             <td class="ssnn file orange">
1144               <br />
1145             </td>
1146           </tr>
1147           <tr>
1148             <td class="nnns component orange">
1149               <br />
1150             </td>
1151             <td class="snns plane orange">restricted structural predecessor for closures</td>
1152             <td class="snns file orange">frsup ( ⦃?,?⦄ ⧁ ⦃?,?⦄ )</td>
1153             <td class="snnn file orange">
1154               <br />
1155             </td>
1156             <td class="snnn file orange">
1157               <br />
1158             </td>
1159             <td class="snnn file orange">
1160               <br />
1161             </td>
1162             <td class="ssnn file orange">
1163               <br />
1164             </td>
1165           </tr>
1166           <tr>
1167             <td class="nnns component orange">
1168               <br />
1169             </td>
1170             <td class="snns plane orange">basic term relocation</td>
1171             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
1172             <td class="snnn file orange">lift_lift_vector</td>
1173             <td class="snnn file orange">
1174               <br />
1175             </td>
1176             <td class="snnn file orange">
1177               <br />
1178             </td>
1179             <td class="ssnn file orange">
1180               <br />
1181             </td>
1182           </tr>
1183           <tr>
1184             <td class="nnns component orange">
1185               <br />
1186             </td>
1187             <td class="nnns plane orange">
1188               <br />
1189             </td>
1190             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
1191             <td class="snnn file orange">lift_lift</td>
1192             <td class="snnn file orange">
1193               <br />
1194             </td>
1195             <td class="snnn file orange">
1196               <br />
1197             </td>
1198             <td class="ssnn file orange">
1199               <br />
1200             </td>
1201           </tr>
1202           <tr>
1203             <td class="snns component red">grammar</td>
1204             <td class="snns plane red">same head term form</td>
1205             <td class="snns file red">tshf ( ? ≈ ? )</td>
1206             <td class="snnn file red">(tshf_tshf)</td>
1207             <td class="snnn file red">
1208               <br />
1209             </td>
1210             <td class="snnn file red">
1211               <br />
1212             </td>
1213             <td class="ssnn file red">
1214               <br />
1215             </td>
1216           </tr>
1217           <tr>
1218             <td class="nnns component red">
1219               <br />
1220             </td>
1221             <td class="snns plane red">same top term constructor</td>
1222             <td class="snns file red">tstc ( ? ≃ ? )</td>
1223             <td class="snnn file red">tstc_tstc tstc_vector</td>
1224             <td class="snnn file red">
1225               <br />
1226             </td>
1227             <td class="snnn file red">
1228               <br />
1229             </td>
1230             <td class="ssnn file red">
1231               <br />
1232             </td>
1233           </tr>
1234           <tr>
1235             <td class="nnns component red">
1236               <br />
1237             </td>
1238             <td class="snns plane red">closures</td>
1239             <td class="snns file red">cl_shift ( ? @@ ? )</td>
1240             <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
1241             <td class="snnn file red">
1242               <br />
1243             </td>
1244             <td class="snnn file red">
1245               <br />
1246             </td>
1247             <td class="ssnn file red">
1248               <br />
1249             </td>
1250           </tr>
1251           <tr>
1252             <td class="nnns component red">
1253               <br />
1254             </td>
1255             <td class="snns plane red">internal syntax</td>
1256             <td class="snns file red">genv</td>
1257             <td class="snnn file red">
1258               <br />
1259             </td>
1260             <td class="snnn file red">
1261               <br />
1262             </td>
1263             <td class="snnn file red">
1264               <br />
1265             </td>
1266             <td class="ssnn file red">
1267               <br />
1268             </td>
1269           </tr>
1270           <tr>
1271             <td class="nnns component red">
1272               <br />
1273             </td>
1274             <td class="nnns plane red">
1275               <br />
1276             </td>
1277             <td class="snns file red">lenv</td>
1278             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
1279             <td class="snnn file red">lenv_length ( |?| )</td>
1280             <td class="snnn file red">lenv_append ( ? @@ ? )</td>
1281             <td class="ssnn file red">lenv_px lenv_px_bi</td>
1282           </tr>
1283           <tr>
1284             <td class="nnns component red">
1285               <br />
1286             </td>
1287             <td class="nnns plane red">
1288               <br />
1289             </td>
1290             <td class="snns file red">term</td>
1291             <td class="snnn file red">term_weight ( ♯{?} )</td>
1292             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
1293             <td class="snnn file red">term_vector</td>
1294             <td class="ssnn file red">
1295               <br />
1296             </td>
1297           </tr>
1298           <tr>
1299             <td class="nnns component red">
1300               <br />
1301             </td>
1302             <td class="nnns plane red">
1303               <br />
1304             </td>
1305             <td class="snns file red">item</td>
1306             <td class="snnn file red">
1307               <br />
1308             </td>
1309             <td class="snnn file red">
1310               <br />
1311             </td>
1312             <td class="snnn file red">
1313               <br />
1314             </td>
1315             <td class="ssnn file red">
1316               <br />
1317             </td>
1318           </tr>
1319           <tr>
1320             <td class="nnss component red">
1321               <br />
1322             </td>
1323             <td class="snss plane red">external syntax</td>
1324             <td class="snss file red">aarity</td>
1325             <td class="snsn file red">
1326               <br />
1327             </td>
1328             <td class="snsn file red">
1329               <br />
1330             </td>
1331             <td class="snsn file red">
1332               <br />
1333             </td>
1334             <td class="sssn file red">
1335               <br />
1336             </td>
1337           </tr>
1338         </tbody>
1339       </table>
1340     </div>
1341
1342    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1343    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1344          one for each component.
1345    </div>
1346    <div class="spacer">
1347       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
1348     </div>
1349     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1350       <br />
1351     </div>
1352     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1353       <a href="http://validator.w3.org/check?uri=referer">
1354         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
1355       </a>
1356       <a href="http://jigsaw.w3.org/css-validator/check/referer">
1357         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
1358       </a>
1359       <a href="http://www.w3.org/XML/">
1360         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
1361       </a>
1362       <a href="http://www.w3.org/Graphics/PNG/">
1363         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
1364       </a>
1365       <a href="http://www.anybrowser.org/campaign/">
1366         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
1367       </a>
1368     </div>
1369     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1370       <br />
1371     </div>
1372     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Mon, 11 Mar 2013 13:47:08 +0100</div>
1373 </body>
1374 </html>