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8     <meta name="author" content="Ferruccio Guidi" />
9     <meta name="description" content="lambdadelta version 2" />
10     <title>lambdadelta version 2</title>
11     <link rel="stylesheet" type="text/css" href="http://lambdadelta.info/css/ld_web.css" />
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15   </head>
16   <body lang="en-US">
17     <div class="spacer">
18       <a href="http://lambdadelta.info/">
19         <img class="icon32" alt="[lambdadelta home]" title="lambdadelta home" src="http://lambdadelta.info/images/crux_32.png" />
20       </a>
21     </div>
22     <div class="head1">cic:/matita/lambdadelta/basic_2/ (λδ version 2)</div>
23     <div class="spacer">
24       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
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">262  </td>
163             <td class="snns plane cyan">characters</td>
164             <td class="snnn number cyan">527314</td>
165             <td class="snns plane cyan">nodes</td>
166             <td class="ssnn number cyan">1440935</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">95</td>
172             <td class="snns plane green">lemmas</td>
173             <td class="snnn number green">1170</td>
174             <td class="snns plane green">total</td>
175             <td class="ssnn number green">1265</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">49</td>
181             <td class="snss plane yellow">defined</td>
182             <td class="snsn number yellow">87</td>
183             <td class="snss plane yellow">total</td>
184             <td class="sssn number yellow">136</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 March 16.</span>
213          Mutual recursive preservation of stratified native validity
214          for hyper computation on closures.
215    </li>
216     </ul>
217    <ul xmlns:ld="http://lambdadelta.info/">
218       <li>
219         <span class="date">2012 October 16.</span>
220          Confluence for context-free parallel reduction on closures.
221    </li>
222     </ul>
223    <ul xmlns:ld="http://lambdadelta.info/">
224       <li>
225         <span class="date">2012 July 26.</span>
226          Term binders polarized to control ζ reduction.
227    </li>
228     </ul>
229    <ul xmlns:ld="http://lambdadelta.info/">
230       <li>
231         <span class="date">2012 April 16.</span>
232          Context-sensitive subject equivalence
233          for atomic arity assignment
234          (anniversary milestone).
235    </li>
236     </ul>
237    <ul xmlns:ld="http://lambdadelta.info/">
238       <li>
239         <span class="date">2012 March 15.</span>
240          Context-sensitive strong normalization
241          for simply typed terms.
242    </li>
243     </ul>
244    <ul xmlns:ld="http://lambdadelta.info/">
245       <li>
246         <span class="date">2012 January 27.</span>
247          Support for abstract candidates of reducibility.
248    </li>
249     </ul>
250    <ul xmlns:ld="http://lambdadelta.info/">
251       <li>
252         <span class="date">2011 September 21.</span>
253          Confluence for context-sensitive parallel reduction on terms.
254    </li>
255     </ul>
256    <ul xmlns:ld="http://lambdadelta.info/">
257       <li>
258         <span class="date">2011 September 6.</span>
259          Confluence for context-free parallel reduction on terms.
260    </li>
261     </ul>
262    <ul xmlns:ld="http://lambdadelta.info/">
263       <li>
264         <span class="date">2011 April 17.</span>
265          Specification starts.
266    </li>
267     </ul>
268
269    <div xmlns:ld="http://lambdadelta.info/" class="head2">Logical Structure of the Specification</div>
270    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in planes and components
271          according to the following table.
272          A notation file covering the whole specification is provided.
273          The notation for the relations or functions introduced in each file
274          is shown in parentheses (? are placeholders).
275    </div>
276    <div xmlns:ld="http://lambdadelta.info/" class="text">
277       <table cellpadding="4" cellspacing="0">
278         <tbody>
279           <tr>
280             <td class="snns component grey">component</td>
281             <td class="snns plane grey">plane</td>
282             <td class="snns file grey">files</td>
283             <td class="snnn file grey">
284               <br />
285             </td>
286             <td class="snnn file grey">
287               <br />
288             </td>
289             <td class="snnn file grey">
290               <br />
291             </td>
292             <td class="ssnn file grey">
293               <br />
294             </td>
295           </tr>
296           <tr>
297             <td class="snns component magenta">dynamic typing</td>
298             <td class="snns plane magenta">"big tree" parallel computation</td>
299             <td class="snns file magenta">yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )</td>
300             <td class="snnn file magenta">yprs_yprs</td>
301             <td class="snnn file magenta">ygt ( ? ⊢ ⦃?,?⦄ &gt;[g] ⦃?,?⦄ )</td>
302             <td class="snnn file magenta">ygt_ygt</td>
303             <td class="ssnn file magenta">
304               <br />
305             </td>
306           </tr>
307           <tr>
308             <td class="nnns component magenta">
309               <br />
310             </td>
311             <td class="snns plane magenta">"big tree" parallel reduction</td>
312             <td class="snns file magenta">ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )</td>
313             <td class="snnn file magenta">ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )</td>
314             <td class="snnn file magenta">
315               <br />
316             </td>
317             <td class="snnn file magenta">
318               <br />
319             </td>
320             <td class="ssnn file magenta">
321               <br />
322             </td>
323           </tr>
324           <tr>
325             <td class="nnns component magenta">
326               <br />
327             </td>
328             <td class="snns plane magenta">local env. ref. for stratified native validity</td>
329             <td class="snns file magenta">lsubsv ( ? ⊢ ? ¡⊑[?] ? )</td>
330             <td class="snnn file magenta">lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv</td>
331             <td class="snnn file magenta">
332               <br />
333             </td>
334             <td class="snnn file magenta">
335               <br />
336             </td>
337             <td class="ssnn file magenta">
338               <br />
339             </td>
340           </tr>
341           <tr>
342             <td class="nnns component magenta">
343               <br />
344             </td>
345             <td class="snns plane magenta">stratified native validity</td>
346             <td class="snns file magenta">snv ( ⦃?,?⦄ ⊢ ? ¡[?] )</td>
347             <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>
348             <td class="snnn file magenta">
349               <br />
350             </td>
351             <td class="snnn file magenta">
352               <br />
353             </td>
354             <td class="ssnn file magenta">
355               <br />
356             </td>
357           </tr>
358           <tr>
359             <td class="snns component prune">equivalence</td>
360             <td class="snns plane prune">focalized equivalence</td>
361             <td class="snns file prune">lfpcs ( ⦃?⦄ ⬌* ⦃?⦄ )</td>
362             <td class="snnn file prune">lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs</td>
363             <td class="snnn file prune">
364               <br />
365             </td>
366             <td class="snnn file prune">
367               <br />
368             </td>
369             <td class="ssnn file prune">
370               <br />
371             </td>
372           </tr>
373           <tr>
374             <td class="nnns component prune">
375               <br />
376             </td>
377             <td class="nnns plane prune">
378               <br />
379             </td>
380             <td class="snns file prune">fpcs ( ⦃?,?⦄ ⬌* ⦃?,?⦄ )</td>
381             <td class="snnn file prune">fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs</td>
382             <td class="snnn file prune">
383               <br />
384             </td>
385             <td class="snnn file prune">
386               <br />
387             </td>
388             <td class="ssnn file prune">
389               <br />
390             </td>
391           </tr>
392           <tr>
393             <td class="nnns component prune">
394               <br />
395             </td>
396             <td class="snns plane prune">local env. ref. for stratified static type assignment</td>
397             <td class="snns file prune">lsubss ( ? •⊑[?] ? )</td>
398             <td class="snnn file prune">lsubss_ldrop lsubss_ssta lsubss_cpcs</td>
399             <td class="snnn file prune">
400               <br />
401             </td>
402             <td class="snnn file prune">
403               <br />
404             </td>
405             <td class="ssnn file prune">
406               <br />
407             </td>
408           </tr>
409           <tr>
410             <td class="nnns component prune">
411               <br />
412             </td>
413             <td class="snns plane prune">context-sensitive equivalence</td>
414             <td class="snns file prune">cpcs ( ? ⊢ ? ⬌* ? )</td>
415             <td class="snnn file prune">cpcs_ltpss_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs</td>
416             <td class="snnn file prune">
417               <br />
418             </td>
419             <td class="snnn file prune">
420               <br />
421             </td>
422             <td class="ssnn file prune">
423               <br />
424             </td>
425           </tr>
426           <tr>
427             <td class="snns component blue">conversion</td>
428             <td class="snns plane blue">focalized conversion</td>
429             <td class="snns file blue">lfpc ( ⦃?⦄ ⬌ ⦃?⦄ )</td>
430             <td class="snnn file blue">lfpc_lfpc</td>
431             <td class="snnn file blue">
432               <br />
433             </td>
434             <td class="snnn file blue">
435               <br />
436             </td>
437             <td class="ssnn file blue">
438               <br />
439             </td>
440           </tr>
441           <tr>
442             <td class="nnns component blue">
443               <br />
444             </td>
445             <td class="nnns plane blue">
446               <br />
447             </td>
448             <td class="snns file blue">fpc ( ⦃?,?⦄ ⬌ ⦃?,?⦄ )</td>
449             <td class="snnn file blue">fpc_fpc</td>
450             <td class="snnn file blue">
451               <br />
452             </td>
453             <td class="snnn file blue">
454               <br />
455             </td>
456             <td class="ssnn file blue">
457               <br />
458             </td>
459           </tr>
460           <tr>
461             <td class="nnns component blue">
462               <br />
463             </td>
464             <td class="snns plane blue">context-sensitive conversion</td>
465             <td class="snns file blue">cpc ( ? ⊢ ? ⬌ ? )</td>
466             <td class="snnn file blue">cpc_cpc</td>
467             <td class="snnn file blue">
468               <br />
469             </td>
470             <td class="snnn file blue">
471               <br />
472             </td>
473             <td class="ssnn file blue">
474               <br />
475             </td>
476           </tr>
477           <tr>
478             <td class="snns component sky">computation</td>
479             <td class="snns plane sky">focalized computation</td>
480             <td class="snns file sky">lfprs ( ⦃?⦄ ➡* ⦃?⦄ )</td>
481             <td class="snnn file sky">lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs</td>
482             <td class="snnn file sky">
483               <br />
484             </td>
485             <td class="snnn file sky">
486               <br />
487             </td>
488             <td class="ssnn file sky">
489               <br />
490             </td>
491           </tr>
492           <tr>
493             <td class="nnns component sky">
494               <br />
495             </td>
496             <td class="nnns plane sky">
497               <br />
498             </td>
499             <td class="snns file sky">fprs ( ⦃?,?⦄ ➡* ⦃?,?⦄ )</td>
500             <td class="snnn file sky">fprs_aaa fprs_fprs</td>
501             <td class="snnn file sky">
502               <br />
503             </td>
504             <td class="snnn file sky">
505               <br />
506             </td>
507             <td class="ssnn file sky">
508               <br />
509             </td>
510           </tr>
511           <tr>
512             <td class="nnns component sky">
513               <br />
514             </td>
515             <td class="snns plane sky">decomposed extended computation</td>
516             <td class="snns file sky">dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )</td>
517             <td class="snnn file sky">dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn dxprs_aaa dxprs_dxprs</td>
518             <td class="snnn file sky">
519               <br />
520             </td>
521             <td class="snnn file sky">
522               <br />
523             </td>
524             <td class="ssnn file sky">
525               <br />
526             </td>
527           </tr>
528           <tr>
529             <td class="nnns component sky">
530               <br />
531             </td>
532             <td class="snns plane sky">weakly normalizing computation</td>
533             <td class="snns file sky">cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
534             <td class="snnn file sky">cpe_cpe</td>
535             <td class="snnn file sky">
536               <br />
537             </td>
538             <td class="snnn file sky">
539               <br />
540             </td>
541             <td class="ssnn file sky">
542               <br />
543             </td>
544           </tr>
545           <tr>
546             <td class="nnns component sky">
547               <br />
548             </td>
549             <td class="snns plane sky">strongly normalizing computation</td>
550             <td class="snns file sky">csn_vector ( ? ⊢ ⬊* ? )</td>
551             <td class="snnn file sky">csn_cpr_vector csn_tstc_vector csn_aaa</td>
552             <td class="snnn file sky">
553               <br />
554             </td>
555             <td class="snnn file sky">
556               <br />
557             </td>
558             <td class="ssnn file sky">
559               <br />
560             </td>
561           </tr>
562           <tr>
563             <td class="nnns component sky">
564               <br />
565             </td>
566             <td class="nnns plane sky">
567               <br />
568             </td>
569             <td class="snns file sky">csn ( ? ⊢ ⬊* ? )</td>
570             <td class="snnn file sky">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
571             <td class="snnn file sky">csn_lift csn_cpr csn_lfpr</td>
572             <td class="snnn file sky">
573               <br />
574             </td>
575             <td class="ssnn file sky">
576               <br />
577             </td>
578           </tr>
579           <tr>
580             <td class="nnns component sky">
581               <br />
582             </td>
583             <td class="snns plane sky">context-sensitive computation</td>
584             <td class="snns file sky">cprs (? ⊢ ? ➡* ?)</td>
585             <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>
586             <td class="snnn file sky">
587               <br />
588             </td>
589             <td class="snnn file sky">
590               <br />
591             </td>
592             <td class="ssnn file sky">
593               <br />
594             </td>
595           </tr>
596           <tr>
597             <td class="nnns component sky">
598               <br />
599             </td>
600             <td class="snns plane sky">context-free computation</td>
601             <td class="snns file sky">ltprs ( ? ➡* ? )</td>
602             <td class="snnn file sky">ltprs_alt ( ? ➡➡* ? )</td>
603             <td class="snnn file sky">ltprs_ldrop ltprs_ltprs</td>
604             <td class="snnn file sky">
605               <br />
606             </td>
607             <td class="ssnn file sky">
608               <br />
609             </td>
610           </tr>
611           <tr>
612             <td class="nnns component sky">
613               <br />
614             </td>
615             <td class="nnns plane sky">
616               <br />
617             </td>
618             <td class="snns file sky">tprs ( ? ➡* ?)</td>
619             <td class="snnn file sky">tprs_lift tprs_tprs</td>
620             <td class="snnn file sky">
621               <br />
622             </td>
623             <td class="snnn file sky">
624               <br />
625             </td>
626             <td class="ssnn file sky">
627               <br />
628             </td>
629           </tr>
630           <tr>
631             <td class="nnns component sky">
632               <br />
633             </td>
634             <td class="snns plane sky">local env. ref. for abstract candidates of reducibility</td>
635             <td class="snns file sky">lsubc ( ? ⊑[?] ? )</td>
636             <td class="snnn file sky">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
637             <td class="snnn file sky">
638               <br />
639             </td>
640             <td class="snnn file sky">
641               <br />
642             </td>
643             <td class="ssnn file sky">
644               <br />
645             </td>
646           </tr>
647           <tr>
648             <td class="nnns component sky">
649               <br />
650             </td>
651             <td class="snns plane sky">support for abstract computation properties</td>
652             <td class="snns file sky">acp</td>
653             <td class="snnn file sky">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
654             <td class="snnn file sky">acp_aaa</td>
655             <td class="snnn file sky">
656               <br />
657             </td>
658             <td class="ssnn file sky">
659               <br />
660             </td>
661           </tr>
662           <tr>
663             <td class="snns component cyan">reducibility</td>
664             <td class="snns plane cyan">context-sensitive focalized reduction</td>
665             <td class="snns file cyan">cfpr ( ? ⊢ ⦃?,?⦄ ➡ ⦃?,?⦄ )</td>
666             <td class="snnn file cyan">cnfpr_ltpss cfpr_aaa cfpr_cpr cfpr_cfpr</td>
667             <td class="snnn file cyan">
668               <br />
669             </td>
670             <td class="snnn file cyan">
671               <br />
672             </td>
673             <td class="ssnn file cyan">
674               <br />
675             </td>
676           </tr>
677           <tr>
678             <td class="nnns component cyan">
679               <br />
680             </td>
681             <td class="snns plane cyan">context-free focalized reduction</td>
682             <td class="snns file cyan">lfpr ( ⦃?⦄ ➡ ⦃?⦄ )</td>
683             <td class="snnn file cyan">lfpr_alt ( ⦃?⦄ ➡➡ ⦃?⦄ )</td>
684             <td class="snnn file cyan">lfpr_aaa lfpr_cpr lfpr_fpr lfpr_lfpr</td>
685             <td class="snnn file cyan">
686               <br />
687             </td>
688             <td class="ssnn file cyan">
689               <br />
690             </td>
691           </tr>
692           <tr>
693             <td class="nnns component cyan">
694               <br />
695             </td>
696             <td class="nnns plane cyan">
697               <br />
698             </td>
699             <td class="snns file cyan">fpr ( ⦃?,?⦄ ➡ ⦃?,?⦄ )</td>
700             <td class="snnn file cyan">fpr_cpr fpr_fpr</td>
701             <td class="snnn file cyan">
702               <br />
703             </td>
704             <td class="snnn file cyan">
705               <br />
706             </td>
707             <td class="ssnn file cyan">
708               <br />
709             </td>
710           </tr>
711           <tr>
712             <td class="nnns component cyan">
713               <br />
714             </td>
715             <td class="snns plane cyan">context-sensitive normal forms</td>
716             <td class="snns file cyan">cnf ( ? ⊢ 𝐍⦃?⦄ )</td>
717             <td class="snnn file cyan">cnf_lift cnf_cif</td>
718             <td class="snnn file cyan">
719               <br />
720             </td>
721             <td class="snnn file cyan">
722               <br />
723             </td>
724             <td class="ssnn file cyan">
725               <br />
726             </td>
727           </tr>
728           <tr>
729             <td class="nnns component cyan">
730               <br />
731             </td>
732             <td class="snns plane cyan">context-sensitive reduction</td>
733             <td class="snns file cyan">cpr ( ? ⊢ ? ➡ ? )</td>
734             <td class="snnn file cyan">cpr_lift cpr_tpss cpr_ltpss_dx cpr_ltpss_sn cpr_delift cpr_aaa cpr_ltpr cpr_cpr</td>
735             <td class="snnn file cyan">
736               <br />
737             </td>
738             <td class="snnn file cyan">
739               <br />
740             </td>
741             <td class="ssnn file cyan">
742               <br />
743             </td>
744           </tr>
745           <tr>
746             <td class="nnns component cyan">
747               <br />
748             </td>
749             <td class="snns plane cyan">context-sensitive reducible forms</td>
750             <td class="snns file cyan">crf ( ? ⊢ 𝐑⦃?⦄ )</td>
751             <td class="snnn file cyan">crf_append</td>
752             <td class="snnn file cyan">cif ( ? ⊢ 𝐈⦃?⦄ )</td>
753             <td class="snnn file cyan">cif_append</td>
754             <td class="ssnn file cyan">
755               <br />
756             </td>
757           </tr>
758           <tr>
759             <td class="nnns component cyan">
760               <br />
761             </td>
762             <td class="snns plane cyan">context-free normal forms</td>
763             <td class="snns file cyan">thnf ( 𝐇𝐍⦃?⦄ )</td>
764             <td class="snnn file cyan">
765               <br />
766             </td>
767             <td class="snnn file cyan">
768               <br />
769             </td>
770             <td class="snnn file cyan">
771               <br />
772             </td>
773             <td class="ssnn file cyan">
774               <br />
775             </td>
776           </tr>
777           <tr>
778             <td class="nnns component cyan">
779               <br />
780             </td>
781             <td class="snns plane cyan">context-free reduction</td>
782             <td class="snns file cyan">ltpr ( ? ➡ ? )</td>
783             <td class="snnn file cyan">ltpr_ldrop ltpr_tps ltpr_tpss ltpr_ltpss_dx ltpr_ltpss_sn ltpr_aaa ltpr_ltpr</td>
784             <td class="snnn file cyan">
785               <br />
786             </td>
787             <td class="snnn file cyan">
788               <br />
789             </td>
790             <td class="ssnn file cyan">
791               <br />
792             </td>
793           </tr>
794           <tr>
795             <td class="nnns component cyan">
796               <br />
797             </td>
798             <td class="nnns plane cyan">
799               <br />
800             </td>
801             <td class="snns file cyan">tpr ( ? ➡ ? )</td>
802             <td class="snnn file cyan">tpr_lift tpr_delift tpr_tpr</td>
803             <td class="snnn file cyan">
804               <br />
805             </td>
806             <td class="snnn file cyan">
807               <br />
808             </td>
809             <td class="ssnn file cyan">
810               <br />
811             </td>
812           </tr>
813           <tr>
814             <td class="snns component water">restricted computation</td>
815             <td class="snns plane water">restricted parallel computation</td>
816             <td class="snns file water">lpqs ( ? ⊢ ➤* ? )</td>
817             <td class="snnn file water">lpqs_ldrop lpqs_cpqs lpqs_lpqs</td>
818             <td class="snnn file water">
819               <br />
820             </td>
821             <td class="snnn file water">
822               <br />
823             </td>
824             <td class="ssnn file water">
825               <br />
826             </td>
827           </tr>
828           <tr>
829             <td class="nnns component water">
830               <br />
831             </td>
832             <td class="nnns plane water">
833               <br />
834             </td>
835             <td class="snns file water">cpqs ( ? ⊢ ? ➤* ? )</td>
836             <td class="snnn file water">cpqs_lift</td>
837             <td class="snnn file water">
838               <br />
839             </td>
840             <td class="snnn file water">
841               <br />
842             </td>
843             <td class="ssnn file water">
844               <br />
845             </td>
846           </tr>
847           <tr>
848             <td class="snns component green">unwind</td>
849             <td class="snns plane green">iterated stratified static type assignment</td>
850             <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
851             <td class="snnn file green">sstas_lift sstas_ltpss_dx sstas_ltpss_sn sstas_aaa sstas_sstas</td>
852             <td class="snnn file green">
853               <br />
854             </td>
855             <td class="snnn file green">
856               <br />
857             </td>
858             <td class="ssnn file green">
859               <br />
860             </td>
861           </tr>
862           <tr>
863             <td class="snns component grass">static typing</td>
864             <td class="snns plane grass">stratified static type assignment</td>
865             <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
866             <td class="snnn file grass">ssta_lift ssta_ltpss_dx ssta_ltpss_sn ssta_aaa ssta_ssta</td>
867             <td class="snnn file grass">
868               <br />
869             </td>
870             <td class="snnn file grass">
871               <br />
872             </td>
873             <td class="ssnn file grass">
874               <br />
875             </td>
876           </tr>
877           <tr>
878             <td class="nnns component grass">
879               <br />
880             </td>
881             <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
882             <td class="snns file grass">lsuba ( ? ⁝⊑ ? )</td>
883             <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
884             <td class="snnn file grass">
885               <br />
886             </td>
887             <td class="snnn file grass">
888               <br />
889             </td>
890             <td class="ssnn file grass">
891               <br />
892             </td>
893           </tr>
894           <tr>
895             <td class="nnns component grass">
896               <br />
897             </td>
898             <td class="snns plane grass">atomic arity assignment</td>
899             <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
900             <td class="snnn file grass">aaa_lift aaa_lifts aaa_ltpss_dx aaa_ltpss_sn aaa_aaa</td>
901             <td class="snnn file grass">
902               <br />
903             </td>
904             <td class="snnn file grass">
905               <br />
906             </td>
907             <td class="ssnn file grass">
908               <br />
909             </td>
910           </tr>
911           <tr>
912             <td class="nnns component grass">
913               <br />
914             </td>
915             <td class="snns plane grass">parameters</td>
916             <td class="snns file grass">sh</td>
917             <td class="snnn file grass">sd</td>
918             <td class="snnn file grass">
919               <br />
920             </td>
921             <td class="snnn file grass">
922               <br />
923             </td>
924             <td class="ssnn file grass">
925               <br />
926             </td>
927           </tr>
928           <tr>
929             <td class="snns component yellow">unfold</td>
930             <td class="snns plane yellow">basic local env. thinning</td>
931             <td class="snns file yellow">thin ( ? ▼*[?,?] ≡ ? )</td>
932             <td class="snnn file yellow">thin_ldrop thin_delift</td>
933             <td class="snnn file yellow">
934               <br />
935             </td>
936             <td class="snnn file yellow">
937               <br />
938             </td>
939             <td class="ssnn file yellow">
940               <br />
941             </td>
942           </tr>
943           <tr>
944             <td class="nnns component yellow">
945               <br />
946             </td>
947             <td class="snns plane yellow">inverse basic term relocation</td>
948             <td class="snns file yellow">delift ( ? ⊢ ? ▼*[?,?] ≡ ? )</td>
949             <td class="snnn file yellow">delift_alt ( ? ⊢ ? ▼▼*[?,?] ≡ ? )</td>
950             <td class="snnn file yellow">delift_lift delift_tpss delift_ltpss delift_delift</td>
951             <td class="snnn file yellow">
952               <br />
953             </td>
954             <td class="ssnn file yellow">
955               <br />
956             </td>
957           </tr>
958           <tr>
959             <td class="nnns component yellow">
960               <br />
961             </td>
962             <td class="snns plane yellow">revised parallel substitution</td>
963             <td class="snns file yellow">lpss ( ? ⊢ ▶* ? )</td>
964             <td class="snnn file yellow">lpss_ldrop lpss_cpss lpss_lpss</td>
965             <td class="snnn file yellow">
966               <br />
967             </td>
968             <td class="snnn file yellow">
969               <br />
970             </td>
971             <td class="ssnn file yellow">
972               <br />
973             </td>
974           </tr>
975           <tr>
976             <td class="nnns component yellow">
977               <br />
978             </td>
979             <td class="nnns plane yellow">
980               <br />
981             </td>
982             <td class="snns file yellow">cpss ( ? ⊢ ? ▶* ? )</td>
983             <td class="snnn file yellow">cpss_lift</td>
984             <td class="snnn file yellow">
985               <br />
986             </td>
987             <td class="snnn file yellow">
988               <br />
989             </td>
990             <td class="ssnn file yellow">
991               <br />
992             </td>
993           </tr>
994           <tr>
995             <td class="nnns component yellow">
996               <br />
997             </td>
998             <td class="snns plane yellow">partial unfold</td>
999             <td class="snns file yellow">ltpss_sn ( ? ⊢ ▶*[?,?] ? )</td>
1000             <td class="snnn file yellow">ltpss_sn_alt ( ? ⊢ ▶▶*[?,?] ? )</td>
1001             <td class="snnn file yellow">ltpss_sn_ldrop ltpss_sn_tps ltpss_sn_tpss ltpss_sn_ltpss_sn</td>
1002             <td class="snnn file yellow">
1003               <br />
1004             </td>
1005             <td class="ssnn file yellow">
1006               <br />
1007             </td>
1008           </tr>
1009           <tr>
1010             <td class="nnns component yellow">
1011               <br />
1012             </td>
1013             <td class="nnns plane yellow">
1014               <br />
1015             </td>
1016             <td class="snns file yellow">ltpss_dx ( ? ▶*[?,?] ? )</td>
1017             <td class="snnn file yellow">ltpss_dx_ldrop ltpss_dx_tps ltpss_dx_tpss ltpss_dx_ltpss_dx</td>
1018             <td class="snnn file yellow">
1019               <br />
1020             </td>
1021             <td class="snnn file yellow">
1022               <br />
1023             </td>
1024             <td class="ssnn file yellow">
1025               <br />
1026             </td>
1027           </tr>
1028           <tr>
1029             <td class="nnns component yellow">
1030               <br />
1031             </td>
1032             <td class="nnns plane yellow">
1033               <br />
1034             </td>
1035             <td class="snns file yellow">tpss ( ? ⊢ ? ▶*[?,?] ? )</td>
1036             <td class="snnn file yellow">tpss_alt ( ? ⊢ ? ▶▶*[?,?] ? )</td>
1037             <td class="snnn file yellow">tpss_lift</td>
1038             <td class="snnn file yellow">tpss_tpss</td>
1039             <td class="ssnn file yellow">
1040               <br />
1041             </td>
1042           </tr>
1043           <tr>
1044             <td class="nnns component yellow">
1045               <br />
1046             </td>
1047             <td class="snns plane yellow">iterated structural successor for closures</td>
1048             <td class="snns file yellow">fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )</td>
1049             <td class="snnn file yellow">fsupp_fsupp</td>
1050             <td class="snnn file yellow">
1051               <br />
1052             </td>
1053             <td class="snnn file yellow">
1054               <br />
1055             </td>
1056             <td class="ssnn file yellow">
1057               <br />
1058             </td>
1059           </tr>
1060           <tr>
1061             <td class="nnns component yellow">
1062               <br />
1063             </td>
1064             <td class="snns plane yellow">generic local env. slicing</td>
1065             <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
1066             <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
1067             <td class="snnn file yellow">
1068               <br />
1069             </td>
1070             <td class="snnn file yellow">
1071               <br />
1072             </td>
1073             <td class="ssnn file yellow">
1074               <br />
1075             </td>
1076           </tr>
1077           <tr>
1078             <td class="nnns component yellow">
1079               <br />
1080             </td>
1081             <td class="snns plane yellow">generic term relocation</td>
1082             <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
1083             <td class="snnn file yellow">lifts_lift_vector</td>
1084             <td class="snnn file yellow">
1085               <br />
1086             </td>
1087             <td class="snnn file yellow">
1088               <br />
1089             </td>
1090             <td class="ssnn file yellow">
1091               <br />
1092             </td>
1093           </tr>
1094           <tr>
1095             <td class="nnns component yellow">
1096               <br />
1097             </td>
1098             <td class="nnns plane yellow">
1099               <br />
1100             </td>
1101             <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
1102             <td class="snnn file yellow">lifts_lift lifts_lifts</td>
1103             <td class="snnn file yellow">
1104               <br />
1105             </td>
1106             <td class="snnn file yellow">
1107               <br />
1108             </td>
1109             <td class="ssnn file yellow">
1110               <br />
1111             </td>
1112           </tr>
1113           <tr>
1114             <td class="nnns component yellow">
1115               <br />
1116             </td>
1117             <td class="snns plane yellow">support for generic relocation</td>
1118             <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
1119             <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
1120             <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
1121             <td class="snnn file yellow">gr2_gr2</td>
1122             <td class="ssnn file yellow">
1123               <br />
1124             </td>
1125           </tr>
1126           <tr>
1127             <td class="snns component orange">substitution</td>
1128             <td class="snns plane orange">parallel substitution</td>
1129             <td class="snns file orange">tps ( ? ⊢ ? ▶[?,?] ? )</td>
1130             <td class="snnn file orange">tps_lift tps_tps</td>
1131             <td class="snnn file orange">
1132               <br />
1133             </td>
1134             <td class="snnn file orange">
1135               <br />
1136             </td>
1137             <td class="ssnn file orange">
1138               <br />
1139             </td>
1140           </tr>
1141           <tr>
1142             <td class="nnns component orange">
1143               <br />
1144             </td>
1145             <td class="snns plane orange">structural successor for closures</td>
1146             <td class="snns file orange">fsup ( ⦃?,?⦄ ⊃ ⦃?,?⦄ )</td>
1147             <td class="snnn file orange">
1148               <br />
1149             </td>
1150             <td class="snnn file orange">
1151               <br />
1152             </td>
1153             <td class="snnn file orange">
1154               <br />
1155             </td>
1156             <td class="ssnn file orange">
1157               <br />
1158             </td>
1159           </tr>
1160           <tr>
1161             <td class="nnns component orange">
1162               <br />
1163             </td>
1164             <td class="snns plane orange">global env. slicing</td>
1165             <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
1166             <td class="snnn file orange">gdrop_gdrop</td>
1167             <td class="snnn file orange">
1168               <br />
1169             </td>
1170             <td class="snnn file orange">
1171               <br />
1172             </td>
1173             <td class="ssnn file orange">
1174               <br />
1175             </td>
1176           </tr>
1177           <tr>
1178             <td class="nnns component orange">
1179               <br />
1180             </td>
1181             <td class="snns plane orange">basic local env. slicing</td>
1182             <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
1183             <td class="snnn file orange">ldrop_append ldrop_lpx ldrop_lpx_sn ldrop_lbotr ldrop_ldrop</td>
1184             <td class="snnn file orange">
1185               <br />
1186             </td>
1187             <td class="snnn file orange">
1188               <br />
1189             </td>
1190             <td class="ssnn file orange">
1191               <br />
1192             </td>
1193           </tr>
1194           <tr>
1195             <td class="nnns component orange">
1196               <br />
1197             </td>
1198             <td class="snns plane orange">local env. ref. for substitution</td>
1199             <td class="snns file orange">lsubr ( ? ⊑[?,?] ? )</td>
1200             <td class="snnn file orange">(lsubr_lsubr)</td>
1201             <td class="snnn file orange">lsubr_lbotr ( ⊒[?,?] ? )</td>
1202             <td class="snnn file orange">
1203               <br />
1204             </td>
1205             <td class="ssnn file orange">
1206               <br />
1207             </td>
1208           </tr>
1209           <tr>
1210             <td class="nnns component orange">
1211               <br />
1212             </td>
1213             <td class="snns plane orange">basic term relocation</td>
1214             <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
1215             <td class="snnn file orange">lift_lift_vector</td>
1216             <td class="snnn file orange">
1217               <br />
1218             </td>
1219             <td class="snnn file orange">
1220               <br />
1221             </td>
1222             <td class="ssnn file orange">
1223               <br />
1224             </td>
1225           </tr>
1226           <tr>
1227             <td class="nnns component orange">
1228               <br />
1229             </td>
1230             <td class="nnns plane orange">
1231               <br />
1232             </td>
1233             <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
1234             <td class="snnn file orange">lift_lift</td>
1235             <td class="snnn file orange">
1236               <br />
1237             </td>
1238             <td class="snnn file orange">
1239               <br />
1240             </td>
1241             <td class="ssnn file orange">
1242               <br />
1243             </td>
1244           </tr>
1245           <tr>
1246             <td class="snns component red">grammar</td>
1247             <td class="snns plane red">same head term form</td>
1248             <td class="snns file red">tshf ( ? ≈ ? )</td>
1249             <td class="snnn file red">(tshf_tshf)</td>
1250             <td class="snnn file red">
1251               <br />
1252             </td>
1253             <td class="snnn file red">
1254               <br />
1255             </td>
1256             <td class="ssnn file red">
1257               <br />
1258             </td>
1259           </tr>
1260           <tr>
1261             <td class="nnns component red">
1262               <br />
1263             </td>
1264             <td class="snns plane red">same top term constructor</td>
1265             <td class="snns file red">tstc ( ? ≃ ? )</td>
1266             <td class="snnn file red">tstc_tstc tstc_vector</td>
1267             <td class="snnn file red">
1268               <br />
1269             </td>
1270             <td class="snnn file red">
1271               <br />
1272             </td>
1273             <td class="ssnn file red">
1274               <br />
1275             </td>
1276           </tr>
1277           <tr>
1278             <td class="nnns component red">
1279               <br />
1280             </td>
1281             <td class="snns plane red">closures</td>
1282             <td class="snns file red">cl_shift ( ? @@ ? )</td>
1283             <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
1284             <td class="snnn file red">
1285               <br />
1286             </td>
1287             <td class="snnn file red">
1288               <br />
1289             </td>
1290             <td class="ssnn file red">
1291               <br />
1292             </td>
1293           </tr>
1294           <tr>
1295             <td class="nnns component red">
1296               <br />
1297             </td>
1298             <td class="snns plane red">internal syntax</td>
1299             <td class="snns file red">genv</td>
1300             <td class="snnn file red">
1301               <br />
1302             </td>
1303             <td class="snnn file red">
1304               <br />
1305             </td>
1306             <td class="snnn file red">
1307               <br />
1308             </td>
1309             <td class="ssnn file red">
1310               <br />
1311             </td>
1312           </tr>
1313           <tr>
1314             <td class="nnns component red">
1315               <br />
1316             </td>
1317             <td class="nnns plane red">
1318               <br />
1319             </td>
1320             <td class="snns file red">lenv</td>
1321             <td class="snnn file red">lenv_weight ( ♯{?} )</td>
1322             <td class="snnn file red">lenv_length ( |?| )</td>
1323             <td class="snnn file red">lenv_append ( ? @@ ? )</td>
1324             <td class="ssnn file red">lenv_px lenv_px_sn lenv_px_bi</td>
1325           </tr>
1326           <tr>
1327             <td class="nnns component red">
1328               <br />
1329             </td>
1330             <td class="nnns plane red">
1331               <br />
1332             </td>
1333             <td class="snns file red">term</td>
1334             <td class="snnn file red">term_weight ( ♯{?} )</td>
1335             <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
1336             <td class="snnn file red">term_vector</td>
1337             <td class="ssnn file red">
1338               <br />
1339             </td>
1340           </tr>
1341           <tr>
1342             <td class="nnns component red">
1343               <br />
1344             </td>
1345             <td class="nnns plane red">
1346               <br />
1347             </td>
1348             <td class="snns file red">item</td>
1349             <td class="snnn file red">
1350               <br />
1351             </td>
1352             <td class="snnn file red">
1353               <br />
1354             </td>
1355             <td class="snnn file red">
1356               <br />
1357             </td>
1358             <td class="ssnn file red">
1359               <br />
1360             </td>
1361           </tr>
1362           <tr>
1363             <td class="nnss component red">
1364               <br />
1365             </td>
1366             <td class="snss plane red">external syntax</td>
1367             <td class="snss file red">aarity</td>
1368             <td class="snsn file red">
1369               <br />
1370             </td>
1371             <td class="snsn file red">
1372               <br />
1373             </td>
1374             <td class="snsn file red">
1375               <br />
1376             </td>
1377             <td class="sssn file red">
1378               <br />
1379             </td>
1380           </tr>
1381         </tbody>
1382       </table>
1383     </div>
1384
1385    <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1386    <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1387          one for each component.
1388    </div>
1389    <div class="spacer">
1390       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
1391     </div>
1392     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1393       <br />
1394     </div>
1395     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1396       <a href="http://validator.w3.org/check?uri=referer">
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1398       </a>
1399       <a href="http://jigsaw.w3.org/css-validator/check/referer">
1400         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
1401       </a>
1402       <a href="http://www.w3.org/XML/">
1403         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
1404       </a>
1405       <a href="http://www.w3.org/Graphics/PNG/">
1406         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
1407       </a>
1408       <a href="http://www.anybrowser.org/campaign/">
1409         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
1410       </a>
1411     </div>
1412     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1413       <br />
1414     </div>
1415     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sun, 07 Apr 2013 23:37:37 +0200</div>
1416 </body>
1417 </html>