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="\lambda\delta home page" />
10 <title>\lambda\delta home page</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="[\lambda\delta home]" title="\lambda\delta home" src="http://lambdadelta.info/images/crux_32.png" />
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" />
26 <div xmlns:ld="http://lambdadelta.info/" class="spacer">
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">301</td>
148 <td class="snns italic water">characters</td>
149 <td class="snnn right italic water">311322</td>
150 <td class="snns italic water">nodes</td>
151 <td class="ssnn right italic water">1450558</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">93</td>
157 <td class="snns italic green">lemmas</td>
158 <td class="snnn right italic green">1054</td>
159 <td class="snns italic green">total</td>
160 <td class="ssnn right italic green">1147</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">91</td>
168 <td class="snss italic grass">total</td>
169 <td class="sssn right italic grass">125</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 capitalize italic gray">section</td>
389 <td class="snns top italic gray">plane</td>
390 <td class="snns top gray">files</td>
391 <td class="ssnn top gray">
396 <td class="snns top capitalize italic blue">rt-conversion</td>
397 <td class="snns top capitalize italic blue">context-sensitive parallel r-conversion</td>
398 <td class="snns top italic blue">for terms</td>
399 <td class="snns top blue">cpc ( ⦃?,?⦄ ⊢ ? ⬌[?] ? )</td>
400 <td class="ssnn top blue">cpc_cpc</td>
403 <td class="snns top capitalize italic sky">rt-computation</td>
404 <td class="snns top capitalize italic sky">uncounted context-sensitive parallel rt-computation</td>
405 <td class="snns top italic sky">refinement for lenvs</td>
406 <td class="snns top sky">lsubsx ( ? ⊢ ? ⊆ⓧ[?,?,?] ? )</td>
407 <td class="ssnn top sky">lsubsx_lfsx lsubsx_lsubsx</td>
410 <td class="nnns top capitalize italic sky">
413 <td class="nnns top capitalize italic sky">
416 <td class="snns top italic sky">strongly normalizing on referred entries for lenvs</td>
417 <td class="snns top sky">lfsx ( ? ⊢ ⬈*[?,?,?] 𝐒⦃?⦄ )</td>
418 <td class="ssnn top sky">lfsx_drops lfsx_fqup lfsx_lfpxs lfsx_lfsx</td>
421 <td class="nnns top capitalize italic sky">
424 <td class="nnns top capitalize italic sky">
427 <td class="snns top italic sky">strongly normalizing for term vectors</td>
428 <td class="snns top sky">csx_vector ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )</td>
429 <td class="ssnn top sky">csx_cnx_vector csx_csx_vector</td>
432 <td class="nnns top capitalize italic sky">
435 <td class="nnns top capitalize italic sky">
438 <td class="snns top italic sky">strongly normalizing for terms</td>
439 <td class="snns top sky">csx ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )</td>
440 <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>
443 <td class="nnns top capitalize italic sky">
446 <td class="nnns top capitalize italic sky">
449 <td class="snns top italic sky">on referred entries for lenvs</td>
450 <td class="snns top sky">lfpxs ( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )</td>
451 <td class="ssnn top sky">lfpxs_length lfpxs_drops lfpxs_fqup lfpxs_lfdeq lfpxs_aaa lfpxs_cpxs lfpxs_lfpxs</td>
454 <td class="nnns top capitalize italic sky">
457 <td class="nnns top capitalize italic sky">
460 <td class="snns top italic sky">for terms</td>
461 <td class="snns top sky">cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )</td>
462 <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>
465 <td class="snns top capitalize italic cyan">rt-transition</td>
466 <td class="snns top capitalize italic cyan">uncounted parallel rst-transition</td>
467 <td class="snns top italic cyan">for closures</td>
468 <td class="snns top cyan">fpbq ( ⦃?,?,?⦄ ≽[?] ⦃?,?,?⦄ )</td>
469 <td class="ssnn top cyan">fpbq_aaa</td>
472 <td class="nnns top capitalize italic cyan">
475 <td class="nnns top capitalize italic cyan">
478 <td class="snns top italic cyan">proper for closures</td>
479 <td class="snns top cyan">fpb ( ⦃?,?,?⦄ ≻[?] ⦃?,?,?⦄ )</td>
480 <td class="ssnn top cyan">fpb_lfdeq</td>
483 <td class="nnns top capitalize italic cyan">
486 <td class="snns top capitalize italic cyan">context-sensitive parallel r-transition</td>
487 <td class="snns top italic cyan">for lenvs on referred entries</td>
488 <td class="snns top cyan">lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
489 <td class="ssnn top cyan">lfpr_length lfpr_drops lfpr_fquq lfpr_fqup lfpr_frees lfpr_aaa lfpr_lfpx lfpr_lfpr</td>
492 <td class="nnns top capitalize italic cyan">
495 <td class="nnns top capitalize italic cyan">
498 <td class="snns top italic cyan">for binders</td>
499 <td class="snns top cyan">cpr_ext ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
500 <td class="ssnn top cyan">
505 <td class="nnns top capitalize italic cyan">
508 <td class="nnns top capitalize italic cyan">
511 <td class="snns top italic cyan">for terms</td>
512 <td class="snns top cyan">cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
513 <td class="ssnn top cyan">cpr_drops</td>
516 <td class="nnns top capitalize italic cyan">
519 <td class="snns top capitalize italic cyan">t-bound context-sensitive parallel rt-transition</td>
520 <td class="snns top italic cyan">for terms</td>
521 <td class="snns top cyan">cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
522 <td class="ssnn top cyan">cpm_simple cpm_drops cpm_lsubr cpm_lfxs cpm_cpx</td>
525 <td class="nnns top capitalize italic cyan">
528 <td class="snns top capitalize italic cyan">uncounted context-sensitive parallel rt-transition</td>
529 <td class="snns top italic cyan">normal form for terms</td>
530 <td class="snns top cyan">cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )</td>
531 <td class="ssnn top cyan">cnx_simple cnx_drops cnx_cnx</td>
534 <td class="nnns top capitalize italic cyan">
537 <td class="nnns top capitalize italic cyan">
540 <td class="snns top italic cyan">for lenvs on referred entries</td>
541 <td class="snns top cyan">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
542 <td class="ssnn top cyan">lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_lfdeq lfpx_aaa lfpx_cpx lfpx_lfpx</td>
545 <td class="nnns top capitalize italic cyan">
548 <td class="nnns top capitalize italic cyan">
551 <td class="snns top italic cyan">for binders</td>
552 <td class="snns top cyan">cpx_ext ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
553 <td class="ssnn top cyan">
558 <td class="nnns top capitalize italic cyan">
561 <td class="nnns top capitalize italic cyan">
564 <td class="snns top italic cyan">for terms</td>
565 <td class="snns top cyan">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
566 <td class="ssnn top cyan">cpx_simple cpx_drops cpx_fqus cpx_lsubr cpx_lfxs</td>
569 <td class="nnns top capitalize italic cyan">
572 <td class="snns top capitalize italic cyan">counted context-sensitive parallel rt-transition</td>
573 <td class="snns top italic cyan">for terms</td>
574 <td class="snns top cyan">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
575 <td class="ssnn top cyan">cpg_simple cpg_drops cpg_lsubr</td>
578 <td class="snns top capitalize italic water">iterated static typing</td>
579 <td class="snns top capitalize italic water">iterated extension on referred entries</td>
580 <td class="snns top italic water" />
581 <td class="snns top water">tc_lfxs ( ? ⦻**[?,?] ? )</td>
582 <td class="ssnn top water">tc_lfxs_length tc_lfxs_lex tc_lfxs_drops tc_lfxs_fqup tc_lfxs_tc_lfxs</td>
585 <td class="snns top capitalize italic green">static typing</td>
586 <td class="snns top capitalize italic green">generic reducibility</td>
587 <td class="snns top italic green" />
588 <td class="snns top green">lsubc ( ? ⊢ ? ⫃[?] ? )</td>
589 <td class="ssnn top green">lsubc_drops lsubc_lsubr lsubc_lsuba</td>
592 <td class="nnns top capitalize italic green">
595 <td class="nnns top capitalize italic green">
598 <td class="snns top italic green" />
599 <td class="snns top green">gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
600 <td class="ssnn top green">gcp_aaa</td>
603 <td class="nnns top capitalize italic green">
606 <td class="nnns top capitalize italic green">
609 <td class="snns top italic green" />
610 <td class="snns top green">gcp</td>
611 <td class="ssnn top green">
616 <td class="nnns top capitalize italic green">
619 <td class="snns top capitalize italic green">atomic arity assignment</td>
620 <td class="snns top italic green" />
621 <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
622 <td class="ssnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
625 <td class="nnns top capitalize italic green">
628 <td class="nnns top capitalize italic green">
631 <td class="snns top italic green" />
632 <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
633 <td class="ssnn top green">aaa_drops aaa_fqus aaa_lfdeq aaa_aaa</td>
636 <td class="nnns top capitalize italic green">
639 <td class="snns top capitalize italic green">degree-based equivalence on referred entries</td>
640 <td class="snns top italic green" />
641 <td class="snns top green">ffdeq ( ⦃?,?,?⦄ ≛[?,?] ⦃?,?,?⦄ )</td>
642 <td class="ssnn top green">ffdeq_fqup ffdeq_ffdeq</td>
645 <td class="nnns top capitalize italic green">
648 <td class="nnns top capitalize italic green">
651 <td class="snns top italic green" />
652 <td class="snns top green">lfdeq ( ? ≛[?,?,?] ? )</td>
653 <td class="ssnn top green">lfdeq_length lfdeq_drops lfdeq_fqup lfdeq_fqus lfdeq_lfdeq</td>
656 <td class="nnns top capitalize italic green">
659 <td class="snns top capitalize italic green">syntactic equivalence on referred entries</td>
660 <td class="snns top italic green" />
661 <td class="snns top green">lfeq ( ? ≡[?] ? )</td>
662 <td class="ssnn top green">lfeq_fqup lfeq_lfeq</td>
665 <td class="nnns top capitalize italic green">
668 <td class="snns top capitalize italic green">generic extension on referred entries</td>
669 <td class="snns top italic green" />
670 <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
671 <td class="ssnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
674 <td class="nnns top capitalize italic green">
677 <td class="snns top capitalize italic green">context-sensitive free variables</td>
678 <td class="snns top italic green" />
679 <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
680 <td class="ssnn top green">lsubf_lsubr lsubf_frees lsubf_lsubf</td>
683 <td class="nnns top capitalize italic green">
686 <td class="nnns top capitalize italic green">
689 <td class="snns top italic green" />
690 <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
691 <td class="ssnn top green">frees_drops frees_fqup frees_frees</td>
694 <td class="nnns top capitalize italic green">
697 <td class="snns top capitalize italic green">restricted ref. for local env.</td>
698 <td class="snns top italic green" />
699 <td class="snns top green">lsubr ( ? ⫃ ? )</td>
700 <td class="ssnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
703 <td class="snns top capitalize italic grass">s-computation</td>
704 <td class="snns top capitalize italic grass">iterated structural successor for closures</td>
705 <td class="snns top italic grass" />
706 <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐*[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
707 <td class="ssnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
710 <td class="nnns top capitalize italic grass">
713 <td class="nnns top capitalize italic grass">
716 <td class="snns top italic grass" />
717 <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
718 <td class="ssnn top grass">fqup_weight fqup_drops fqup_fqup</td>
721 <td class="snns top capitalize italic yellow">s-transition</td>
722 <td class="snns top capitalize italic yellow">structural successor for closures</td>
723 <td class="snns top italic yellow" />
724 <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
725 <td class="ssnn top yellow">fquq_length fquq_weight</td>
728 <td class="nnns top capitalize italic yellow">
731 <td class="nnns top capitalize italic yellow">
734 <td class="snns top italic yellow" />
735 <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
736 <td class="ssnn top yellow">fqu_length fqu_weight</td>
739 <td class="snns top capitalize italic orange">relocation</td>
740 <td class="snns top capitalize italic orange">generic slicing for local environments</td>
741 <td class="snns top italic orange" />
742 <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
743 <td class="ssnn top orange">
748 <td class="nnns top capitalize italic orange">
751 <td class="nnns top capitalize italic orange">
754 <td class="snns top italic orange" />
755 <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
756 <td class="ssnn top orange">drops_lstar drops_weight drops_length drops_cext2 drops_lexs drops_lreq drops_drops</td>
759 <td class="nnns top capitalize italic orange">
762 <td class="snns top capitalize italic orange">generic relocation</td>
763 <td class="snns top italic orange" />
764 <td class="snns top orange">lifts_bind ( ⬆*[?] ? ≡ ? )</td>
765 <td class="ssnn top orange">lifts_weight_bind lifts_lifts_bind</td>
768 <td class="nnns top capitalize italic orange">
771 <td class="nnns top capitalize italic orange">
774 <td class="snns top italic orange" />
775 <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
776 <td class="ssnn top orange">lifts_lifts_vector</td>
779 <td class="nnns top capitalize italic orange">
782 <td class="nnns top capitalize italic orange">
785 <td class="snns top italic orange" />
786 <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
787 <td class="ssnn top orange">lifts_simple lifts_weight lifts_tdeq lifts_lifts</td>
790 <td class="nnns top capitalize italic orange">
793 <td class="snns top capitalize italic orange">ranged equivalence for local environments</td>
794 <td class="snns top italic orange" />
795 <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
796 <td class="ssnn top orange">lreq_length lreq_lreq</td>
799 <td class="nnns top capitalize italic orange">
802 <td class="snns top capitalize italic orange">generic entrywise extension</td>
803 <td class="snns top italic orange" />
804 <td class="snns top orange">lex ( ? ⦻[?] ? )</td>
805 <td class="ssnn top orange">
810 <td class="nnns top capitalize italic orange">
813 <td class="nnns top capitalize italic orange">
816 <td class="snns top italic orange" />
817 <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
818 <td class="ssnn top orange">lexs_tc lexs_length lexs_lexs</td>
821 <td class="snns top capitalize italic red">syntax</td>
822 <td class="snns top capitalize italic red">append for local environments</td>
823 <td class="snns top italic red" />
824 <td class="snns top red">append ( ? @@ ? )</td>
825 <td class="ssnn top red">append_length</td>
828 <td class="nnns top capitalize italic red">
831 <td class="snns top capitalize italic red">head equivalence for terms</td>
832 <td class="snns top italic red" />
833 <td class="snns top red">theq ( ? ⩳[?,?] ? )</td>
834 <td class="ssnn top red">theq_simple theq_tdeq theq_theq theq_simple_vector</td>
837 <td class="nnns top capitalize italic red">
840 <td class="snns top capitalize italic red">degree-based equivalence</td>
841 <td class="snns top italic red" />
842 <td class="snns top red">tdeq_ext ( ? ≛[?,?] ? ) ( ? ⊢ ? ≛[?,?] ? )</td>
843 <td class="ssnn top red">
848 <td class="nnns top capitalize italic red">
851 <td class="nnns top capitalize italic red">
854 <td class="snns top italic red" />
855 <td class="snns top red">tdeq ( ? ≛[?,?] ? )</td>
856 <td class="ssnn top red">tdeq_tdeq</td>
859 <td class="nnns top capitalize italic red">
862 <td class="snns top capitalize italic red">closures</td>
863 <td class="snns top italic red" />
864 <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
865 <td class="ssnn top red">
870 <td class="nnns top capitalize italic red">
873 <td class="nnns top capitalize italic red">
876 <td class="snns top italic red" />
877 <td class="snns top red">cl_restricted_weight ( ♯{?,?} )</td>
878 <td class="ssnn top red">
883 <td class="nnns top capitalize italic red">
886 <td class="snns top capitalize italic red">global environments</td>
887 <td class="snns top italic red" />
888 <td class="snns top red">genv</td>
889 <td class="ssnn top red">
894 <td class="nnns top capitalize italic red">
897 <td class="snns top capitalize italic red">local environments</td>
898 <td class="snns top italic red" />
899 <td class="snns top red">ceq_ext</td>
900 <td class="ssnn top red">ceq_ext_ceq_ext</td>
903 <td class="nnns top capitalize italic red">
906 <td class="nnns top capitalize italic red">
909 <td class="snns top italic red" />
910 <td class="snns top red">cext2</td>
911 <td class="ssnn top red">
916 <td class="nnns top capitalize italic red">
919 <td class="nnns top capitalize italic red">
922 <td class="snns top italic red" />
923 <td class="snns top red">lenv_length ( |?| )</td>
924 <td class="ssnn top red">
929 <td class="nnns top capitalize italic red">
932 <td class="nnns top capitalize italic red">
935 <td class="snns top italic red" />
936 <td class="snns top red">lenv_weight ( ♯{?} )</td>
937 <td class="ssnn top red">
942 <td class="nnns top capitalize italic red">
945 <td class="nnns top capitalize italic red">
948 <td class="snns top italic red" />
949 <td class="snns top red">lenv</td>
950 <td class="ssnn top red">
955 <td class="nnns top capitalize italic red">
958 <td class="snns top capitalize italic red">binders for local environments</td>
959 <td class="snns top italic red" />
960 <td class="snns top red">ext2</td>
961 <td class="ssnn top red">ext2_tc ext2_ext2</td>
964 <td class="nnns top capitalize italic red">
967 <td class="nnns top capitalize italic red">
970 <td class="snns top italic red" />
971 <td class="snns top red">bind</td>
972 <td class="ssnn top red">bind_weight</td>
975 <td class="nnns top capitalize italic red">
978 <td class="snns top capitalize italic red">terms</td>
979 <td class="snns top italic red" />
980 <td class="snns top red">term_vector ( Ⓐ?.? )</td>
981 <td class="ssnn top red">
986 <td class="nnns top capitalize italic red">
989 <td class="nnns top capitalize italic red">
992 <td class="snns top italic red" />
993 <td class="snns top red">term_simple ( 𝐒⦃?⦄ )</td>
994 <td class="ssnn top red">
999 <td class="nnns top capitalize italic red">
1002 <td class="nnns top capitalize italic red">
1005 <td class="snns top italic red" />
1006 <td class="snns top red">term_weight ( ♯{?} )</td>
1007 <td class="ssnn top red">
1012 <td class="nnns top capitalize italic red">
1015 <td class="nnns top capitalize italic red">
1018 <td class="snns top italic red" />
1019 <td class="snns top red">term</td>
1020 <td class="ssnn top red">
1025 <td class="nnns top capitalize italic red">
1028 <td class="snns top capitalize italic red">items</td>
1029 <td class="snns top italic red" />
1030 <td class="snns top red">item_sd</td>
1031 <td class="ssnn top red">
1036 <td class="nnns top capitalize italic red">
1039 <td class="nnns top capitalize italic red">
1042 <td class="snns top italic red" />
1043 <td class="snns top red">item_sh</td>
1044 <td class="ssnn top red">
1049 <td class="nnns top capitalize italic red">
1052 <td class="nnns top capitalize italic red">
1055 <td class="snns top italic red" />
1056 <td class="snns top red">item</td>
1057 <td class="ssnn top red">
1062 <td class="nnss top capitalize italic red">
1065 <td class="snss top capitalize italic red">atomic arities</td>
1066 <td class="snss top italic red" />
1067 <td class="snss top red">aarity</td>
1068 <td class="sssn top red">
1075 <div class="spacer">
1076 <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
1078 <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1081 <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1082 <a href="http://validator.w3.org/check?uri=referer">
1083 <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
1085 <a href="http://jigsaw.w3.org/css-validator/check/referer">
1086 <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
1088 <a href="http://www.w3.org/XML/">
1089 <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
1091 <a href="http://www.w3.org/Graphics/PNG/">
1092 <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
1094 <a href="http://www.anybrowser.org/campaign/">
1095 <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
1098 <div xmlns:ld="http://lambdadelta.info/" class="spacer">
1101 <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Wed, 22 Nov 2017 22:20:05 +0100</div>