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22 <div class="head1">cic:/matita/lambdadelta/basic_2/ (core λδ version 2)</div>
24 <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
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29 <div xmlns:ld="http://lambdadelta.info/" class="text">
30 <table cellpadding="4" cellspacing="0">
33 <td class="snns capitalize italic sky">
34 <a href="http://lambdadelta.info/home.html">home</a>
36 <td class="snns capitalize italic magenta">
37 <a href="http://lambdadelta.info/news.html">news</a>
39 <td class="snns capitalize italic white">
40 <a href="http://lambdadelta.info/specification.html">specification</a>
42 <td class="snnn capitalize italic white">
45 <td class="snnn capitalize italic white">
48 <td class="snns capitalize italic orange">
49 <a href="http://lambdadelta.info/documentation.html">documentation</a>
51 <td class="snns capitalize italic green">
52 <a href="http://lambdadelta.info/implementation.html">implementation</a>
54 <td class="ssnn capitalize italic green">
59 <td class="snns capitalize sky">
60 <a href="http://lambdadelta.info/home.html#foreword">foreword</a>
62 <td class="snns capitalize magenta">
63 <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
65 <td class="snns capitalize white">
66 <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
68 <td class="snnn capitalize white">(<a href="http://lambdadelta.info/ground_2.html">background</a> - <a href="http://lambdadelta.info/basic_2.html">core</a> - <a href="http://lambdadelta.info/apps_2.html">applications</a>)</td>
69 <td class="snnn capitalize white">
72 <td class="snns capitalize orange">
73 <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
75 <td class="snns capitalize green">
76 <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
78 <td class="ssnn capitalize green">
79 <a href="http://lambdadelta.info/osn/">Open Symbolic Notation (OSN)</a>
83 <td class="snss capitalize sky">
84 <a href="http://lambdadelta.info/home.html#citations">citations</a>
86 <td class="snss capitalize magenta">
87 <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
89 <td class="snss capitalize white">
90 <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
92 <td class="snsn capitalize white">(<a href="http://lambdadelta.info/ground_1.html">background</a> - <a href="http://lambdadelta.info/basic_1.html">core</a>)</td>
93 <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
94 <td class="snss capitalize orange">
95 <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
97 <td class="snss capitalize green">
98 <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
100 <td class="sssn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
106 <section>System's Syntax and Behavior</section>
107 <body>This is a summary of the "block structure"
108 of the System's syntactic items and reductions.
110 <table name="basic_2_blk"/>
111 <body>* In terms only.
112 ** In terms and local environments only.
113 *** In global environments only.
114 **** Sort level k in terms only.
117 <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="summary">Summary of the Specification <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png" />
119 <div xmlns:ld="http://lambdadelta.info/" class="text">Here is a numerical account of the specification's contents
122 <div xmlns:ld="http://lambdadelta.info/" class="text">
123 <table cellpadding="4" cellspacing="0">
126 <td class="snns capitalize italic gray">category</td>
127 <td class="snns italic gray">objects</td>
128 <td class="snnn right italic gray">
131 <td class="snnn italic gray">
134 <td class="snnn right italic gray">
137 <td class="snnn italic gray">
140 <td class="ssnn right italic gray">
145 <td class="snns capitalize italic water">sizes</td>
146 <td class="snns italic water">files</td>
147 <td class="snnn right italic water">291</td>
148 <td class="snns italic water">characters</td>
149 <td class="snnn right italic water">304017</td>
150 <td class="snns italic water">nodes</td>
151 <td class="ssnn right italic water">1426457</td>
154 <td class="snns capitalize italic green">propositions</td>
155 <td class="snns italic green">theorems</td>
156 <td class="snnn right italic green">86</td>
157 <td class="snns italic green">lemmas</td>
158 <td class="snnn right italic green">1024</td>
159 <td class="snns italic green">total</td>
160 <td class="ssnn right italic green">1110</td>
163 <td class="snss capitalize italic grass">concepts</td>
164 <td class="snss italic grass">declared</td>
165 <td class="snsn right italic grass">34</td>
166 <td class="snss italic grass">defined</td>
167 <td class="snsn right italic grass">84</td>
168 <td class="snss italic grass">total</td>
169 <td class="sssn right italic grass">118</td>
174 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="B">Stage "B"</div>
175 <ul xmlns:ld="http://lambdadelta.info/">
177 <span class="emph alpha">Ongoing.</span>
178 Context-sensitive subject equivalence
179 for native type assignment.
182 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A2">Stage "A2": "Extending the Applicability Condition"</div>
183 <ul xmlns:ld="http://lambdadelta.info/">
185 <span class="emph alpha">2017 October 17.</span>
186 Exclusion binder in local environments.
187 Syntactic component updated:
188 syntax, relocation, s_transition, s_computation, static, i_static.
191 <ul xmlns:ld="http://lambdadelta.info/">
193 <span class="emph alpha">2017 April 16.</span>
194 Strong rt-normalization
195 for simply typed terms
196 (anniversary milestone).
199 <ul xmlns:ld="http://lambdadelta.info/">
201 <span class="emph alpha">2017 March 16.</span>
202 First behavioral component reconstructed:
206 <ul xmlns:ld="http://lambdadelta.info/">
208 <span class="emph alpha">2017 February 19.</span>
209 Generic candidates of reducibility.
212 <ul xmlns:ld="http://lambdadelta.info/">
214 <span class="emph alpha">2017 January 17.</span>
215 Confluence for parallel r-transition on referred entries of local environments.
218 <ul xmlns:ld="http://lambdadelta.info/">
220 <span class="emph alpha">2016 September 15.</span>
221 Confluence for context-sensitive parallel r-transition on terms.
224 <ul xmlns:ld="http://lambdadelta.info/">
226 <span class="emph alpha">2016 April 16.</span>
227 Syntactic component reconstructed:
228 syntax, relocation, s_transition, s_computation, static
229 (anniversary milestone).
232 <ul xmlns:ld="http://lambdadelta.info/">
234 <span class="emph alpha">2016 March 25.</span>
235 Relocation with reference transforming maps (rtmap).
238 <ul xmlns:ld="http://lambdadelta.info/">
240 <span class="emph alpha">2015 October 9.</span>
241 λδ version 2A2 is started.
244 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
245 <ul xmlns:ld="http://lambdadelta.info/">
247 <span class="emph delta">2015 August 27.</span>
248 λδ version 2A1 appears too complex and is dismissed.
251 <ul xmlns:ld="http://lambdadelta.info/">
253 <span class="emph gamma">2014 October 28.</span>
254 λδ version 2A1 is released.
257 <ul xmlns:ld="http://lambdadelta.info/">
259 <span class="emph beta">2014 September 9.</span>
260 Iterated static type assignment defined (more elegantly)
261 as a primitive notion.
264 <ul xmlns:ld="http://lambdadelta.info/">
266 <span class="emph beta">2014 June 18.</span>
267 Preservation of stratified native validity
268 for context-sensitive computation on terms.
271 <ul xmlns:ld="http://lambdadelta.info/">
273 <span class="emph alpha">2014 June 9.</span>
274 Strong qrst-normalization
275 for simply typed terms.
278 <ul xmlns:ld="http://lambdadelta.info/">
280 <span class="emph alpha">2014 April 16.</span>
281 Lazy equivalence on local environments
282 added as q-step to rst-computation on closures
283 (anniversary milestone).
286 <ul xmlns:ld="http://lambdadelta.info/">
288 <span class="emph alpha">2014 January 20.</span>
289 Parametrized slicing on local environments
290 comprises both versions of this operation
291 (one from basic_1, the other used in basic_2 till now).
294 <ul xmlns:ld="http://lambdadelta.info/">
296 <span class="emph alpha">2013 August 7.</span>
297 Passive support for global environments.
300 <ul xmlns:ld="http://lambdadelta.info/">
302 <span class="emph alpha">2013 July 27.</span>
303 Reaxiomatized β-reductum as in rt-reduction.
306 <ul xmlns:ld="http://lambdadelta.info/">
308 <span class="emph alpha">2013 July 20.</span>
309 Context-sensitive strong rt-normalization
310 for simply typed terms.
313 <ul xmlns:ld="http://lambdadelta.info/">
315 <span class="emph alpha">2013 April 16.</span>
316 Reaxiomatized substitution and reduction
317 commute with respect to subclosure
318 (anniversary milestone).
321 <ul xmlns:ld="http://lambdadelta.info/">
323 <span class="emph alpha">2013 March 16.</span>
324 Mutual recursive preservation of stratified native validity
325 for rst-computation on closures.
328 <ul xmlns:ld="http://lambdadelta.info/">
330 <span class="emph alpha">2012 October 16.</span>
331 Confluence for context-free parallel reduction on closures.
334 <ul xmlns:ld="http://lambdadelta.info/">
336 <span class="emph alpha">2012 July 26.</span>
337 Term binders polarized to control ζ-reduction (not released).
340 <ul xmlns:ld="http://lambdadelta.info/">
342 <span class="emph alpha">2012 April 16.</span>
343 Context-sensitive subject equivalence
344 for atomic arity assignment
345 (anniversary milestone).
348 <ul xmlns:ld="http://lambdadelta.info/">
350 <span class="emph alpha">2012 March 15.</span>
351 Context-sensitive strong normalization
352 for simply typed terms.
355 <ul xmlns:ld="http://lambdadelta.info/">
357 <span class="emph alpha">2012 January 27.</span>
358 Generic candidates of reducibility.
361 <ul xmlns:ld="http://lambdadelta.info/">
363 <span class="emph alpha">2011 September 21.</span>
364 Confluence for context-sensitive parallel reduction on terms.
367 <ul xmlns:ld="http://lambdadelta.info/">
369 <span class="emph alpha">2011 September 6.</span>
370 Confluence for context-free parallel reduction on terms.
373 <ul xmlns:ld="http://lambdadelta.info/">
375 <span class="emph alpha">2011 April 17.</span>
376 λδ version 2 is started.
379 <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="structure">Logical Structure of the Specification <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png" />
381 <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
383 <div xmlns:ld="http://lambdadelta.info/" class="text">
384 <table cellpadding="4" cellspacing="0">
387 <td class="snns top capitalize italic gray">component</td>
388 <td class="snns top italic gray">plane</td>
389 <td class="snns top gray">files</td>
390 <td class="ssnn top gray">
395 <td class="snns top capitalize italic blue">rt-conversion</td>
396 <td class="snns top italic blue">context-sensitive r-conversion</td>
397 <td class="snns top blue">cpc ( ⦃?,?⦄ ⊢ ? ⬌[?] ? )</td>
398 <td class="ssnn top blue">cpc_cpc</td>
401 <td class="snns top capitalize italic sky">rt-computation</td>
402 <td class="snns top italic sky">uncounted context-sensitive rt-computation</td>
403 <td class="snns top sky">lsubsx ( ? ⊢ ? ⊆ⓧ[?,?,?] ? )</td>
404 <td class="ssnn top sky">lsubsx_lfsx lsubsx_lsubsx</td>
407 <td class="nnns top capitalize italic sky">
410 <td class="nnns top italic sky">
413 <td class="snns top sky">lfsx ( ? ⊢ ⬈*[?,?,?] 𝐒⦃?⦄ )</td>
414 <td class="ssnn top sky">lfsx_drops lfsx_fqup lfsx_lfpxs lfsx_lfsx</td>
417 <td class="nnns top capitalize italic sky">
420 <td class="nnns top italic sky">
423 <td class="snns top sky">csx_vector ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )</td>
424 <td class="ssnn top sky">csx_cnx_vector csx_csx_vector</td>
427 <td class="nnns top capitalize italic sky">
430 <td class="nnns top italic sky">
433 <td class="snns top sky">csx ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )</td>
434 <td class="ssnn top sky">csx_simple csx_simple_theq csx_drops csx_lsubr csx_lfdeq csx_aaa csx_gcp csx_gcr csx_lfpx csx_cnx csx_cpxs csx_lfpxs csx_csx</td>
437 <td class="nnns top capitalize italic sky">
440 <td class="nnns top italic sky">
443 <td class="snns top sky">lfpxs ( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )</td>
444 <td class="ssnn top sky">lfpxs_length lfpxs_drops lfpxs_fqup lfpxs_lfdeq lfpxs_aaa lfpxs_cpxs lfpxs_lfpxs</td>
447 <td class="nnns top capitalize italic sky">
450 <td class="nnns top italic sky">
453 <td class="snns top sky">cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )</td>
454 <td class="ssnn top sky">cpxs_tdeq cpxs_theq cpxs_theq_vector cpxs_drops cpxs_fqus cpxs_lsubr cpxs_lfdeq cpxs_aaa cpxs_lfpx cpxs_cnx cpxs_cpxs</td>
457 <td class="snns top capitalize italic cyan">rt-transition</td>
458 <td class="snns top italic cyan">uncounted rst-transition</td>
459 <td class="snns top cyan">fpbq ( ⦃?,?,?⦄ ≽[?] ⦃?,?,?⦄ )</td>
460 <td class="ssnn top cyan">fpbq_aaa</td>
463 <td class="nnns top capitalize italic cyan">
466 <td class="nnns top italic cyan">
469 <td class="snns top cyan">fpb ( ⦃?,?,?⦄ ≻[?] ⦃?,?,?⦄ )</td>
470 <td class="ssnn top cyan">fpb_lfdeq</td>
473 <td class="nnns top capitalize italic cyan">
476 <td class="snns top italic cyan">t-bound context-sensitive rt-transition</td>
477 <td class="snns top cyan">lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
478 <td class="ssnn top cyan">lfpr_length lfpr_drops lfpr_fquq lfpr_fqup lfpr_frees lfpr_aaa lfpr_lfpx lfpr_lfpr</td>
481 <td class="nnns top capitalize italic cyan">
484 <td class="nnns top italic cyan">
487 <td class="snns top cyan">cpr_ext ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
488 <td class="ssnn top cyan">
493 <td class="nnns top capitalize italic cyan">
496 <td class="nnns top italic cyan">
499 <td class="snns top cyan">cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
500 <td class="ssnn top cyan">cpr_drops</td>
503 <td class="nnns top capitalize italic cyan">
506 <td class="nnns top italic cyan">
509 <td class="snns top cyan">cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
510 <td class="ssnn top cyan">cpm_simple cpm_drops cpm_lsubr cpm_lfxs cpm_cpx</td>
513 <td class="nnns top capitalize italic cyan">
516 <td class="snns top italic cyan">uncounted context-sensitive rt-transition</td>
517 <td class="snns top cyan">cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )</td>
518 <td class="ssnn top cyan">cnx_simple cnx_drops cnx_cnx</td>
521 <td class="nnns top capitalize italic cyan">
524 <td class="nnns top italic cyan">
527 <td class="snns top cyan">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
528 <td class="ssnn top cyan">lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_lfdeq lfpx_aaa lfpx_cpx lfpx_lfpx</td>
531 <td class="nnns top capitalize italic cyan">
534 <td class="nnns top italic cyan">
537 <td class="snns top cyan">cpx_ext ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
538 <td class="ssnn top cyan">
543 <td class="nnns top capitalize italic cyan">
546 <td class="nnns top italic cyan">
549 <td class="snns top cyan">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
550 <td class="ssnn top cyan">cpx_simple cpx_drops cpx_fqus cpx_lsubr cpx_lfxs</td>
553 <td class="nnns top capitalize italic cyan">
556 <td class="snns top italic cyan">counted context-sensitive rt-transition</td>
557 <td class="snns top cyan">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
558 <td class="ssnn top cyan">cpg_simple cpg_drops cpg_lsubr</td>
561 <td class="snns top capitalize italic water">iterated static typing</td>
562 <td class="snns top italic water">iterated extension on referred entries</td>
563 <td class="snns top water">tc_lfxs ( ? ⦻**[?,?] ? )</td>
564 <td class="ssnn top water">tc_lfxs_length tc_lfxs_drops tc_lfxs_fqup tc_lfxs_tc_lfxs</td>
567 <td class="snns top capitalize italic green">static typing</td>
568 <td class="snns top italic green">generic reducibility</td>
569 <td class="snns top green">lsubc ( ? ⊢ ? ⫃[?] ? )</td>
570 <td class="ssnn top green">lsubc_drops lsubc_lsubr lsubc_lsuba</td>
573 <td class="nnns top capitalize italic green">
576 <td class="nnns top italic green">
579 <td class="snns top green">gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
580 <td class="ssnn top green">gcp_aaa</td>
583 <td class="nnns top capitalize italic green">
586 <td class="nnns top italic green">
589 <td class="snns top green">gcp</td>
590 <td class="ssnn top green">
595 <td class="nnns top capitalize italic green">
598 <td class="snns top italic green">atomic arity assignment</td>
599 <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
600 <td class="ssnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
603 <td class="nnns top capitalize italic green">
606 <td class="nnns top italic green">
609 <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
610 <td class="ssnn top green">aaa_drops aaa_fqus aaa_lfdeq aaa_aaa</td>
613 <td class="nnns top capitalize italic green">
616 <td class="snns top italic green">degree-based equivalence on referred entries</td>
617 <td class="snns top green">ffdeq ( ⦃?,?,?⦄ ≛[?,?] ⦃?,?,?⦄ )</td>
618 <td class="ssnn top green">ffdeq_fqup ffdeq_ffdeq</td>
621 <td class="nnns top capitalize italic green">
624 <td class="nnns top italic green">
627 <td class="snns top green">lfdeq ( ? ≛[?,?,?] ? )</td>
628 <td class="ssnn top green">lfdeq_length lfdeq_drops lfdeq_fqup lfdeq_fqus lfdeq_lfdeq</td>
631 <td class="nnns top capitalize italic green">
634 <td class="snns top italic green">generic extension on referred entries</td>
635 <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
636 <td class="ssnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
639 <td class="nnns top capitalize italic green">
642 <td class="snns top italic green">context-sensitive free variables</td>
643 <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
644 <td class="ssnn top green">lsubf_lsubr lsubf_frees lsubf_lsubf</td>
647 <td class="nnns top capitalize italic green">
650 <td class="nnns top italic green">
653 <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
654 <td class="ssnn top green">frees_drops frees_fqup frees_frees</td>
657 <td class="nnns top capitalize italic green">
660 <td class="snns top italic green">restricted ref. for local env.</td>
661 <td class="snns top green">lsubr ( ? ⫃ ? )</td>
662 <td class="ssnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
665 <td class="snns top capitalize italic grass">s-computation</td>
666 <td class="snns top italic grass">iterated structural successor for closures</td>
667 <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐*[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
668 <td class="ssnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
671 <td class="nnns top capitalize italic grass">
674 <td class="nnns top italic grass">
677 <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
678 <td class="ssnn top grass">fqup_weight fqup_drops fqup_fqup</td>
681 <td class="snns top capitalize italic yellow">s-transition</td>
682 <td class="snns top italic yellow">structural successor for closures</td>
683 <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
684 <td class="ssnn top yellow">fquq_length fquq_weight</td>
687 <td class="nnns top capitalize italic yellow">
690 <td class="nnns top italic yellow">
693 <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
694 <td class="ssnn top yellow">fqu_length fqu_weight</td>
697 <td class="snns top capitalize italic orange">relocation</td>
698 <td class="snns top italic orange">generic slicing for local environments</td>
699 <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
700 <td class="ssnn top orange">
705 <td class="nnns top capitalize italic orange">
708 <td class="nnns top italic orange">
711 <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
712 <td class="ssnn top orange">drops_lstar drops_weight drops_length drops_ext2 drops_lexs drops_lreq drops_drops</td>
715 <td class="nnns top capitalize italic orange">
718 <td class="snns top italic orange">generic relocation</td>
719 <td class="snns top orange">lifts_bind ( ⬆*[?] ? ≡ ? )</td>
720 <td class="ssnn top orange">lifts_weight_bind lifts_lifts_bind</td>
723 <td class="nnns top capitalize italic orange">
726 <td class="nnns top italic orange">
729 <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
730 <td class="ssnn top orange">lifts_lifts_vector</td>
733 <td class="nnns top capitalize italic orange">
736 <td class="nnns top italic orange">
739 <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
740 <td class="ssnn top orange">lifts_simple lifts_weight lifts_tdeq lifts_lifts</td>
743 <td class="nnns top capitalize italic orange">
746 <td class="snns top italic orange">ranged equivalence for local environments</td>
747 <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
748 <td class="ssnn top orange">lreq_length lreq_lreq</td>
751 <td class="nnns top capitalize italic orange">
754 <td class="snns top italic orange">generic entrywise extension</td>
755 <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
756 <td class="ssnn top orange">lexs_length lexs_lexs</td>
759 <td class="snns top capitalize italic red">syntax</td>
760 <td class="snns top italic red">append for local environments</td>
761 <td class="snns top red">append ( ? @@ ? )</td>
762 <td class="ssnn top red">append_length</td>
765 <td class="nnns top capitalize italic red">
768 <td class="snns top italic red">head equivalence for terms</td>
769 <td class="snns top red">theq ( ? ⩳[?,?] ? )</td>
770 <td class="ssnn top red">theq_simple theq_tdeq theq_theq theq_simple_vector</td>
773 <td class="nnns top capitalize italic red">
776 <td class="snns top italic red">degree-based equivalence</td>
777 <td class="snns top red">tdeq_ext ( ? ≛[?,?] ? ) ( ? ⊢ ? ≛[?,?] ? )</td>
778 <td class="ssnn top red">
783 <td class="nnns top capitalize italic red">
786 <td class="nnns top italic red">
789 <td class="snns top red">tdeq ( ? ≛[?,?] ? )</td>
790 <td class="ssnn top red">tdeq_tdeq</td>
793 <td class="nnns top capitalize italic red">
796 <td class="snns top italic red">closures</td>
797 <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
798 <td class="ssnn top red">
803 <td class="nnns top capitalize italic red">
806 <td class="nnns top italic red">
809 <td class="snns top red">cl_restricted_weight ( ♯{?,?} )</td>
810 <td class="ssnn top red">
815 <td class="nnns top capitalize italic red">
818 <td class="snns top italic red">global environments</td>
819 <td class="snns top red">genv</td>
820 <td class="ssnn top red">
825 <td class="nnns top capitalize italic red">
828 <td class="snns top italic red">local environments</td>
829 <td class="snns top red">lenv_ext2</td>
830 <td class="ssnn top red">
835 <td class="nnns top capitalize italic red">
838 <td class="nnns top italic red">
841 <td class="snns top red">lenv_length ( |?| )</td>
842 <td class="ssnn top red">
847 <td class="nnns top capitalize italic red">
850 <td class="nnns top italic red">
853 <td class="snns top red">lenv_weight ( ♯{?} )</td>
854 <td class="ssnn top red">
859 <td class="nnns top capitalize italic red">
862 <td class="nnns top italic red">
865 <td class="snns top red">lenv</td>
866 <td class="ssnn top red">
871 <td class="nnns top capitalize italic red">
874 <td class="snns top italic red">binders for local environments</td>
875 <td class="snns top red">ext2</td>
876 <td class="ssnn top red">ext2_ext2</td>
879 <td class="nnns top capitalize italic red">
882 <td class="nnns top italic red">
885 <td class="snns top red">bind</td>
886 <td class="ssnn top red">bind_weight</td>
889 <td class="nnns top capitalize italic red">
892 <td class="snns top italic red">terms</td>
893 <td class="snns top red">term_vector ( Ⓐ?.? )</td>
894 <td class="ssnn top red">
899 <td class="nnns top capitalize italic red">
902 <td class="nnns top italic red">
905 <td class="snns top red">term_simple ( 𝐒⦃?⦄ )</td>
906 <td class="ssnn top red">
911 <td class="nnns top capitalize italic red">
914 <td class="nnns top italic red">
917 <td class="snns top red">term_weight ( ♯{?} )</td>
918 <td class="ssnn top red">
923 <td class="nnns top capitalize italic red">
926 <td class="nnns top italic red">
929 <td class="snns top red">term</td>
930 <td class="ssnn top red">
935 <td class="nnns top capitalize italic red">
938 <td class="snns top italic red">items</td>
939 <td class="snns top red">item_sd</td>
940 <td class="ssnn top red">
945 <td class="nnns top capitalize italic red">
948 <td class="nnns top italic red">
951 <td class="snns top red">item_sh</td>
952 <td class="ssnn top red">
957 <td class="nnns top capitalize italic red">
960 <td class="nnns top italic red">
963 <td class="snns top red">item</td>
964 <td class="ssnn top red">
969 <td class="nnss top capitalize italic red">
972 <td class="snss top italic red">atomic arities</td>
973 <td class="snss top red">aarity</td>
974 <td class="sssn top red">
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