1 <?xml version="1.0" encoding="UTF-8"?>
2 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN" "http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd">
3 <html xmlns="http://www.w3.org/1999/xhtml" dir="ltr" lang="en-us">
5 <meta http-equiv="Content-Language" content="en-us" />
6 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
7 <meta http-equiv="Content-Style-Type" content="text/css" />
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" />
12 <link rel="stylesheet" type="text/css" href="http://lambdadelta.info/css/lddl.css" />
13 <link rel="stylesheet" type="text/css" href="http://lambdadelta.info/css/xhtbl.css" />
14 <link rel="shortcut icon" href="http://lambdadelta.info/images/crux_16.ico" />
18 <a href="http://lambdadelta.info/">
19 <img class="icon32" alt="[lambdadelta home]" title="lambdadelta home" src="http://lambdadelta.info/images/crux_32.png" />
22 <div class="head1">cic:/matita/lambdadelta/basic_2/ (λδ version 2)</div>
24 <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
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.
30 <div xmlns:ld="http://lambdadelta.info/" class="text">
31 <table cellpadding="4" cellspacing="0">
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>
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>
52 <td class="nnns text">
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>
63 <td class="nnns text">
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">$p</td>
74 <td class="nnns text">
77 <td class="snns plane blue">native type annotation *</td>
78 <td class="snns text blue">Γ ⊢ ⓝW</td>
79 <td class="snns text blue">no</td>
80 <td class="snns text blue">no</td>
81 <td class="snns text blue">yes</td>
82 <td class="ssns text blue">no</td>
85 <td class="snns text">{X | Γ ⊢ X = V}</td>
86 <td class="snns plane sky">local abbreviation *</td>
87 <td class="snns text sky">Γ ⊢ +δV</td>
88 <td class="snns text sky">no</td>
89 <td class="snns text sky">local →δ</td>
90 <td class="snns text sky">yes</td>
91 <td class="ssns text sky">#i</td>
94 <td class="nnns text">
97 <td class="snns plane cyan">local definition **</td>
98 <td class="snns text cyan">Γ ⊢ -δV</td>
99 <td class="snns text cyan">no</td>
100 <td class="snns text cyan">local →δ</td>
101 <td class="snns text cyan">no</td>
102 <td class="ssns text cyan">#i</td>
105 <td class="nnns text">
108 <td class="snns plane water">global definition ***</td>
109 <td class="snns text water">Γ ⊢ pδV</td>
110 <td class="snns text water">no</td>
111 <td class="snns text water">global →δ</td>
112 <td class="snns text water">no</td>
113 <td class="ssns text water">$p</td>
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>
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.
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
137 <div xmlns:ld="http://lambdadelta.info/" class="text">
138 <table cellpadding="4" cellspacing="0">
141 <td class="snns component grey">category</td>
142 <td class="snns plane grey">objects</td>
143 <td class="snnn number grey">
146 <td class="snnn plane grey">
149 <td class="snnn number grey">
152 <td class="snnn plane grey">
155 <td class="ssnn number grey">
160 <td class="snns component cyan">sizes</td>
161 <td class="snns plane cyan">files</td>
162 <td class="snnn number cyan">250 </td>
163 <td class="snns plane cyan">characters</td>
164 <td class="snnn number cyan">484782</td>
165 <td class="snns plane cyan">nodes</td>
166 <td class="ssnn number cyan">1304867</td>
169 <td class="snns component green">propositions</td>
170 <td class="snns plane green">theorems</td>
171 <td class="snnn number green">84</td>
172 <td class="snns plane green">lemmas</td>
173 <td class="snnn number green">1112</td>
174 <td class="snns plane green">total</td>
175 <td class="ssnn number green">1196</td>
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">83</td>
183 <td class="snss plane yellow">total</td>
184 <td class="sssn number yellow">128</td>
189 <ul xmlns:ld="http://lambdadelta.info/">
191 <span class="date">In progress.</span>
192 Context-sensitive subject equivalence
193 for native type assignment.
196 <ul xmlns:ld="http://lambdadelta.info/">
198 <span class="date">In progress.</span>
199 Closure of extended context-sensitive computation
203 <ul xmlns:ld="http://lambdadelta.info/">
205 <span class="date">In progress.</span>
206 Extended context-sensitive strong normalization
207 for simply typed terms.
210 <ul xmlns:ld="http://lambdadelta.info/">
212 <span class="date">2013 March 16.</span>
213 Mutual recursive preservation of stratified native validity
214 for hyper computation on closures.
217 <ul xmlns:ld="http://lambdadelta.info/">
219 <span class="date">2012 October 16.</span>
220 Confluence for context-free parallel reduction on closures.
223 <ul xmlns:ld="http://lambdadelta.info/">
225 <span class="date">2012 July 26.</span>
226 Term binders polarized to control ζ reduction.
229 <ul xmlns:ld="http://lambdadelta.info/">
231 <span class="date">2012 April 16.</span>
232 Context-sensitive subject equivalence
233 for atomic arity assignment
234 (anniversary milestone).
237 <ul xmlns:ld="http://lambdadelta.info/">
239 <span class="date">2012 March 15.</span>
240 Context-sensitive strong normalization
241 for simply typed terms.
244 <ul xmlns:ld="http://lambdadelta.info/">
246 <span class="date">2012 January 27.</span>
247 Support for abstract candidates of reducibility.
250 <ul xmlns:ld="http://lambdadelta.info/">
252 <span class="date">2011 September 21.</span>
253 Confluence for context-sensitive parallel reduction on terms.
256 <ul xmlns:ld="http://lambdadelta.info/">
258 <span class="date">2011 September 6.</span>
259 Confluence for context-free parallel reduction on terms.
262 <ul xmlns:ld="http://lambdadelta.info/">
264 <span class="date">2011 April 17.</span>
265 Specification starts.
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).
276 <div xmlns:ld="http://lambdadelta.info/" class="text">
277 <table cellpadding="4" cellspacing="0">
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">
286 <td class="snnn file grey">
289 <td class="snnn file grey">
292 <td class="ssnn file grey">
297 <td class="snns component prune">dynamic typing</td>
298 <td class="snns plane prune">"big tree" parallel computation</td>
299 <td class="snns file prune">yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )</td>
300 <td class="snnn file prune">yprs_yprs</td>
301 <td class="snnn file prune">ygt ( ? ⊢ ⦃?,?⦄ >[g] ⦃?,?⦄ )</td>
302 <td class="snnn file prune">ygt_ygt</td>
303 <td class="ssnn file prune">
308 <td class="nnns component prune">
311 <td class="snns plane prune">"big tree" parallel reduction</td>
312 <td class="snns file prune">ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )</td>
313 <td class="snnn file prune">ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )</td>
314 <td class="snnn file prune">
317 <td class="snnn file prune">
320 <td class="ssnn file prune">
325 <td class="nnns component prune">
328 <td class="snns plane prune">local env. ref. for stratified native validity</td>
329 <td class="snns file prune">lsubsv ( ? ⊢ ? ⊩:⊑[?] ? )</td>
330 <td class="snnn file prune">lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv</td>
331 <td class="snnn file prune">
334 <td class="snnn file prune">
337 <td class="ssnn file prune">
342 <td class="nnns component prune">
345 <td class="snns plane prune">stratified native validity</td>
346 <td class="snns file prune">snv ( ⦃?,?⦄ ⊩ ? :[?] )</td>
347 <td class="snnn file prune">snv_lift snv_ltpss_dx snv_ltpss_sn snv_aaa snv_ssta snv_sstas snv_ssta_ltpr snv_ltpr snv_cpcs</td>
348 <td class="snnn file prune">
351 <td class="snnn file prune">
354 <td class="ssnn file prune">
359 <td class="snns component blue">equivalence</td>
360 <td class="snns plane blue">focalized equivalence</td>
361 <td class="snns file blue">lfpcs ( ⦃?⦄ ⬌* ⦃?⦄ )</td>
362 <td class="snnn file blue">lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs</td>
363 <td class="snnn file blue">
366 <td class="snnn file blue">
369 <td class="ssnn file blue">
374 <td class="nnns component blue">
377 <td class="nnns plane blue">
380 <td class="snns file blue">fpcs ( ⦃?,?⦄ ⬌* ⦃?,?⦄ )</td>
381 <td class="snnn file blue">fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs</td>
382 <td class="snnn file blue">
385 <td class="snnn file blue">
388 <td class="ssnn file blue">
393 <td class="nnns component blue">
396 <td class="snns plane blue">local env. ref. for stratified static type assignment</td>
397 <td class="snns file blue">lsubss ( ? •⊑[?] ? )</td>
398 <td class="snnn file blue">lsubss_ldrop lsubss_ssta lsubss_cpcs</td>
399 <td class="snnn file blue">
402 <td class="snnn file blue">
405 <td class="ssnn file blue">
410 <td class="nnns component blue">
413 <td class="snns plane blue">context-sensitive equivalence</td>
414 <td class="snns file blue">cpcs ( ? ⊢ ? ⬌* ? )</td>
415 <td class="snnn file blue">cpcs_ltpss_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs</td>
416 <td class="snnn file blue">
419 <td class="snnn file blue">
422 <td class="ssnn file blue">
427 <td class="snns component sky">conversion</td>
428 <td class="snns plane sky">focalized conversion</td>
429 <td class="snns file sky">lfpc ( ⦃?⦄ ⬌ ⦃?⦄ )</td>
430 <td class="snnn file sky">lfpc_lfpc</td>
431 <td class="snnn file sky">
434 <td class="snnn file sky">
437 <td class="ssnn file sky">
442 <td class="nnns component sky">
445 <td class="nnns plane sky">
448 <td class="snns file sky">fpc ( ⦃?,?⦄ ⬌ ⦃?,?⦄ )</td>
449 <td class="snnn file sky">fpc_fpc</td>
450 <td class="snnn file sky">
453 <td class="snnn file sky">
456 <td class="ssnn file sky">
461 <td class="nnns component sky">
464 <td class="snns plane sky">context-sensitive conversion</td>
465 <td class="snns file sky">cpc ( ? ⊢ ? ⬌ ? )</td>
466 <td class="snnn file sky">cpc_cpc</td>
467 <td class="snnn file sky">
470 <td class="snnn file sky">
473 <td class="ssnn file sky">
478 <td class="snns component cyan">computation</td>
479 <td class="snns plane cyan">focalized computation</td>
480 <td class="snns file cyan">lfprs ( ⦃?⦄ ➡* ⦃?⦄ )</td>
481 <td class="snnn file cyan">lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs</td>
482 <td class="snnn file cyan">
485 <td class="snnn file cyan">
488 <td class="ssnn file cyan">
493 <td class="nnns component cyan">
496 <td class="nnns plane cyan">
499 <td class="snns file cyan">fprs ( ⦃?,?⦄ ➡* ⦃?,?⦄ )</td>
500 <td class="snnn file cyan">fprs_aaa fprs_fprs</td>
501 <td class="snnn file cyan">
504 <td class="snnn file cyan">
507 <td class="ssnn file cyan">
512 <td class="nnns component cyan">
515 <td class="snns plane cyan">decomposed extended computation</td>
516 <td class="snns file cyan">dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )</td>
517 <td class="snnn file cyan">dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn dxprs_aaa dxprs_dxprs</td>
518 <td class="snnn file cyan">
521 <td class="snnn file cyan">
524 <td class="ssnn file cyan">
529 <td class="nnns component cyan">
532 <td class="snns plane cyan">weakly normalizing computation</td>
533 <td class="snns file cyan">cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
534 <td class="snnn file cyan">cpe_cpe</td>
535 <td class="snnn file cyan">
538 <td class="snnn file cyan">
541 <td class="ssnn file cyan">
546 <td class="nnns component cyan">
549 <td class="snns plane cyan">strongly normalizing computation</td>
550 <td class="snns file cyan">csn_vector ( ? ⊢ ⬊* ? )</td>
551 <td class="snnn file cyan">csn_cpr_vector csn_tstc_vector csn_aaa</td>
552 <td class="snnn file cyan">
555 <td class="snnn file cyan">
558 <td class="ssnn file cyan">
563 <td class="nnns component cyan">
566 <td class="nnns plane cyan">
569 <td class="snns file cyan">csn ( ? ⊢ ⬊* ? )</td>
570 <td class="snnn file cyan">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
571 <td class="snnn file cyan">csn_lift csn_cpr csn_lfpr</td>
572 <td class="snnn file cyan">
575 <td class="ssnn file cyan">
580 <td class="nnns component cyan">
583 <td class="snns plane cyan">context-sensitive computation</td>
584 <td class="snns file cyan">cprs (? ⊢ ? ➡* ?)</td>
585 <td class="snnn file cyan">cprs_lift cprs_tpss cprs_ltpss_dx cprs_ltpss_sn cprs_delift cprs_aaa cprs_ltpr cprs_lfpr cprs_cprs cprs_lfprs cprs_tstc cprs_tstc_vector</td>
586 <td class="snnn file cyan">
589 <td class="snnn file cyan">
592 <td class="ssnn file cyan">
597 <td class="nnns component cyan">
600 <td class="snns plane cyan">context-free computation</td>
601 <td class="snns file cyan">ltprs ( ? ➡* ? )</td>
602 <td class="snnn file cyan">ltprs_alt ( ? ➡➡* ? )</td>
603 <td class="snnn file cyan">ltprs_ldrop ltprs_ltprs</td>
604 <td class="snnn file cyan">
607 <td class="ssnn file cyan">
612 <td class="nnns component cyan">
615 <td class="nnns plane cyan">
618 <td class="snns file cyan">tprs ( ? ➡* ?)</td>
619 <td class="snnn file cyan">tprs_lift tprs_tprs</td>
620 <td class="snnn file cyan">
623 <td class="snnn file cyan">
626 <td class="ssnn file cyan">
631 <td class="nnns component cyan">
634 <td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</td>
635 <td class="snns file cyan">lsubc ( ? ⊑[?] ? )</td>
636 <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
637 <td class="snnn file cyan">
640 <td class="snnn file cyan">
643 <td class="ssnn file cyan">
648 <td class="nnns component cyan">
651 <td class="snns plane cyan">support for abstract computation properties</td>
652 <td class="snns file cyan">acp</td>
653 <td class="snnn file cyan">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
654 <td class="snnn file cyan">acp_aaa</td>
655 <td class="snnn file cyan">
658 <td class="ssnn file cyan">
663 <td class="snns component water">reducibility</td>
664 <td class="snns plane water">context-sensitive focalized reduction</td>
665 <td class="snns file water">cfpr ( ? ⊢ ⦃?,?⦄ ➡ ⦃?,?⦄ )</td>
666 <td class="snnn file water">cnfpr_ltpss cfpr_aaa cfpr_cpr cfpr_cfpr</td>
667 <td class="snnn file water">
670 <td class="snnn file water">
673 <td class="ssnn file water">
678 <td class="nnns component water">
681 <td class="snns plane water">context-free focalized reduction</td>
682 <td class="snns file water">lfpr ( ⦃?⦄ ➡ ⦃?⦄ )</td>
683 <td class="snnn file water">lfpr_alt ( ⦃?⦄ ➡➡ ⦃?⦄ )</td>
684 <td class="snnn file water">lfpr_aaa lfpr_cpr lfpr_fpr lfpr_lfpr</td>
685 <td class="snnn file water">
688 <td class="ssnn file water">
693 <td class="nnns component water">
696 <td class="nnns plane water">
699 <td class="snns file water">fpr ( ⦃?,?⦄ ➡ ⦃?,?⦄ )</td>
700 <td class="snnn file water">fpr_cpr fpr_fpr</td>
701 <td class="snnn file water">
704 <td class="snnn file water">
707 <td class="ssnn file water">
712 <td class="nnns component water">
715 <td class="snns plane water">context-sensitive normal forms</td>
716 <td class="snns file water">cnf ( ? ⊢ 𝐍⦃?⦄ )</td>
717 <td class="snnn file water">cnf_lift cnf_cif</td>
718 <td class="snnn file water">
721 <td class="snnn file water">
724 <td class="ssnn file water">
729 <td class="nnns component water">
732 <td class="snns plane water">context-sensitive reduction</td>
733 <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
734 <td class="snnn file water">cpr_lift cpr_tpss cpr_ltpss_dx cpr_ltpss_sn cpr_delift cpr_aaa cpr_ltpr cpr_cpr</td>
735 <td class="snnn file water">
738 <td class="snnn file water">
741 <td class="ssnn file water">
746 <td class="nnns component water">
749 <td class="snns plane water">context-sensitive reducible forms</td>
750 <td class="snns file water">crf ( ? ⊢ 𝐑⦃?⦄ )</td>
751 <td class="snnn file water">crf_append</td>
752 <td class="snnn file water">cif ( ? ⊢ 𝐈⦃?⦄ )</td>
753 <td class="snnn file water">cif_append</td>
754 <td class="ssnn file water">
759 <td class="nnns component water">
762 <td class="snns plane water">context-free normal forms</td>
763 <td class="snns file water">thnf ( 𝐇𝐍⦃?⦄ )</td>
764 <td class="snnn file water">
767 <td class="snnn file water">
770 <td class="snnn file water">
773 <td class="ssnn file water">
778 <td class="nnns component water">
781 <td class="snns plane water">context-free reduction</td>
782 <td class="snns file water">ltpr ( ? ➡ ? )</td>
783 <td class="snnn file water">ltpr_ldrop ltpr_tps ltpr_ltpss_dx ltpr_ltpss_sn ltpr_aaa ltpr_ltpr</td>
784 <td class="snnn file water">
787 <td class="snnn file water">
790 <td class="ssnn file water">
795 <td class="nnns component water">
798 <td class="nnns plane water">
801 <td class="snns file water">tpr ( ? ➡ ? )</td>
802 <td class="snnn file water">tpr_lift tpr_tps tpr_tpss tpr_delift tpr_tpr</td>
803 <td class="snnn file water">
806 <td class="snnn file water">
809 <td class="ssnn file water">
814 <td class="snns component green">unwind</td>
815 <td class="snns plane green">iterated stratified static type assignment</td>
816 <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
817 <td class="snnn file green">sstas_lift sstas_ltpss_dx sstas_ltpss_sn sstas_aaa sstas_sstas</td>
818 <td class="snnn file green">
821 <td class="snnn file green">
824 <td class="ssnn file green">
829 <td class="snns component grass">static typing</td>
830 <td class="snns plane grass">stratified static type assignment</td>
831 <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
832 <td class="snnn file grass">ssta_lift ssta_ltpss_dx ssta_ltpss_sn ssta_aaa ssta_ssta</td>
833 <td class="snnn file grass">
836 <td class="snnn file grass">
839 <td class="ssnn file grass">
844 <td class="nnns component grass">
847 <td class="snns plane grass">local env. ref. for atomic arity assignment</td>
848 <td class="snns file grass">lsuba ( ? ⁝⊑ ? )</td>
849 <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
850 <td class="snnn file grass">
853 <td class="snnn file grass">
856 <td class="ssnn file grass">
861 <td class="nnns component grass">
864 <td class="snns plane grass">atomic arity assignment</td>
865 <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
866 <td class="snnn file grass">aaa_lift aaa_lifts aaa_ltpss_dx aaa_ltpss_sn aaa_aaa</td>
867 <td class="snnn file grass">
870 <td class="snnn file grass">
873 <td class="ssnn file grass">
878 <td class="nnns component grass">
881 <td class="snns plane grass">parameters</td>
882 <td class="snns file grass">sh</td>
883 <td class="snnn file grass">sd</td>
884 <td class="snnn file grass">
887 <td class="snnn file grass">
890 <td class="ssnn file grass">
895 <td class="snns component yellow">unfold</td>
896 <td class="snns plane yellow">basic local env. thinning</td>
897 <td class="snns file yellow">thin ( ? ▼*[?,?] ≡ ? )</td>
898 <td class="snnn file yellow">thin_ldrop thin_delift</td>
899 <td class="snnn file yellow">
902 <td class="snnn file yellow">
905 <td class="ssnn file yellow">
910 <td class="nnns component yellow">
913 <td class="snns plane yellow">inverse basic term relocation</td>
914 <td class="snns file yellow">delift ( ? ⊢ ? ▼*[?,?] ≡ ? )</td>
915 <td class="snnn file yellow">delift_alt ( ? ⊢ ? ▼▼*[?,?] ≡ ? )</td>
916 <td class="snnn file yellow">delift_lift delift_tpss delift_ltpss delift_delift</td>
917 <td class="snnn file yellow">
920 <td class="ssnn file yellow">
925 <td class="nnns component yellow">
928 <td class="snns plane yellow">partial unfold</td>
929 <td class="snns file yellow">ltpss_sn ( ? ⊢ ▶*[?,?] ? )</td>
930 <td class="snnn file yellow">ltpss_sn_alt ( ? ⊢ ▶▶*[?,?] ? )</td>
931 <td class="snnn file yellow">ltpss_sn_ldrop ltpss_sn_tps ltpss_sn_tpss ltpss_sn_ltpss_sn</td>
932 <td class="snnn file yellow">
935 <td class="ssnn file yellow">
940 <td class="nnns component yellow">
943 <td class="nnns plane yellow">
946 <td class="snns file yellow">ltpss_dx ( ? ▶*[?,?] ? )</td>
947 <td class="snnn file yellow">ltpss_dx_ldrop ltpss_dx_tps ltpss_dx_tpss ltpss_dx_ltpss_dx</td>
948 <td class="snnn file yellow">
951 <td class="snnn file yellow">
954 <td class="ssnn file yellow">
959 <td class="nnns component yellow">
962 <td class="nnns plane yellow">
965 <td class="snns file yellow">tpss ( ? ⊢ ? ▶*[?,?] ? )</td>
966 <td class="snnn file yellow">tpss_alt ( ? ⊢ ? ▶▶*[?,?] ? )</td>
967 <td class="snnn file yellow">tpss_lift</td>
968 <td class="snnn file yellow">tpss_tpss</td>
969 <td class="ssnn file yellow">
974 <td class="nnns component yellow">
977 <td class="snns plane yellow">generic local env. slicing</td>
978 <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
979 <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
980 <td class="snnn file yellow">
983 <td class="snnn file yellow">
986 <td class="ssnn file yellow">
991 <td class="nnns component yellow">
994 <td class="snns plane yellow">iterated restricted structural predecessor for closures</td>
995 <td class="snns file yellow">frsups ( ⦃?,?⦄ ⧁* ⦃?,?⦄ )</td>
996 <td class="snnn file yellow">frsups_frsups</td>
997 <td class="snnn file yellow">
1000 <td class="snnn file yellow">
1003 <td class="ssnn file yellow">
1008 <td class="nnns component yellow">
1011 <td class="nnns plane yellow">
1014 <td class="snns file yellow">frsupp ( ⦃?,?⦄ ⧁+ ⦃?,?⦄ )</td>
1015 <td class="snnn file yellow">frsupp_frsupp</td>
1016 <td class="snnn file yellow">
1019 <td class="snnn file yellow">
1022 <td class="ssnn file yellow">
1027 <td class="nnns component yellow">
1030 <td class="snns plane yellow">generic term relocation</td>
1031 <td class="snns file yellow">lifts_vector ( ⇧*[?] ? ≡ ? )</td>
1032 <td class="snnn file yellow">lifts_lift_vector</td>
1033 <td class="snnn file yellow">
1036 <td class="snnn file yellow">
1039 <td class="ssnn file yellow">
1044 <td class="nnns component yellow">
1047 <td class="nnns plane yellow">
1050 <td class="snns file yellow">lifts ( ⇧*[?] ? ≡ ? )</td>
1051 <td class="snnn file yellow">lifts_lift lifts_lifts</td>
1052 <td class="snnn file yellow">
1055 <td class="snnn file yellow">
1058 <td class="ssnn file yellow">
1063 <td class="nnns component yellow">
1066 <td class="snns plane yellow">support for generic relocation</td>
1067 <td class="snns file yellow">gr2 ( @⦃?,?⦄ ≡ ? )</td>
1068 <td class="snnn file yellow">gr2_plus ( ? + ? )</td>
1069 <td class="snnn file yellow">gr2_minus ( ? ▭ ? ≡ ? )</td>
1070 <td class="snnn file yellow">gr2_gr2</td>
1071 <td class="ssnn file yellow">
1076 <td class="snns component orange">substitution</td>
1077 <td class="snns plane orange">parallel substitution</td>
1078 <td class="snns file orange">tps ( ? ⊢ ? ▶[?,?] ? )</td>
1079 <td class="snnn file orange">tps_lift tps_tps</td>
1080 <td class="snnn file orange">
1083 <td class="snnn file orange">
1086 <td class="ssnn file orange">
1091 <td class="nnns component orange">
1094 <td class="snns plane orange">global env. slicing</td>
1095 <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
1096 <td class="snnn file orange">gdrop_gdrop</td>
1097 <td class="snnn file orange">
1100 <td class="snnn file orange">
1103 <td class="ssnn file orange">
1108 <td class="nnns component orange">
1111 <td class="snns plane orange">basic local env. slicing</td>
1112 <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
1113 <td class="snnn file orange">ldrop_append ldrop_lpx ldrop_sfr ldrop_ldrop</td>
1114 <td class="snnn file orange">
1117 <td class="snnn file orange">
1120 <td class="ssnn file orange">
1125 <td class="nnns component orange">
1128 <td class="snns plane orange">local env. ref. for substitution</td>
1129 <td class="snns file orange">lsubs ( ? ≼[?,?] ? )</td>
1130 <td class="snnn file orange">(lsubs_lsubs)</td>
1131 <td class="snnn file orange">lsubs_sfr ( ≽[?,?] ? )</td>
1132 <td class="snnn file orange">
1135 <td class="ssnn file orange">
1140 <td class="nnns component orange">
1143 <td class="snns plane orange">restricted structural predecessor for closures</td>
1144 <td class="snns file orange">frsup ( ⦃?,?⦄ ⧁ ⦃?,?⦄ )</td>
1145 <td class="snnn file orange">
1148 <td class="snnn file orange">
1151 <td class="snnn file orange">
1154 <td class="ssnn file orange">
1159 <td class="nnns component orange">
1162 <td class="snns plane orange">basic term relocation</td>
1163 <td class="snns file orange">lift_vector ( ⇧[?,?] ? ≡ ? )</td>
1164 <td class="snnn file orange">lift_lift_vector</td>
1165 <td class="snnn file orange">
1168 <td class="snnn file orange">
1171 <td class="ssnn file orange">
1176 <td class="nnns component orange">
1179 <td class="nnns plane orange">
1182 <td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
1183 <td class="snnn file orange">lift_lift</td>
1184 <td class="snnn file orange">
1187 <td class="snnn file orange">
1190 <td class="ssnn file orange">
1195 <td class="snns component red">grammar</td>
1196 <td class="snns plane red">same head term form</td>
1197 <td class="snns file red">tshf ( ? ≈ ? )</td>
1198 <td class="snnn file red">(tshf_tshf)</td>
1199 <td class="snnn file red">
1202 <td class="snnn file red">
1205 <td class="ssnn file red">
1210 <td class="nnns component red">
1213 <td class="snns plane red">same top term constructor</td>
1214 <td class="snns file red">tstc ( ? ≃ ? )</td>
1215 <td class="snnn file red">tstc_tstc tstc_vector</td>
1216 <td class="snnn file red">
1219 <td class="snnn file red">
1222 <td class="ssnn file red">
1227 <td class="nnns component red">
1230 <td class="snns plane red">closures</td>
1231 <td class="snns file red">cl_shift ( ? @@ ? )</td>
1232 <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
1233 <td class="snnn file red">
1236 <td class="snnn file red">
1239 <td class="ssnn file red">
1244 <td class="nnns component red">
1247 <td class="snns plane red">internal syntax</td>
1248 <td class="snns file red">genv</td>
1249 <td class="snnn file red">
1252 <td class="snnn file red">
1255 <td class="snnn file red">
1258 <td class="ssnn file red">
1263 <td class="nnns component red">
1266 <td class="nnns plane red">
1269 <td class="snns file red">lenv</td>
1270 <td class="snnn file red">lenv_weight ( ♯{?} )</td>
1271 <td class="snnn file red">lenv_length ( |?| )</td>
1272 <td class="snnn file red">lenv_append ( ? @@ ? )</td>
1273 <td class="ssnn file red">lenv_px lenv_px_bi</td>
1276 <td class="nnns component red">
1279 <td class="nnns plane red">
1282 <td class="snns file red">term</td>
1283 <td class="snnn file red">term_weight ( ♯{?} )</td>
1284 <td class="snnn file red">term_simple ( 𝐒⦃?⦄ )</td>
1285 <td class="snnn file red">term_vector</td>
1286 <td class="ssnn file red">
1291 <td class="nnns component red">
1294 <td class="nnns plane red">
1297 <td class="snns file red">item</td>
1298 <td class="snnn file red">
1301 <td class="snnn file red">
1304 <td class="snnn file red">
1307 <td class="ssnn file red">
1312 <td class="nnss component red">
1315 <td class="snss plane red">external syntax</td>
1316 <td class="snss file red">aarity</td>
1317 <td class="snsn file red">
1320 <td class="snsn file red">
1323 <td class="snsn file red">
1326 <td class="sssn file red">
1334 <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
1335 <div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
1336 one for each component.
1338 <div class="spacer">
1339 <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
1341 <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1344 <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1345 <a href="http://validator.w3.org/check?uri=referer">
1346 <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
1348 <a href="http://jigsaw.w3.org/css-validator/check/referer">
1349 <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
1351 <a href="http://www.w3.org/XML/">
1352 <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
1354 <a href="http://www.w3.org/Graphics/PNG/">
1355 <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
1357 <a href="http://www.anybrowser.org/campaign/">
1358 <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
1361 <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1364 <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sat, 16 Mar 2013 23:25:31 +0100</div>