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">233  </td>
 163             <td class="snns plane cyan">characters</td>
 164             <td class="snnn number cyan">408114</td>
 165             <td class="snns plane cyan">nodes</td>
 166             <td class="ssnn number cyan">1092089</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">85</td>
 172             <td class="snns plane green">lemmas</td>
 173             <td class="snnn number green">934</td>
 174             <td class="snns plane green">total</td>
 175             <td class="ssnn number green">1019</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">44</td>
 181             <td class="snss plane yellow">defined</td>
 182             <td class="snsn number yellow">80</td>
 183             <td class="snss plane yellow">total</td>
 184             <td class="sssn number yellow">124</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 magenta">dynamic typing</td>
 306             <td class="snns plane magenta">"big tree" parallel computation</td>
 307             <td class="snns file magenta">yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )</td>
 308             <td class="snnn file magenta">yprs_yprs</td>
 309             <td class="snnn file magenta">ygt ( ? ⊢ ⦃?,?⦄ &gt;[g] ⦃?,?⦄ )</td>
 310             <td class="snnn file magenta">ygt_ygt</td>
 311             <td class="ssnn file magenta">
 312               <br />
 313             </td>
 314           </tr>
 315           <tr>
 316             <td class="nnns component magenta">
 317               <br />
 318             </td>
 319             <td class="snns plane magenta">"big tree" parallel reduction</td>
 320             <td class="snns file magenta">ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )</td>
 321             <td class="snnn file magenta">ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )</td>
 322             <td class="snnn file magenta">
 323               <br />
 324             </td>
 325             <td class="snnn file magenta">
 326               <br />
 327             </td>
 328             <td class="ssnn file magenta">
 329               <br />
 330             </td>
 331           </tr>
 332           <tr>
 333             <td class="nnns component magenta">
 334               <br />
 335             </td>
 336             <td class="snns plane magenta">local env. ref. for stratified native validity</td>
 337             <td class="snns file magenta">lsubsv ( ? ⊢ ? ¡⊑[?] ? )</td>
 338             <td class="snnn file magenta">lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv</td>
 339             <td class="snnn file magenta">
 340               <br />
 341             </td>
 342             <td class="snnn file magenta">
 343               <br />
 344             </td>
 345             <td class="ssnn file magenta">
 346               <br />
 347             </td>
 348           </tr>
 349           <tr>
 350             <td class="nnns component magenta">
 351               <br />
 352             </td>
 353             <td class="snns plane magenta">stratified native validity</td>
 354             <td class="snns file magenta">snv ( ⦃?,?⦄ ⊢ ? ¡[?] )</td>
 355             <td class="snnn file magenta">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 magenta">
 357               <br />
 358             </td>
 359             <td class="snnn file magenta">
 360               <br />
 361             </td>
 362             <td class="ssnn file magenta">
 363               <br />
 364             </td>
 365           </tr>
 366           <tr>
 367             <td class="snns component prune">equivalence</td>
 368             <td class="snns plane prune">focalized equivalence</td>
 369             <td class="snns file prune">lfpcs ( ⦃?⦄ ⬌* ⦃?⦄ )</td>
 370             <td class="snnn file prune">lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs</td>
 371             <td class="snnn file prune">
 372               <br />
 373             </td>
 374             <td class="snnn file prune">
 375               <br />
 376             </td>
 377             <td class="ssnn file prune">
 378               <br />
 379             </td>
 380           </tr>
 381           <tr>
 382             <td class="nnns component prune">
 383               <br />
 384             </td>
 385             <td class="nnns plane prune">
 386               <br />
 387             </td>
 388             <td class="snns file prune">fpcs ( ⦃?,?⦄ ⬌* ⦃?,?⦄ )</td>
 389             <td class="snnn file prune">fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs</td>
 390             <td class="snnn file prune">
 391               <br />
 392             </td>
 393             <td class="snnn file prune">
 394               <br />
 395             </td>
 396             <td class="ssnn file prune">
 397               <br />
 398             </td>
 399           </tr>
 400           <tr>
 401             <td class="nnns component prune">
 402               <br />
 403             </td>
 404             <td class="snns plane prune">local env. ref. for stratified static type assignment</td>
 405             <td class="snns file prune">lsubss ( ? •⊑[?] ? )</td>
 406             <td class="snnn file prune">lsubss_ldrop lsubss_ssta lsubss_cpcs</td>
 407             <td class="snnn file prune">
 408               <br />
 409             </td>
 410             <td class="snnn file prune">
 411               <br />
 412             </td>
 413             <td class="ssnn file prune">
 414               <br />
 415             </td>
 416           </tr>
 417           <tr>
 418             <td class="nnns component prune">
 419               <br />
 420             </td>
 421             <td class="snns plane prune">context-sensitive equivalence</td>
 422             <td class="snns file prune">cpcs ( ? ⊢ ? ⬌* ? )</td>
 423             <td class="snnn file prune">cpcs_ltpss_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs</td>
 424             <td class="snnn file prune">
 425               <br />
 426             </td>
 427             <td class="snnn file prune">
 428               <br />
 429             </td>
 430             <td class="ssnn file prune">
 431               <br />
 432             </td>
 433           </tr>
 434           <tr>
 435             <td class="snns component blue">conversion</td>
 436             <td class="snns plane blue">focalized conversion</td>
 437             <td class="snns file blue">lfpc ( ⦃?⦄ ⬌ ⦃?⦄ )</td>
 438             <td class="snnn file blue">lfpc_lfpc</td>
 439             <td class="snnn file blue">
 440               <br />
 441             </td>
 442             <td class="snnn file blue">
 443               <br />
 444             </td>
 445             <td class="ssnn file blue">
 446               <br />
 447             </td>
 448           </tr>
 449           <tr>
 450             <td class="nnns component blue">
 451               <br />
 452             </td>
 453             <td class="nnns plane blue">
 454               <br />
 455             </td>
 456             <td class="snns file blue">fpc ( ⦃?,?⦄ ⬌ ⦃?,?⦄ )</td>
 457             <td class="snnn file blue">fpc_fpc</td>
 458             <td class="snnn file blue">
 459               <br />
 460             </td>
 461             <td class="snnn file blue">
 462               <br />
 463             </td>
 464             <td class="ssnn file blue">
 465               <br />
 466             </td>
 467           </tr>
 468           <tr>
 469             <td class="nnns component blue">
 470               <br />
 471             </td>
 472             <td class="snns plane blue">context-sensitive conversion</td>
 473             <td class="snns file blue">cpc ( ? ⊢ ? ⬌ ? )</td>
 474             <td class="snnn file blue">cpc_cpc</td>
 475             <td class="snnn file blue">
 476               <br />
 477             </td>
 478             <td class="snnn file blue">
 479               <br />
 480             </td>
 481             <td class="ssnn file blue">
 482               <br />
 483             </td>
 484           </tr>
 485           <tr>
 486             <td class="snns component sky">computation</td>
 487             <td class="snns plane sky">focalized computation</td>
 488             <td class="snns file sky">lfprs ( ⦃?⦄ ➡* ⦃?⦄ )</td>
 489             <td class="snnn file sky">lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs</td>
 490             <td class="snnn file sky">
 491               <br />
 492             </td>
 493             <td class="snnn file sky">
 494               <br />
 495             </td>
 496             <td class="ssnn file sky">
 497               <br />
 498             </td>
 499           </tr>
 500           <tr>
 501             <td class="nnns component sky">
 502               <br />
 503             </td>
 504             <td class="nnns plane sky">
 505               <br />
 506             </td>
 507             <td class="snns file sky">fprs ( ⦃?,?⦄ ➡* ⦃?,?⦄ )</td>
 508             <td class="snnn file sky">fprs_aaa fprs_fprs</td>
 509             <td class="snnn file sky">
 510               <br />
 511             </td>
 512             <td class="snnn file sky">
 513               <br />
 514             </td>
 515             <td class="ssnn file sky">
 516               <br />
 517             </td>
 518           </tr>
 519           <tr>
 520             <td class="nnns component sky">
 521               <br />
 522             </td>
 523             <td class="snns plane sky">decomposed extended computation</td>
 524             <td class="snns file sky">dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )</td>
 525             <td class="snnn file sky">dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn dxprs_aaa dxprs_dxprs</td>
 526             <td class="snnn file sky">
 527               <br />
 528             </td>
 529             <td class="snnn file sky">
 530               <br />
 531             </td>
 532             <td class="ssnn file sky">
 533               <br />
 534             </td>
 535           </tr>
 536           <tr>
 537             <td class="nnns component sky">
 538               <br />
 539             </td>
 540             <td class="snns plane sky">weakly normalizing computation</td>
 541             <td class="snns file sky">cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
 542             <td class="snnn file sky">cpe_cpe</td>
 543             <td class="snnn file sky">
 544               <br />
 545             </td>
 546             <td class="snnn file sky">
 547               <br />
 548             </td>
 549             <td class="ssnn file sky">
 550               <br />
 551             </td>
 552           </tr>
 553           <tr>
 554             <td class="nnns component sky">
 555               <br />
 556             </td>
 557             <td class="snns plane sky">strongly normalizing computation</td>
 558             <td class="snns file sky">csn_vector ( ? ⊢ ⬊* ? )</td>
 559             <td class="snnn file sky">csn_cpr_vector csn_tstc_vector csn_aaa</td>
 560             <td class="snnn file sky">
 561               <br />
 562             </td>
 563             <td class="snnn file sky">
 564               <br />
 565             </td>
 566             <td class="ssnn file sky">
 567               <br />
 568             </td>
 569           </tr>
 570           <tr>
 571             <td class="nnns component sky">
 572               <br />
 573             </td>
 574             <td class="nnns plane sky">
 575               <br />
 576             </td>
 577             <td class="snns file sky">csn ( ? ⊢ ⬊* ? )</td>
 578             <td class="snnn file sky">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
 579             <td class="snnn file sky">csn_lift csn_cpr csn_lfpr</td>
 580             <td class="snnn file sky">
 581               <br />
 582             </td>
 583             <td class="ssnn file sky">
 584               <br />
 585             </td>
 586           </tr>
 587           <tr>
 588             <td class="nnns component sky">
 589               <br />
 590             </td>
 591             <td class="snns plane sky">context-sensitive computation</td>
 592             <td class="snns file sky">cprs (? ⊢ ? ➡* ?)</td>
 593             <td class="snnn file sky">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 sky">
 595               <br />
 596             </td>
 597             <td class="snnn file sky">
 598               <br />
 599             </td>
 600             <td class="ssnn file sky">
 601               <br />
 602             </td>
 603           </tr>
 604           <tr>
 605             <td class="nnns component sky">
 606               <br />
 607             </td>
 608             <td class="snns plane sky">context-free computation</td>
 609             <td class="snns file sky">ltprs ( ? ➡* ? )</td>
 610             <td class="snnn file sky">ltprs_alt ( ? ➡➡* ? )</td>
 611             <td class="snnn file sky">ltprs_ldrop ltprs_ltprs</td>
 612             <td class="snnn file sky">
 613               <br />
 614             </td>
 615             <td class="ssnn file sky">
 616               <br />
 617             </td>
 618           </tr>
 619           <tr>
 620             <td class="nnns component sky">
 621               <br />
 622             </td>
 623             <td class="nnns plane sky">
 624               <br />
 625             </td>
 626             <td class="snns file sky">tprs ( ? ➡* ?)</td>
 627             <td class="snnn file sky">tprs_lift tprs_tprs</td>
 628             <td class="snnn file sky">
 629               <br />
 630             </td>
 631             <td class="snnn file sky">
 632               <br />
 633             </td>
 634             <td class="ssnn file sky">
 635               <br />
 636             </td>
 637           </tr>
 638           <tr>
 639             <td class="nnns component sky">
 640               <br />
 641             </td>
 642             <td class="snns plane sky">local env. ref. for abstract candidates of reducibility</td>
 643             <td class="snns file sky">lsubc ( ? ⊑[?] ? )</td>
 644             <td class="snnn file sky">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
 645             <td class="snnn file sky">
 646               <br />
 647             </td>
 648             <td class="snnn file sky">
 649               <br />
 650             </td>
 651             <td class="ssnn file sky">
 652               <br />
 653             </td>
 654           </tr>
 655           <tr>
 656             <td class="nnns component sky">
 657               <br />
 658             </td>
 659             <td class="snns plane sky">support for abstract computation properties</td>
 660             <td class="snns file sky">acp</td>
 661             <td class="snnn file sky">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
 662             <td class="snnn file sky">acp_aaa</td>
 663             <td class="snnn file sky">
 664               <br />
 665             </td>
 666             <td class="ssnn file sky">
 667               <br />
 668             </td>
 669           </tr>
 670           <tr>
 671             <td class="snns component cyan">reducibility</td>
 672             <td class="snns plane cyan">context-sensitive focalized reduction</td>
 673             <td class="snns file cyan">cfpr ( ? ⊢ ⦃?,?⦄ ➡ ⦃?,?⦄ )</td>
 674             <td class="snnn file cyan">cnfpr_ltpss cfpr_aaa cfpr_cpr cfpr_cfpr</td>
 675             <td class="snnn file cyan">
 676               <br />
 677             </td>
 678             <td class="snnn file cyan">
 679               <br />
 680             </td>
 681             <td class="ssnn file cyan">
 682               <br />
 683             </td>
 684           </tr>
 685           <tr>
 686             <td class="nnns component cyan">
 687               <br />
 688             </td>
 689             <td class="snns plane cyan">context-free focalized reduction</td>
 690             <td class="snns file cyan">lfpr ( ⦃?⦄ ➡ ⦃?⦄ )</td>
 691             <td class="snnn file cyan">lfpr_alt ( ⦃?⦄ ➡➡ ⦃?⦄ )</td>
 692             <td class="snnn file cyan">lfpr_aaa lfpr_cpr lfpr_fpr lfpr_lfpr</td>
 693             <td class="snnn file cyan">
 694               <br />
 695             </td>
 696             <td class="ssnn file cyan">
 697               <br />
 698             </td>
 699           </tr>
 700           <tr>
 701             <td class="nnns component cyan">
 702               <br />
 703             </td>
 704             <td class="nnns plane cyan">
 705               <br />
 706             </td>
 707             <td class="snns file cyan">fpr ( ⦃?,?⦄ ➡ ⦃?,?⦄ )</td>
 708             <td class="snnn file cyan">fpr_cpr fpr_fpr</td>
 709             <td class="snnn file cyan">
 710               <br />
 711             </td>
 712             <td class="snnn file cyan">
 713               <br />
 714             </td>
 715             <td class="ssnn file cyan">
 716               <br />
 717             </td>
 718           </tr>
 719           <tr>
 720             <td class="nnns component cyan">
 721               <br />
 722             </td>
 723             <td class="snns plane cyan">context-sensitive normal forms</td>
 724             <td class="snns file cyan">cnf ( ? ⊢ 𝐍⦃?⦄ )</td>
 725             <td class="snnn file cyan">cnf_lift cnf_cif</td>
 726             <td class="snnn file cyan">
 727               <br />
 728             </td>
 729             <td class="snnn file cyan">
 730               <br />
 731             </td>
 732             <td class="ssnn file cyan">
 733               <br />
 734             </td>
 735           </tr>
 736           <tr>
 737             <td class="nnns component cyan">
 738               <br />
 739             </td>
 740             <td class="snns plane cyan">revised context-sensitive reduction</td>
 741             <td class="snns file cyan">lpr ( ? ⊢ ➡ ? )</td>
 742             <td class="snnn file cyan">lpr_ldrop lpr_cpr lpr_lpr</td>
 743             <td class="snnn file cyan">
 744               <br />
 745             </td>
 746             <td class="snnn file cyan">
 747               <br />
 748             </td>
 749             <td class="ssnn file cyan">
 750               <br />
 751             </td>
 752           </tr>
 753           <tr>
 754             <td class="nnns component cyan">
 755               <br />
 756             </td>
 757             <td class="nnns plane cyan">
 758               <br />
 759             </td>
 760             <td class="snns file cyan">cpr ( ? ⊢ ? ➡ ? )</td>
 761             <td class="snnn file cyan">cpr_lift</td>
 762             <td class="snnn file cyan">
 763               <br />
 764             </td>
 765             <td class="snnn file cyan">
 766               <br />
 767             </td>
 768             <td class="ssnn file cyan">
 769               <br />
 770             </td>
 771           </tr>
 772           <tr>
 773             <td class="nnns component cyan">
 774               <br />
 775             </td>
 776             <td class="snns plane cyan">context-sensitive reduction</td>
 777             <td class="snns file cyan">cpr ( ? ⊢ ? ➡ ? )</td>
 778             <td class="snnn file cyan">cpr_lift cpr_tpss cpr_ltpss_dx cpr_ltpss_sn cpr_delift cpr_aaa cpr_ltpr cpr_cpr</td>
 779             <td class="snnn file cyan">
 780               <br />
 781             </td>
 782             <td class="snnn file cyan">
 783               <br />
 784             </td>
 785             <td class="ssnn file cyan">
 786               <br />
 787             </td>
 788           </tr>
 789           <tr>
 790             <td class="nnns component cyan">
 791               <br />
 792             </td>
 793             <td class="snns plane cyan">context-sensitive reducible forms</td>
 794             <td class="snns file cyan">crf ( ? ⊢ 𝐑⦃?⦄ )</td>
 795             <td class="snnn file cyan">crf_append</td>
 796             <td class="snnn file cyan">cif ( ? ⊢ 𝐈⦃?⦄ )</td>
 797             <td class="snnn file cyan">cif_append</td>
 798             <td class="ssnn file cyan">
 799               <br />
 800             </td>
 801           </tr>
 802           <tr>
 803             <td class="nnns component cyan">
 804               <br />
 805             </td>
 806             <td class="snns plane cyan">context-free normal forms</td>
 807             <td class="snns file cyan">thnf ( 𝐇𝐍⦃?⦄ )</td>
 808             <td class="snnn file cyan">
 809               <br />
 810             </td>
 811             <td class="snnn file cyan">
 812               <br />
 813             </td>
 814             <td class="snnn file cyan">
 815               <br />
 816             </td>
 817             <td class="ssnn file cyan">
 818               <br />
 819             </td>
 820           </tr>
 821           <tr>
 822             <td class="nnns component cyan">
 823               <br />
 824             </td>
 825             <td class="snns plane cyan">context-free reduction</td>
 826             <td class="snns file cyan">ltpr ( ? ➡ ? )</td>
 827             <td class="snnn file cyan">ltpr_ldrop ltpr_tps ltpr_tpss ltpr_ltpss_dx ltpr_ltpss_sn ltpr_aaa ltpr_ltpr</td>
 828             <td class="snnn file cyan">
 829               <br />
 830             </td>
 831             <td class="snnn file cyan">
 832               <br />
 833             </td>
 834             <td class="ssnn file cyan">
 835               <br />
 836             </td>
 837           </tr>
 838           <tr>
 839             <td class="nnns component cyan">
 840               <br />
 841             </td>
 842             <td class="nnns plane cyan">
 843               <br />
 844             </td>
 845             <td class="snns file cyan">tpr ( ? ➡ ? )</td>
 846             <td class="snnn file cyan">tpr_lift tpr_delift tpr_tpr</td>
 847             <td class="snnn file cyan">
 848               <br />
 849             </td>
 850             <td class="snnn file cyan">
 851               <br />
 852             </td>
 853             <td class="ssnn file cyan">
 854               <br />
 855             </td>
 856           </tr>
 857           <tr>
 858             <td class="snns component water">restricted computation</td>
 859             <td class="snns plane water">restricted parallel computation</td>
 860             <td class="snns file water">lpqs ( ? ⊢ ➤* ? )</td>
 861             <td class="snnn file water">lpqs_ldrop lpqs_cpqs lpqs_lpqs</td>
 862             <td class="snnn file water">
 863               <br />
 864             </td>
 865             <td class="snnn file water">
 866               <br />
 867             </td>
 868             <td class="ssnn file water">
 869               <br />
 870             </td>
 871           </tr>
 872           <tr>
 873             <td class="nnns component water">
 874               <br />
 875             </td>
 876             <td class="nnns plane water">
 877               <br />
 878             </td>
 879             <td class="snns file water">cpqs ( ? ⊢ ? ➤* ? )</td>
 880             <td class="snnn file water">cpqs_lift</td>
 881             <td class="snnn file water">
 882               <br />
 883             </td>
 884             <td class="snnn file water">
 885               <br />
 886             </td>
 887             <td class="ssnn file water">
 888               <br />
 889             </td>
 890           </tr>
 891           <tr>
 892             <td class="snns component green">unwind</td>
 893             <td class="snns plane green">iterated stratified static type assignment</td>
 894             <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
 895             <td class="snnn file green">sstas_lift sstas_lpss sstas_aaa sstas_sstas</td>
 896             <td class="snnn file green">
 897               <br />
 898             </td>
 899             <td class="snnn file green">
 900               <br />
 901             </td>
 902             <td class="ssnn file green">
 903               <br />
 904             </td>
 905           </tr>
 906           <tr>
 907             <td class="snns component grass">static typing</td>
 908             <td class="snns plane grass">stratified static type assignment</td>
 909             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 910             <td class="snnn file grass">ssta_lift ssta_lpss ssta_aaa ssta_ssta</td>
 911             <td class="snnn file grass">
 912               <br />
 913             </td>
 914             <td class="snnn file grass">
 915               <br />
 916             </td>
 917             <td class="ssnn file grass">
 918               <br />
 919             </td>
 920           </tr>
 921           <tr>
 922             <td class="nnns component grass">
 923               <br />
 924             </td>
 925             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
 926             <td class="snns file grass">lsuba ( ? ⁝⊑ ? )</td>
 927             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
 928             <td class="snnn file grass">
 929               <br />
 930             </td>
 931             <td class="snnn file grass">
 932               <br />
 933             </td>
 934             <td class="ssnn file grass">
 935               <br />
 936             </td>
 937           </tr>
 938           <tr>
 939             <td class="nnns component grass">
 940               <br />
 941             </td>
 942             <td class="snns plane grass">atomic arity assignment</td>
 943             <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
 944             <td class="snnn file grass">aaa_lift aaa_lifts aaa_lpss aaa_aaa</td>
 945             <td class="snnn file grass">
 946               <br />
 947             </td>
 948             <td class="snnn file grass">
 949               <br />
 950             </td>
 951             <td class="ssnn file grass">
 952               <br />
 953             </td>
 954           </tr>
 955           <tr>
 956             <td class="nnns component grass">
 957               <br />
 958             </td>
 959             <td class="snns plane grass">parameters</td>
 960             <td class="snns file grass">sh</td>
 961             <td class="snnn file grass">sd</td>
 962             <td class="snnn file grass">
 963               <br />
 964             </td>
 965             <td class="snnn file grass">
 966               <br />
 967             </td>
 968             <td class="ssnn file grass">
 969               <br />
 970             </td>
 971           </tr>
 972           <tr>
 973             <td class="snns component yellow">unfold</td>
 974             <td class="snns plane yellow">parallel substitution</td>
 975             <td class="snns file yellow">lpss ( ? ⊢ ▶* ? )</td>
 976             <td class="snnn file yellow">lpss_ldrop lpss_cpss lpss_lpss</td>
 977             <td class="snnn file yellow">
 978               <br />
 979             </td>
 980             <td class="snnn file yellow">
 981               <br />
 982             </td>
 983             <td class="ssnn file yellow">
 984               <br />
 985             </td>
 986           </tr>
 987           <tr>
 988             <td class="nnns component yellow">
 989               <br />
 990             </td>
 991             <td class="nnns plane yellow">
 992               <br />
 993             </td>
 994             <td class="snns file yellow">cpss ( ? ⊢ ? ▶* ? )</td>
 995             <td class="snnn file yellow">cpss_lift</td>
 996             <td class="snnn file yellow">
 997               <br />
 998             </td>
 999             <td class="snnn file yellow">
1000               <br />
1001             </td>
1002             <td class="ssnn file yellow">
1003               <br />
1004             </td>
1005           </tr>
1006           <tr>
1007             <td class="nnns component yellow">
1008               <br />
1009             </td>
1010             <td class="snns plane yellow">iterated structural successor for closures</td>
1011             <td class="snns file yellow">fsups ( ⦃?,?⦄ ⊃* ⦃?,?⦄ )</td>
1012             <td class="snnn file yellow">fsups_fsups</td>
1013             <td class="snnn file yellow">
1014               <br />
1015             </td>
1016             <td class="snnn file yellow">
1017               <br />
1018             </td>
1019             <td class="ssnn file yellow">
1020               <br />
1021             </td>
1022           </tr>
1023           <tr>
1024             <td class="nnns component yellow">
1025               <br />
1026             </td>
1027             <td class="nnns plane yellow">
1028               <br />
1029             </td>
1030             <td class="snns file yellow">fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )</td>
1031             <td class="snnn file yellow">fsupp_fsupp</td>
1032             <td class="snnn file yellow">
1033               <br />
1034             </td>
1035             <td class="snnn file yellow">
1036               <br />
1037             </td>
1038             <td class="ssnn file yellow">
1039               <br />
1040             </td>
1041           </tr>
1042           <tr>
1043             <td class="nnns component yellow">
1044               <br />
1045             </td>
1046             <td class="snns plane yellow">generic local env. slicing</td>
1047             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
1048             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
1049             <td class="snnn file yellow">
1050               <br />
1051             </td>
1052             <td class="snnn file yellow">
1053               <br />
1054             </td>
1055             <td class="ssnn file yellow">
1056               <br />
1057             </td>
1058           </tr>
1059           <tr>
1060             <td class="nnns component yellow">
1061               <br />
1062             </td>
1063             <td class="snns plane yellow">generic term relocation</td>
1064             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
1065             <td class="snnn file yellow">lifts_lift_vector</td>
1066             <td class="snnn file yellow">
1067               <br />
1068             </td>
1069             <td class="snnn file yellow">
1070               <br />
1071             </td>
1072             <td class="ssnn file yellow">
1073               <br />
1074             </td>
1075           </tr>
1076           <tr>
1077             <td class="nnns component yellow">
1078               <br />
1079             </td>
1080             <td class="nnns plane yellow">
1081               <br />
1082             </td>
1083             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
1084             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
1085             <td class="snnn file yellow">
1086               <br />
1087             </td>
1088             <td class="snnn file yellow">
1089               <br />
1090             </td>
1091             <td class="ssnn file yellow">
1092               <br />
1093             </td>
1094           </tr>
1095           <tr>
1096             <td class="nnns component yellow">
1097               <br />
1098             </td>
1099             <td class="snns plane yellow">support for generic relocation</td>
1100             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
1101             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
1102             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
1103             <td class="snnn file yellow">gr2_gr2</td>
1104             <td class="ssnn file yellow">
1105               <br />
1106             </td>
1107           </tr>
1108           <tr>
1109             <td class="snns component orange">substitution</td>
1110             <td class="snns plane orange">structural successor for closures</td>
1111             <td class="snns file orange">fsup ( ⦃?,?⦄ ⊃ ⦃?,?⦄ )</td>
1112             <td class="snnn file orange">
1113               <br />
1114             </td>
1115             <td class="snnn file orange">
1116               <br />
1117             </td>
1118             <td class="snnn file orange">
1119               <br />
1120             </td>
1121             <td class="ssnn file orange">
1122               <br />
1123             </td>
1124           </tr>
1125           <tr>
1126             <td class="nnns component orange">
1127               <br />
1128             </td>
1129             <td class="snns plane orange">global env. slicing</td>
1130             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
1131             <td class="snnn file orange">gdrop_gdrop</td>
1132             <td class="snnn file orange">
1133               <br />
1134             </td>
1135             <td class="snnn file orange">
1136               <br />
1137             </td>
1138             <td class="ssnn file orange">
1139               <br />
1140             </td>
1141           </tr>
1142           <tr>
1143             <td class="nnns component orange">
1144               <br />
1145             </td>
1146             <td class="snns plane orange">basic local env. slicing</td>
1147             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
1148             <td class="snnn file orange">ldrop_append ldrop_lpx ldrop_lpx_sn ldrop_lbotr ldrop_ldrop</td>
1149             <td class="snnn file orange">
1150               <br />
1151             </td>
1152             <td class="snnn file orange">
1153               <br />
1154             </td>
1155             <td class="ssnn file orange">
1156               <br />
1157             </td>
1158           </tr>
1159           <tr>
1160             <td class="nnns component orange">
1161               <br />
1162             </td>
1163             <td class="snns plane orange">local env. ref. for substitution</td>
1164             <td class="snns file orange">lsubr ( ? ⊑[?,?] ? )</td>
1165             <td class="snnn file orange">(lsubr_lsubr)</td>
1166             <td class="snnn file orange">lsubr_lbotr ( ⊒[?,?] ? )</td>
1167             <td class="snnn file orange">
1168               <br />
1169             </td>
1170             <td class="ssnn file orange">
1171               <br />
1172             </td>
1173           </tr>
1174           <tr>
1175             <td class="nnns component orange">
1176               <br />
1177             </td>
1178             <td class="snns plane orange">basic term relocation</td>
1179             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
1180             <td class="snnn file orange">lift_lift_vector</td>
1181             <td class="snnn file orange">
1182               <br />
1183             </td>
1184             <td class="snnn file orange">
1185               <br />
1186             </td>
1187             <td class="ssnn file orange">
1188               <br />
1189             </td>
1190           </tr>
1191           <tr>
1192             <td class="nnns component orange">
1193               <br />
1194             </td>
1195             <td class="nnns plane orange">
1196               <br />
1197             </td>
1198             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
1199             <td class="snnn file orange">lift_lift</td>
1200             <td class="snnn file orange">
1201               <br />
1202             </td>
1203             <td class="snnn file orange">
1204               <br />
1205             </td>
1206             <td class="ssnn file orange">
1207               <br />
1208             </td>
1209           </tr>
1210           <tr>
1211             <td class="snns component red">grammar</td>
1212             <td class="snns plane red">same head term form</td>
1213             <td class="snns file red">tshf ( ? ≈ ? )</td>
1214             <td class="snnn file red">(tshf_tshf)</td>
1215             <td class="snnn file red">
1216               <br />
1217             </td>
1218             <td class="snnn file red">
1219               <br />
1220             </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="snns plane red">same top term constructor</td>
1230             <td class="snns file red">tstc ( ? ≃ ? )</td>
1231             <td class="snnn file red">tstc_tstc tstc_vector</td>
1232             <td class="snnn file red">
1233               <br />
1234             </td>
1235             <td class="snnn file red">
1236               <br />
1237             </td>
1238             <td class="ssnn file red">
1239               <br />
1240             </td>
1241           </tr>
1242           <tr>
1243             <td class="nnns component red">
1244               <br />
1245             </td>
1246             <td class="snns plane red">closures</td>
1247             <td class="snns file red">cl_shift ( ? @@ ? )</td>
1248             <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
1249             <td class="snnn file red">
1250               <br />
1251             </td>
1252             <td class="snnn file red">
1253               <br />
1254             </td>
1255             <td class="ssnn file red">
1256               <br />
1257             </td>
1258           </tr>
1259           <tr>
1260             <td class="nnns component red">
1261               <br />
1262             </td>
1263             <td class="snns plane red">internal syntax</td>
1264             <td class="snns file red">genv</td>
1265             <td class="snnn file red">
1266               <br />
1267             </td>
1268             <td class="snnn file red">
1269               <br />
1270             </td>
1271             <td class="snnn file red">
1272               <br />
1273             </td>
1274             <td class="ssnn file red">
1275               <br />
1276             </td>
1277           </tr>
1278           <tr>
1279             <td class="nnns component red">
1280               <br />
1281             </td>
1282             <td class="nnns plane red">
1283               <br />
1284             </td>
1285             <td class="snns file red">lenv</td>
1286             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
1287             <td class="snnn file red">lenv_length ( |?| )</td>
1288             <td class="snnn file red">lenv_append ( ? @@ ? )</td>
1289             <td class="ssnn file red">lenv_px lenv_px_sn lenv_px_bi</td>
1290           </tr>
1291           <tr>
1292             <td class="nnns component red">
1293               <br />
1294             </td>
1295             <td class="nnns plane red">
1296               <br />
1297             </td>
1298             <td class="snns file red">term</td>
1299             <td class="snnn file red">term_weight ( ♯{?} )</td>
1300             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
1301             <td class="snnn file red">term_vector</td>
1302             <td class="ssnn file red">
1303               <br />
1304             </td>
1305           </tr>
1306           <tr>
1307             <td class="nnns component red">
1308               <br />
1309             </td>
1310             <td class="nnns plane red">
1311               <br />
1312             </td>
1313             <td class="snns file red">item</td>
1314             <td class="snnn file red">
1315               <br />
1316             </td>
1317             <td class="snnn file red">
1318               <br />
1319             </td>
1320             <td class="snnn file red">
1321               <br />
1322             </td>
1323             <td class="ssnn file red">
1324               <br />
1325             </td>
1326           </tr>
1327           <tr>
1328             <td class="nnss component red">
1329               <br />
1330             </td>
1331             <td class="snss plane red">external syntax</td>
1332             <td class="snss file red">aarity</td>
1333             <td class="snsn file red">
1334               <br />
1335             </td>
1336             <td class="snsn file red">
1337               <br />
1338             </td>
1339             <td class="snsn file red">
1340               <br />
1341             </td>
1342             <td class="sssn file red">
1343               <br />
1344             </td>
1345           </tr>
1346         </tbody>
1347       </table>
1348     </div>
1349
1350    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1351    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1352          one for each component.
1353    </div>
1354    <div class="spacer">
1355       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
1356     </div>
1357     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1358       <br />
1359     </div>
1360     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1361       <a href="http://validator.w3.org/check?uri=referer">
1362         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
1363       </a>
1364       <a href="http://jigsaw.w3.org/css-validator/check/referer">
1365         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
1366       </a>
1367       <a href="http://www.w3.org/XML/">
1368         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
1369       </a>
1370       <a href="http://www.w3.org/Graphics/PNG/">
1371         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
1372       </a>
1373       <a href="http://www.anybrowser.org/campaign/">
1374         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
1375       </a>
1376     </div>
1377     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1378       <br />
1379     </div>
1380     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Tue, 16 Apr 2013 21:51:34 +0200</div>
1381 </body>
1382 </html>