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">198  </td>
 163             <td class="snns plane cyan">characters</td>
 164             <td class="snnn number cyan">414004</td>
 165             <td class="snns plane cyan">nodes</td>
 166             <td class="ssnn number cyan">1213218</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">89</td>
 172             <td class="snns plane green">lemmas</td>
 173             <td class="snnn number green">877</td>
 174             <td class="snns plane green">total</td>
 175             <td class="ssnn number green">966</td>
 176           </tr>
 177           <tr>
 178             <td class="snss component yellow">concepts</td>
 179             <td class="snss plane yellow">declared</td>
 180             <td class="snsn number yellow">45</td>
 181             <td class="snss plane yellow">defined</td>
 182             <td class="snsn number yellow">79</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 context-sensitive extended 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          Reaxiomatized β-reductum as in extended β-reduction
 207    </li>
 208     </ul>
 209    <ul xmlns:ld="http://lambdadelta.info/">
 210       <li>
 211         <span class="date">2013 July 20.</span>
 212          Context-sensitive extended strong normalization
 213          for simply typed terms.
 214    </li>
 215     </ul>
 216    <ul xmlns:ld="http://lambdadelta.info/">
 217       <li>
 218         <span class="date">2013 April 16.</span>
 219          Reaxiomatized substitution and reduction
 220          commute with respect to subclosure
 221          (anniversary milestone).
 222    </li>
 223     </ul>
 224    <ul xmlns:ld="http://lambdadelta.info/">
 225       <li>
 226         <span class="date">2013 March 16.</span>
 227          Mutual recursive preservation of stratified native validity
 228          for hyper computation on closures.
 229    </li>
 230     </ul>
 231    <ul xmlns:ld="http://lambdadelta.info/">
 232       <li>
 233         <span class="date">2012 October 16.</span>
 234          Confluence for context-free parallel reduction on closures.
 235    </li>
 236     </ul>
 237    <ul xmlns:ld="http://lambdadelta.info/">
 238       <li>
 239         <span class="date">2012 July 26.</span>
 240          Term binders polarized to control ζ-reduction.
 241    </li>
 242     </ul>
 243    <ul xmlns:ld="http://lambdadelta.info/">
 244       <li>
 245         <span class="date">2012 April 16.</span>
 246          Context-sensitive subject equivalence
 247          for atomic arity assignment
 248          (anniversary milestone).
 249    </li>
 250     </ul>
 251    <ul xmlns:ld="http://lambdadelta.info/">
 252       <li>
 253         <span class="date">2012 March 15.</span>
 254          Context-sensitive strong normalization
 255          for simply typed terms.
 256    </li>
 257     </ul>
 258    <ul xmlns:ld="http://lambdadelta.info/">
 259       <li>
 260         <span class="date">2012 January 27.</span>
 261          Support for abstract candidates of reducibility.
 262    </li>
 263     </ul>
 264    <ul xmlns:ld="http://lambdadelta.info/">
 265       <li>
 266         <span class="date">2011 September 21.</span>
 267          Confluence for context-sensitive parallel reduction on terms.
 268    </li>
 269     </ul>
 270    <ul xmlns:ld="http://lambdadelta.info/">
 271       <li>
 272         <span class="date">2011 September 6.</span>
 273          Confluence for context-free parallel reduction on terms.
 274    </li>
 275     </ul>
 276    <ul xmlns:ld="http://lambdadelta.info/">
 277       <li>
 278         <span class="date">2011 April 17.</span>
 279          Specification starts.
 280    </li>
 281     </ul>
 282
 283    <div xmlns:ld="http://lambdadelta.info/" class="head2">Logical Structure of the Specification</div>
 284    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in planes and components
 285          according to the following table.
 286          A notation file covering the whole specification is provided.
 287          The notation for the relations or functions introduced in each file
 288          is shown in parentheses (? are placeholders).
 289    </div>
 290    <div xmlns:ld="http://lambdadelta.info/" class="text">
 291       <table cellpadding="4" cellspacing="0">
 292         <tbody>
 293           <tr>
 294             <td class="snns component grey">component</td>
 295             <td class="snns plane grey">plane</td>
 296             <td class="snns file grey">files</td>
 297             <td class="snnn file grey">
 298               <br />
 299             </td>
 300             <td class="snnn file grey">
 301               <br />
 302             </td>
 303             <td class="ssnn file grey">
 304               <br />
 305             </td>
 306           </tr>
 307           <tr>
 308             <td class="snns component prune">dynamic typing</td>
 309             <td class="snns plane prune">"big tree" parallel computation</td>
 310             <td class="snns file prune">yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )</td>
 311             <td class="snnn file prune">yprs_yprs</td>
 312             <td class="snnn file prune">ygt ( ? ⊢ ⦃?,?⦄ &gt;[g] ⦃?,?⦄ )</td>
 313             <td class="ssnn file prune">ygt_ygt</td>
 314           </tr>
 315           <tr>
 316             <td class="nnns component prune">
 317               <br />
 318             </td>
 319             <td class="snns plane prune">"big tree" parallel reduction</td>
 320             <td class="snns file prune">ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )</td>
 321             <td class="snnn file prune">ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )</td>
 322             <td class="snnn file prune">
 323               <br />
 324             </td>
 325             <td class="ssnn file prune">
 326               <br />
 327             </td>
 328           </tr>
 329           <tr>
 330             <td class="nnns component prune">
 331               <br />
 332             </td>
 333             <td class="snns plane prune">local env. ref. for stratified native validity</td>
 334             <td class="snns file prune">lsubsv ( ? ⊢ ? ¡⊑[?] ? )</td>
 335             <td class="snnn file prune">lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv</td>
 336             <td class="snnn file prune">
 337               <br />
 338             </td>
 339             <td class="ssnn file prune">
 340               <br />
 341             </td>
 342           </tr>
 343           <tr>
 344             <td class="nnns component prune">
 345               <br />
 346             </td>
 347             <td class="snns plane prune">stratified native validity</td>
 348             <td class="snns file prune">snv ( ⦃?,?⦄ ⊢ ? ¡[?] )</td>
 349             <td class="snnn file prune">snv_lift snv_lpss snv_aaa snv_ssta snv_sstas snv_ssta_lpr snv_lpr snv_cpcs</td>
 350             <td class="snnn file prune">
 351               <br />
 352             </td>
 353             <td class="ssnn file prune">
 354               <br />
 355             </td>
 356           </tr>
 357           <tr>
 358             <td class="snns component blue">equivalence</td>
 359             <td class="snns plane blue">local env. ref. for stratified static type assignment</td>
 360             <td class="snns file blue">lsubss ( ? •⊑[?] ? )</td>
 361             <td class="snnn file blue">lsubss_ldrop lsubss_ssta lsubss_cpcs</td>
 362             <td class="snnn file blue">
 363               <br />
 364             </td>
 365             <td class="ssnn file blue">
 366               <br />
 367             </td>
 368           </tr>
 369           <tr>
 370             <td class="nnns component blue">
 371               <br />
 372             </td>
 373             <td class="snns plane blue">context-sensitive equivalence</td>
 374             <td class="snns file blue">cpcs ( ? ⊢ ? ⬌* ? )</td>
 375             <td class="snnn file blue">cpcs_lpss cpcs_aaa cpcs_cprs cpcs_cpcs</td>
 376             <td class="snnn file blue">
 377               <br />
 378             </td>
 379             <td class="ssnn file blue">
 380               <br />
 381             </td>
 382           </tr>
 383           <tr>
 384             <td class="snns component sky">conversion</td>
 385             <td class="snns plane sky">context-sensitive conversion</td>
 386             <td class="snns file sky">cpc ( ? ⊢ ? ⬌ ? )</td>
 387             <td class="snnn file sky">cpc_cpc</td>
 388             <td class="snnn file sky">
 389               <br />
 390             </td>
 391             <td class="ssnn file sky">
 392               <br />
 393             </td>
 394           </tr>
 395           <tr>
 396             <td class="snns component cyan">computation</td>
 397             <td class="snns plane cyan">context-sensitive extended evaluation</td>
 398             <td class="snns file cyan">cpxe ( ⦃?,?⦄ ⊢ ➡*[?] 𝐍⦃?⦄ )</td>
 399             <td class="snnn file cyan">
 400               <br />
 401             </td>
 402             <td class="snnn file cyan">
 403               <br />
 404             </td>
 405             <td class="ssnn file cyan">
 406               <br />
 407             </td>
 408           </tr>
 409           <tr>
 410             <td class="nnns component cyan">
 411               <br />
 412             </td>
 413             <td class="snns plane cyan">context-sensitive evaluation</td>
 414             <td class="snns file cyan">cpre ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
 415             <td class="snnn file cyan">cpre_cpre</td>
 416             <td class="snnn file cyan">
 417               <br />
 418             </td>
 419             <td class="ssnn file cyan">
 420               <br />
 421             </td>
 422           </tr>
 423           <tr>
 424             <td class="nnns component cyan">
 425               <br />
 426             </td>
 427             <td class="snns plane cyan">strongly normalizing computation</td>
 428             <td class="snns file cyan">csn_vector ( ? ⊢ ⬊* ? )</td>
 429             <td class="snnn file cyan">csn_tstc_vector csn_aaa</td>
 430             <td class="snnn file cyan">
 431               <br />
 432             </td>
 433             <td class="ssnn file cyan">
 434               <br />
 435             </td>
 436           </tr>
 437           <tr>
 438             <td class="nnns component cyan">
 439               <br />
 440             </td>
 441             <td class="nnns plane cyan">
 442               <br />
 443             </td>
 444             <td class="snns file cyan">csn ( ? ⊢ ⬊* ? )</td>
 445             <td class="snnn file cyan">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
 446             <td class="snnn file cyan">csn_lift csn_lpx</td>
 447             <td class="ssnn file cyan">
 448               <br />
 449             </td>
 450           </tr>
 451           <tr>
 452             <td class="nnns component cyan">
 453               <br />
 454             </td>
 455             <td class="snns plane cyan">decomposed extended computation</td>
 456             <td class="snns file cyan">dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )</td>
 457             <td class="snnn file cyan">dxprs_lift dxprs_lpss dxprs_aaa dxprs_dxprs</td>
 458             <td class="snnn file cyan">
 459               <br />
 460             </td>
 461             <td class="ssnn file cyan">
 462               <br />
 463             </td>
 464           </tr>
 465           <tr>
 466             <td class="nnns component cyan">
 467               <br />
 468             </td>
 469             <td class="snns plane cyan">context-sensitive extended computation</td>
 470             <td class="snns file cyan">lpxs ( ⦃?,?⦄ ⊢ ➡*[?] ? )</td>
 471             <td class="snnn file cyan">lpxs_alt ( ⦃?,?⦄ ⊢ ➡➡*[?] ? )</td>
 472             <td class="snnn file cyan">lpxs_ldrop lpxs_aaa lpxs_cpxs lpxs_lpxs</td>
 473             <td class="ssnn file cyan">
 474               <br />
 475             </td>
 476           </tr>
 477           <tr>
 478             <td class="nnns component cyan">
 479               <br />
 480             </td>
 481             <td class="nnns plane cyan">
 482               <br />
 483             </td>
 484             <td class="snns file cyan">cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?] ? )</td>
 485             <td class="snnn file cyan">cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_aaa cpxs_cpxs</td>
 486             <td class="snnn file cyan">
 487               <br />
 488             </td>
 489             <td class="ssnn file cyan">
 490               <br />
 491             </td>
 492           </tr>
 493           <tr>
 494             <td class="nnns component cyan">
 495               <br />
 496             </td>
 497             <td class="snns plane cyan">context-sensitive computation</td>
 498             <td class="snns file cyan">lprs ( ? ⊢ ➡* ? )</td>
 499             <td class="snnn file cyan">lprs_alt ( ? ⊢ ➡➡* ? )</td>
 500             <td class="snnn file cyan">lprs_ldrop lprs_lpss lprs_cprs lprs_lprs</td>
 501             <td class="ssnn file cyan">
 502               <br />
 503             </td>
 504           </tr>
 505           <tr>
 506             <td class="nnns component cyan">
 507               <br />
 508             </td>
 509             <td class="nnns plane cyan">
 510               <br />
 511             </td>
 512             <td class="snns file cyan">cprs ( ? ⊢ ? ➡* ?)</td>
 513             <td class="snnn file cyan">cprs_lift cprs_lpss cprs_cprs</td>
 514             <td class="snnn file cyan">
 515               <br />
 516             </td>
 517             <td class="ssnn file cyan">
 518               <br />
 519             </td>
 520           </tr>
 521           <tr>
 522             <td class="nnns component cyan">
 523               <br />
 524             </td>
 525             <td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</td>
 526             <td class="snns file cyan">lsubc ( ? ⊑[?] ? )</td>
 527             <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
 528             <td class="snnn file cyan">
 529               <br />
 530             </td>
 531             <td class="ssnn file cyan">
 532               <br />
 533             </td>
 534           </tr>
 535           <tr>
 536             <td class="nnns component cyan">
 537               <br />
 538             </td>
 539             <td class="snns plane cyan">support for abstract computation properties</td>
 540             <td class="snns file cyan">acp</td>
 541             <td class="snnn file cyan">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
 542             <td class="snnn file cyan">acp_aaa</td>
 543             <td class="ssnn file cyan">
 544               <br />
 545             </td>
 546           </tr>
 547           <tr>
 548             <td class="snns component water">reduction</td>
 549             <td class="snns plane water">context-sensitive extended normal forms</td>
 550             <td class="snns file water">cnx ( ⦃?,?⦄ ⊢ 𝐍[?]⦃?⦄ )</td>
 551             <td class="snnn file water">cnx_lift cnx_crx cnx_cix</td>
 552             <td class="snnn file water">
 553               <br />
 554             </td>
 555             <td class="ssnn file water">
 556               <br />
 557             </td>
 558           </tr>
 559           <tr>
 560             <td class="nnns component water">
 561               <br />
 562             </td>
 563             <td class="snns plane water">context-sensitive extended reduction</td>
 564             <td class="snns file water">lpx ( ⦃?,?⦄ ⊢ ➡[?] ? )</td>
 565             <td class="snnn file water">lpx_ldrop lpx_aaa</td>
 566             <td class="snnn file water">
 567               <br />
 568             </td>
 569             <td class="ssnn file water">
 570               <br />
 571             </td>
 572           </tr>
 573           <tr>
 574             <td class="nnns component water">
 575               <br />
 576             </td>
 577             <td class="nnns plane water">
 578               <br />
 579             </td>
 580             <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 581             <td class="snnn file water">cpx_lift cpx_cix</td>
 582             <td class="snnn file water">
 583               <br />
 584             </td>
 585             <td class="ssnn file water">
 586               <br />
 587             </td>
 588           </tr>
 589           <tr>
 590             <td class="nnns component water">
 591               <br />
 592             </td>
 593             <td class="snns plane water">context-sensitive extended irreducible forms</td>
 594             <td class="snns file water">cix ( ⦃?,?⦄ ⊢ 𝐈[?]⦃?⦄ )</td>
 595             <td class="snnn file water">cix_append cix_lift</td>
 596             <td class="snnn file water">
 597               <br />
 598             </td>
 599             <td class="ssnn file water">
 600               <br />
 601             </td>
 602           </tr>
 603           <tr>
 604             <td class="nnns component water">
 605               <br />
 606             </td>
 607             <td class="snns plane water">context-sensitive extended reducible forms</td>
 608             <td class="snns file water">crx ( ⦃?,?⦄ ⊢ 𝐑[?]⦃?⦄ )</td>
 609             <td class="snnn file water">crx_append crx_lift</td>
 610             <td class="snnn file water">
 611               <br />
 612             </td>
 613             <td class="ssnn file water">
 614               <br />
 615             </td>
 616           </tr>
 617           <tr>
 618             <td class="nnns component water">
 619               <br />
 620             </td>
 621             <td class="snns plane water">local env. ref. for extended reduction</td>
 622             <td class="snns file water">lsubx ( ? ⓝ⊑ ? )</td>
 623             <td class="snnn file water">lsubx_lsubx</td>
 624             <td class="snnn file water">
 625               <br />
 626             </td>
 627             <td class="ssnn file water">
 628               <br />
 629             </td>
 630           </tr>
 631           <tr>
 632             <td class="nnns component water">
 633               <br />
 634             </td>
 635             <td class="snns plane water">context-sensitive normal forms</td>
 636             <td class="snns file water">cnr ( ? ⊢ 𝐍⦃?⦄ )</td>
 637             <td class="snnn file water">cnr_lift cnr_crr cnr_cir</td>
 638             <td class="snnn file water">
 639               <br />
 640             </td>
 641             <td class="ssnn file water">
 642               <br />
 643             </td>
 644           </tr>
 645           <tr>
 646             <td class="nnns component water">
 647               <br />
 648             </td>
 649             <td class="snns plane water">context-sensitive reduction</td>
 650             <td class="snns file water">lpr ( ? ⊢ ➡ ? )</td>
 651             <td class="snnn file water">lpr_ldrop lpr_lpss lpr_lpr</td>
 652             <td class="snnn file water">
 653               <br />
 654             </td>
 655             <td class="ssnn file water">
 656               <br />
 657             </td>
 658           </tr>
 659           <tr>
 660             <td class="nnns component water">
 661               <br />
 662             </td>
 663             <td class="nnns plane water">
 664               <br />
 665             </td>
 666             <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
 667             <td class="snnn file water">cpr_lift cpr_cir</td>
 668             <td class="snnn file water">
 669               <br />
 670             </td>
 671             <td class="ssnn file water">
 672               <br />
 673             </td>
 674           </tr>
 675           <tr>
 676             <td class="nnns component water">
 677               <br />
 678             </td>
 679             <td class="snns plane water">context-sensitive irreducible forms</td>
 680             <td class="snns file water">cir ( ? ⊢ 𝐈⦃?⦄ )</td>
 681             <td class="snnn file water">cir_append cir_lift</td>
 682             <td class="snnn file water">
 683               <br />
 684             </td>
 685             <td class="ssnn file water">
 686               <br />
 687             </td>
 688           </tr>
 689           <tr>
 690             <td class="nnns component water">
 691               <br />
 692             </td>
 693             <td class="snns plane water">context-sensitive reducible forms</td>
 694             <td class="snns file water">crr ( ? ⊢ 𝐑⦃?⦄ )</td>
 695             <td class="snnn file water">crr_append crr_lift</td>
 696             <td class="snnn file water">
 697               <br />
 698             </td>
 699             <td class="ssnn file water">
 700               <br />
 701             </td>
 702           </tr>
 703           <tr>
 704             <td class="snns component green">unfold</td>
 705             <td class="snns plane green">restricted parallel computation</td>
 706             <td class="snns file green">lpqs ( ? ⊢ ➤* ? )</td>
 707             <td class="snnn file green">lpqs_ldrop lpqs_cpqs lpqs_lpqs</td>
 708             <td class="snnn file green">
 709               <br />
 710             </td>
 711             <td class="ssnn file green">
 712               <br />
 713             </td>
 714           </tr>
 715           <tr>
 716             <td class="nnns component green">
 717               <br />
 718             </td>
 719             <td class="nnns plane green">
 720               <br />
 721             </td>
 722             <td class="snns file green">cpqs ( ? ⊢ ? ➤* ? )</td>
 723             <td class="snnn file green">cpqs_lift</td>
 724             <td class="snnn file green">
 725               <br />
 726             </td>
 727             <td class="ssnn file green">
 728               <br />
 729             </td>
 730           </tr>
 731           <tr>
 732             <td class="nnns component green">
 733               <br />
 734             </td>
 735             <td class="snns plane green">unfold</td>
 736             <td class="snns file green">unfold ( ? ⊢ ? ⧫* ? )</td>
 737             <td class="snnn file green">
 738               <br />
 739             </td>
 740             <td class="snnn file green">
 741               <br />
 742             </td>
 743             <td class="ssnn file green">
 744               <br />
 745             </td>
 746           </tr>
 747           <tr>
 748             <td class="nnns component green">
 749               <br />
 750             </td>
 751             <td class="snns plane green">iterated stratified static type assignment</td>
 752             <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
 753             <td class="snnn file green">sstas_lift sstas_lpss sstas_aaa sstas_sstas</td>
 754             <td class="snnn file green">
 755               <br />
 756             </td>
 757             <td class="ssnn file green">
 758               <br />
 759             </td>
 760           </tr>
 761           <tr>
 762             <td class="snns component grass">static typing</td>
 763             <td class="snns plane grass">stratified static type assignment</td>
 764             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
 765             <td class="snnn file grass">ssta_lift ssta_lpss ssta_aaa ssta_ssta</td>
 766             <td class="snnn file grass">
 767               <br />
 768             </td>
 769             <td class="ssnn file grass">
 770               <br />
 771             </td>
 772           </tr>
 773           <tr>
 774             <td class="nnns component grass">
 775               <br />
 776             </td>
 777             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
 778             <td class="snns file grass">lsuba ( ? ⁝⊑ ? )</td>
 779             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
 780             <td class="snnn file grass">
 781               <br />
 782             </td>
 783             <td class="ssnn file grass">
 784               <br />
 785             </td>
 786           </tr>
 787           <tr>
 788             <td class="nnns component grass">
 789               <br />
 790             </td>
 791             <td class="snns plane grass">atomic arity assignment</td>
 792             <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
 793             <td class="snnn file grass">aaa_lift aaa_lifts aaa_lpss aaa_aaa</td>
 794             <td class="snnn file grass">
 795               <br />
 796             </td>
 797             <td class="ssnn file grass">
 798               <br />
 799             </td>
 800           </tr>
 801           <tr>
 802             <td class="nnns component grass">
 803               <br />
 804             </td>
 805             <td class="snns plane grass">parameters</td>
 806             <td class="snns file grass">sh</td>
 807             <td class="snnn file grass">sd</td>
 808             <td class="snnn file grass">
 809               <br />
 810             </td>
 811             <td class="ssnn file grass">
 812               <br />
 813             </td>
 814           </tr>
 815           <tr>
 816             <td class="snns component yellow">substitution</td>
 817             <td class="snns plane yellow">parallel substitution</td>
 818             <td class="snns file yellow">lpss ( ? ⊢ ▶* ? )</td>
 819             <td class="snnn file yellow">lpss_ldrop lpss_cpss lpss_lpss</td>
 820             <td class="snnn file yellow">
 821               <br />
 822             </td>
 823             <td class="ssnn file yellow">
 824               <br />
 825             </td>
 826           </tr>
 827           <tr>
 828             <td class="nnns component yellow">
 829               <br />
 830             </td>
 831             <td class="nnns plane yellow">
 832               <br />
 833             </td>
 834             <td class="snns file yellow">cpss ( ? ⊢ ? ▶* ? )</td>
 835             <td class="snnn file yellow">cpss_lift</td>
 836             <td class="snnn file yellow">
 837               <br />
 838             </td>
 839             <td class="ssnn file yellow">
 840               <br />
 841             </td>
 842           </tr>
 843           <tr>
 844             <td class="nnns component yellow">
 845               <br />
 846             </td>
 847             <td class="snns plane yellow">local env. ref. for substitution</td>
 848             <td class="snns file yellow">lsubr ( ? ⊑ ? )</td>
 849             <td class="snnn file yellow">lsubr_lsubr</td>
 850             <td class="snnn file yellow">
 851               <br />
 852             </td>
 853             <td class="ssnn file yellow">
 854               <br />
 855             </td>
 856           </tr>
 857           <tr>
 858             <td class="nnns component yellow">
 859               <br />
 860             </td>
 861             <td class="snns plane yellow">iterated structural successor for closures</td>
 862             <td class="snns file yellow">fsups ( ⦃?,?⦄ ⊃* ⦃?,?⦄ )</td>
 863             <td class="snnn file yellow">fsups_fsups</td>
 864             <td class="snnn file yellow">
 865               <br />
 866             </td>
 867             <td class="ssnn file yellow">
 868               <br />
 869             </td>
 870           </tr>
 871           <tr>
 872             <td class="nnns component yellow">
 873               <br />
 874             </td>
 875             <td class="nnns plane yellow">
 876               <br />
 877             </td>
 878             <td class="snns file yellow">fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )</td>
 879             <td class="snnn file yellow">fsupp_fsupp</td>
 880             <td class="snnn file yellow">
 881               <br />
 882             </td>
 883             <td class="ssnn file yellow">
 884               <br />
 885             </td>
 886           </tr>
 887           <tr>
 888             <td class="nnns component yellow">
 889               <br />
 890             </td>
 891             <td class="snns plane yellow">generic local env. slicing</td>
 892             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
 893             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
 894             <td class="snnn file yellow">
 895               <br />
 896             </td>
 897             <td class="ssnn file yellow">
 898               <br />
 899             </td>
 900           </tr>
 901           <tr>
 902             <td class="nnns component yellow">
 903               <br />
 904             </td>
 905             <td class="snns plane yellow">generic term relocation</td>
 906             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
 907             <td class="snnn file yellow">lifts_lift_vector</td>
 908             <td class="snnn file yellow">
 909               <br />
 910             </td>
 911             <td class="ssnn file yellow">
 912               <br />
 913             </td>
 914           </tr>
 915           <tr>
 916             <td class="nnns component yellow">
 917               <br />
 918             </td>
 919             <td class="nnns plane yellow">
 920               <br />
 921             </td>
 922             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
 923             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
 924             <td class="snnn file yellow">
 925               <br />
 926             </td>
 927             <td class="ssnn file yellow">
 928               <br />
 929             </td>
 930           </tr>
 931           <tr>
 932             <td class="nnns component yellow">
 933               <br />
 934             </td>
 935             <td class="snns plane yellow">support for generic relocation</td>
 936             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
 937             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
 938             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
 939             <td class="ssnn file yellow">gr2_gr2</td>
 940           </tr>
 941           <tr>
 942             <td class="snns component orange">relocation</td>
 943             <td class="snns plane orange">structural successor for closures</td>
 944             <td class="snns file orange">fsup ( ⦃?,?⦄ ⊃ ⦃?,?⦄ )</td>
 945             <td class="snnn file orange">fsupq ( ⦃?,?⦄ ⊃⸮ ⦃?,?⦄ )</td>
 946             <td class="snnn file orange">fsupq_alt</td>
 947             <td class="ssnn file orange">
 948               <br />
 949             </td>
 950           </tr>
 951           <tr>
 952             <td class="nnns component orange">
 953               <br />
 954             </td>
 955             <td class="snns plane orange">global env. slicing</td>
 956             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
 957             <td class="snnn file orange">gdrop_gdrop</td>
 958             <td class="snnn file orange">
 959               <br />
 960             </td>
 961             <td class="ssnn file orange">
 962               <br />
 963             </td>
 964           </tr>
 965           <tr>
 966             <td class="nnns component orange">
 967               <br />
 968             </td>
 969             <td class="snns plane orange">basic local env. slicing</td>
 970             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
 971             <td class="snnn file orange">ldrop_append ldrop_lpx_sn ldrop_ldrop</td>
 972             <td class="snnn file orange">
 973               <br />
 974             </td>
 975             <td class="ssnn file orange">
 976               <br />
 977             </td>
 978           </tr>
 979           <tr>
 980             <td class="nnns component orange">
 981               <br />
 982             </td>
 983             <td class="snns plane orange">basic term relocation</td>
 984             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
 985             <td class="snnn file orange">lift_lift_vector</td>
 986             <td class="snnn file orange">
 987               <br />
 988             </td>
 989             <td class="ssnn file orange">
 990               <br />
 991             </td>
 992           </tr>
 993           <tr>
 994             <td class="nnns component orange">
 995               <br />
 996             </td>
 997             <td class="nnns plane orange">
 998               <br />
 999             </td>
1000             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
1001             <td class="snnn file orange">lift_lift</td>
1002             <td class="snnn file orange">
1003               <br />
1004             </td>
1005             <td class="ssnn file orange">
1006               <br />
1007             </td>
1008           </tr>
1009           <tr>
1010             <td class="snns component red">grammar</td>
1011             <td class="snns plane red">pointwise extension of a relation</td>
1012             <td class="snns file red">lpx_sn</td>
1013             <td class="snnn file red">lpx_sn_tc lpx_sn_lpx_sn</td>
1014             <td class="snnn file red">
1015               <br />
1016             </td>
1017             <td class="ssnn file red">
1018               <br />
1019             </td>
1020           </tr>
1021           <tr>
1022             <td class="nnns component red">
1023               <br />
1024             </td>
1025             <td class="snns plane red">same top term constructor</td>
1026             <td class="snns file red">tstc ( ? ≃ ? )</td>
1027             <td class="snnn file red">tstc_tstc tstc_vector</td>
1028             <td class="snnn file red">
1029               <br />
1030             </td>
1031             <td class="ssnn file red">
1032               <br />
1033             </td>
1034           </tr>
1035           <tr>
1036             <td class="nnns component red">
1037               <br />
1038             </td>
1039             <td class="snns plane red">closures</td>
1040             <td class="snns file red">cl_shift ( ? @@ ? )</td>
1041             <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
1042             <td class="snnn file red">
1043               <br />
1044             </td>
1045             <td class="ssnn file red">
1046               <br />
1047             </td>
1048           </tr>
1049           <tr>
1050             <td class="nnns component red">
1051               <br />
1052             </td>
1053             <td class="snns plane red">internal syntax</td>
1054             <td class="snns file red">genv</td>
1055             <td class="snnn file red">
1056               <br />
1057             </td>
1058             <td class="snnn file red">
1059               <br />
1060             </td>
1061             <td class="ssnn file red">
1062               <br />
1063             </td>
1064           </tr>
1065           <tr>
1066             <td class="nnns component red">
1067               <br />
1068             </td>
1069             <td class="nnns plane red">
1070               <br />
1071             </td>
1072             <td class="snns file red">lenv</td>
1073             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
1074             <td class="snnn file red">lenv_length ( |?| )</td>
1075             <td class="ssnn file red">lenv_append ( ? @@ ? )</td>
1076           </tr>
1077           <tr>
1078             <td class="nnns component red">
1079               <br />
1080             </td>
1081             <td class="nnns plane red">
1082               <br />
1083             </td>
1084             <td class="snns file red">term</td>
1085             <td class="snnn file red">term_weight ( ♯{?} )</td>
1086             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
1087             <td class="ssnn file red">term_vector</td>
1088           </tr>
1089           <tr>
1090             <td class="nnns component red">
1091               <br />
1092             </td>
1093             <td class="nnns plane red">
1094               <br />
1095             </td>
1096             <td class="snns file red">item</td>
1097             <td class="snnn file red">
1098               <br />
1099             </td>
1100             <td class="snnn file red">
1101               <br />
1102             </td>
1103             <td class="ssnn file red">
1104               <br />
1105             </td>
1106           </tr>
1107           <tr>
1108             <td class="nnss component red">
1109               <br />
1110             </td>
1111             <td class="snss plane red">external syntax</td>
1112             <td class="snss file red">aarity</td>
1113             <td class="snsn file red">
1114               <br />
1115             </td>
1116             <td class="snsn file red">
1117               <br />
1118             </td>
1119             <td class="sssn file red">
1120               <br />
1121             </td>
1122           </tr>
1123         </tbody>
1124       </table>
1125     </div>
1126
1127    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1128    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1129          one for each component.
1130    </div>
1131    <div class="spacer">
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1147       <a href="http://www.w3.org/Graphics/PNG/">
1148         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
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1151         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
1152       </a>
1153     </div>
1154     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1155       <br />
1156     </div>
1157     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sun, 21 Jul 2013 00:11:48 +0200</div>
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