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22 <div class="head1">cic:/matita/lambdadelta/basic_2/ (core λδ version 2)</div>
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29 <div xmlns:ld="http://lambdadelta.info/" class="text">
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33 <td class="snns capitalize italic sky">
34 <a href="http://lambdadelta.info/index.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/index.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#lddl">library</a>
78 <td class="ssnn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
81 <td class="snss capitalize sky">
82 <a href="http://lambdadelta.info/index.html#citations">citations</a>
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85 <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
87 <td class="snss capitalize white">
88 <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
90 <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>
91 <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
92 <td class="snss capitalize orange">
93 <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
95 <td class="snss capitalize green">
96 <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
98 <td class="sssn capitalize green">
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="[spacer]" title="lambdadelta 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 cyan">sizes</td>
146 <td class="snns italic cyan">files</td>
147 <td class="snnn right italic cyan">83</td>
148 <td class="snns italic cyan">characters</td>
149 <td class="snnn right italic cyan">55955</td>
150 <td class="snns italic cyan">nodes</td>
151 <td class="ssnn right italic cyan">191279</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">33</td>
157 <td class="snns italic green">lemmas</td>
158 <td class="snnn right italic green">211</td>
159 <td class="snns italic green">total</td>
160 <td class="ssnn right italic green">244</td>
163 <td class="snss capitalize italic yellow">concepts</td>
164 <td class="snss italic yellow">declared</td>
165 <td class="snsn right italic yellow">15</td>
166 <td class="snss italic yellow">defined</td>
167 <td class="snsn right italic yellow">23</td>
168 <td class="snss italic yellow">total</td>
169 <td class="sssn right italic yellow">38</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">2015 October 9.</span>
186 λδ version 2A2 is started.
189 <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
190 <ul xmlns:ld="http://lambdadelta.info/">
192 <span class="emph delta">2015 August 27.</span>
193 λδ version 2A1 appears too complex and is dismissed.
196 <ul xmlns:ld="http://lambdadelta.info/">
198 <span class="emph gamma">2014 October 28.</span>
199 λδ version 2A1 is released.
202 <ul xmlns:ld="http://lambdadelta.info/">
204 <span class="emph beta">2014 September 9.</span>
205 Iterated static type assignment defined (more elegantly)
206 as a primitive notion.
209 <ul xmlns:ld="http://lambdadelta.info/">
211 <span class="emph beta">2014 June 18.</span>
212 Preservation of stratified native validity
213 for context-sensitive computation on terms.
216 <ul xmlns:ld="http://lambdadelta.info/">
218 <span class="emph alpha">2014 June 9.</span>
219 Strong qrst-normalization
220 for simply typed terms.
223 <ul xmlns:ld="http://lambdadelta.info/">
225 <span class="emph alpha">2014 April 16.</span>
226 Lazy equivalence on local environments
227 added as q-step to rst-computation on closures
228 (anniversary milestone).
231 <ul xmlns:ld="http://lambdadelta.info/">
233 <span class="emph alpha">2014 January 20.</span>
234 Parametrized slicing of local environments
235 comprises both versions of this operation
236 (one from basic_1, the other used in basic_2 till now).
239 <ul xmlns:ld="http://lambdadelta.info/">
241 <span class="emph alpha">2013 August 7.</span>
242 Passive support for global environments.
245 <ul xmlns:ld="http://lambdadelta.info/">
247 <span class="emph alpha">2013 July 27.</span>
248 Reaxiomatized β-reductum as in rt-reduction.
251 <ul xmlns:ld="http://lambdadelta.info/">
253 <span class="emph alpha">2013 July 20.</span>
254 Context-sensitive strong rt-normalization
255 for simply typed terms.
258 <ul xmlns:ld="http://lambdadelta.info/">
260 <span class="emph alpha">2013 April 16.</span>
261 Reaxiomatized substitution and reduction
262 commute with respect to subclosure
263 (anniversary milestone).
266 <ul xmlns:ld="http://lambdadelta.info/">
268 <span class="emph alpha">2013 March 16.</span>
269 Mutual recursive preservation of stratified native validity
270 for rst-computation on closures.
273 <ul xmlns:ld="http://lambdadelta.info/">
275 <span class="emph alpha">2012 October 16.</span>
276 Confluence for context-free parallel reduction on closures.
279 <ul xmlns:ld="http://lambdadelta.info/">
281 <span class="emph alpha">2012 July 26.</span>
282 Term binders polarized to control ζ-reduction (not released).
285 <ul xmlns:ld="http://lambdadelta.info/">
287 <span class="emph alpha">2012 April 16.</span>
288 Context-sensitive subject equivalence
289 for atomic arity assignment
290 (anniversary milestone).
293 <ul xmlns:ld="http://lambdadelta.info/">
295 <span class="emph alpha">2012 March 15.</span>
296 Context-sensitive strong normalization
297 for simply typed terms.
300 <ul xmlns:ld="http://lambdadelta.info/">
302 <span class="emph alpha">2012 January 27.</span>
303 Support for abstract candidates of reducibility.
306 <ul xmlns:ld="http://lambdadelta.info/">
308 <span class="emph alpha">2011 September 21.</span>
309 Confluence for context-sensitive parallel reduction on terms.
312 <ul xmlns:ld="http://lambdadelta.info/">
314 <span class="emph alpha">2011 September 6.</span>
315 Confluence for context-free parallel reduction on terms.
318 <ul xmlns:ld="http://lambdadelta.info/">
320 <span class="emph alpha">2011 April 17.</span>
321 λδ version 2 is started.
324 <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="structure">Logical Structure of the Specification <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b4.png" />
326 <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
328 <div xmlns:ld="http://lambdadelta.info/" class="text">
329 <table cellpadding="4" cellspacing="0">
332 <td class="snns top capitalize italic gray">component</td>
333 <td class="snns top italic gray">plane</td>
334 <td class="snns top gray">files</td>
335 <td class="snnn top gray">
338 <td class="snnn top gray">
341 <td class="ssnn top gray">
346 <td class="snns top capitalize italic yellow">relocation</td>
347 <td class="snns top italic yellow">ranged equivalence for closures</td>
348 <td class="snns top yellow">freq ( ⦃?,?,?⦄ ≡ ⦃?,?,?⦄ )</td>
349 <td class="snnn top yellow">freq_freq</td>
350 <td class="snnn top yellow">
353 <td class="ssnn top yellow">
358 <td class="nnns top capitalize italic yellow">
361 <td class="snns top italic yellow">context-sensitive free variables</td>
362 <td class="snns top yellow">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
363 <td class="snnn top yellow">frees_weight frees_lreq frees_frees</td>
364 <td class="snnn top yellow">
367 <td class="ssnn top yellow">
372 <td class="nnns top capitalize italic yellow">
375 <td class="snns top italic yellow">generic slicing for local environments</td>
376 <td class="snns top yellow">drops_vector ( ⬇*[?,?] ? ≡ ? )</td>
377 <td class="snnn top yellow">
380 <td class="snnn top yellow">
383 <td class="ssnn top yellow">
388 <td class="nnns top capitalize italic yellow">
391 <td class="nnns top italic yellow">
394 <td class="snns top yellow">drops ( ⬇*[?,?] ? ≡ ? )</td>
395 <td class="snnn top yellow">drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops</td>
396 <td class="snnn top yellow">
399 <td class="ssnn top yellow">
404 <td class="nnns top capitalize italic yellow">
407 <td class="snns top italic yellow">generic relocation for terms</td>
408 <td class="snns top yellow">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
409 <td class="snnn top yellow">lifts_lift_vector</td>
410 <td class="snnn top yellow">
413 <td class="ssnn top yellow">
418 <td class="nnns top capitalize italic yellow">
421 <td class="nnns top italic yellow">
424 <td class="snns top yellow">lifts ( ⬆*[?] ? ≡ ? )</td>
425 <td class="snnn top yellow">lifts_simple lifts_weight lifts_lifts</td>
426 <td class="snnn top yellow">
429 <td class="ssnn top yellow">
434 <td class="nnns top capitalize italic yellow">
437 <td class="snns top italic yellow">ranged equivalence for local environments</td>
438 <td class="snns top yellow">lreq ( ? ≡[?] ? )</td>
439 <td class="snnn top yellow">lreq_length lreq_lreq</td>
440 <td class="snnn top yellow">
443 <td class="ssnn top yellow">
448 <td class="nnns top capitalize italic yellow">
451 <td class="snns top italic yellow">generic entrywise extension of context-sensitive relations for terma</td>
452 <td class="snns top yellow">lexs ( ? ⦻*[?,?,?] ? )</td>
453 <td class="snnn top yellow">lexs_length lexs_lexs</td>
454 <td class="snnn top yellow">
457 <td class="ssnn top yellow">
462 <td class="snns top capitalize italic orange" />
463 <td class="snns top italic orange" />
464 <td class="snns top orange">
467 <td class="snnn top orange">
470 <td class="snnn top orange">
473 <td class="ssnn top orange">
478 <td class="snns top capitalize italic red">grammar</td>
479 <td class="snns top italic red">context-sensitive equivalences for terms</td>
480 <td class="snns top red">ceq</td>
481 <td class="snnn top red">ceq_ceq</td>
482 <td class="snnn top red">
485 <td class="ssnn top red">
490 <td class="nnns top capitalize italic red">
493 <td class="snns top italic red">same top term structure</td>
494 <td class="snns top red">tsts ( ? ≂ ? )</td>
495 <td class="snnn top red">tsts_tsts tsts_vector</td>
496 <td class="snnn top red">
499 <td class="ssnn top red">
504 <td class="nnns top capitalize italic red">
507 <td class="snns top italic red">closures</td>
508 <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
509 <td class="snnn top red">cl_restricted_weight ( ♯{?,?} )</td>
510 <td class="snnn top red">
513 <td class="ssnn top red">
518 <td class="nnns top capitalize italic red">
521 <td class="snns top italic red">internal syntax</td>
522 <td class="snns top red">genv</td>
523 <td class="snnn top red">
526 <td class="snnn top red">
529 <td class="ssnn top red">
534 <td class="nnns top capitalize italic red">
537 <td class="nnns top italic red">
540 <td class="snns top red">lenv</td>
541 <td class="snnn top red">lenv_weight ( ♯{?} )</td>
542 <td class="snnn top red">lenv_length ( |?| )</td>
543 <td class="ssnn top red">lenv_append ( ? @@ ? )</td>
546 <td class="nnns top capitalize italic red">
549 <td class="nnns top italic red">
552 <td class="snns top red">term</td>
553 <td class="snnn top red">term_weight ( ♯{?} )</td>
554 <td class="snnn top red">term_simple ( 𝐒⦃?⦄ )</td>
555 <td class="ssnn top red">term_vector ( Ⓐ?.? )</td>
558 <td class="nnns top capitalize italic red">
561 <td class="nnns top italic red">
564 <td class="snns top red">item</td>
565 <td class="snnn top red">
568 <td class="snnn top red">
571 <td class="ssnn top red">
576 <td class="nnss top capitalize italic red">
579 <td class="snss top italic red">external syntax</td>
580 <td class="snss top red">aarity</td>
581 <td class="snsn top red">
584 <td class="snsn top red">
587 <td class="sssn top red">
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620 <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sun, 27 Mar 2016 18:42:29 +0200</div>