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- <meta name="description" content="lambdadelta version 2" />
- <title>lambdadelta version 2</title>
+ <meta name="description" content="\lambda\delta version 2" />
+ <title>\lambda\delta version 2</title>
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- <div xmlns:ld="http://lambdadelta.info/" class="head2">System's Syntax and Behavior</div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">This is a summary of the "block structure"
- of the System's syntactic items and reductions.
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">
- <table cellpadding="4" cellspacing="0">
- <tbody>
- <tr>
- <td class="snns text grey">domain</td>
- <td class="snns plane grey">block</td>
- <td class="snns text grey">leader</td>
- <td class="snns text grey">applicator (with →θ)*</td>
- <td class="snns text grey">reduction</td>
- <td class="snns text grey">→ζ *</td>
- <td class="ssns text grey">reference *</td>
- </tr>
- <tr>
- <td class="snns text">{X | Γ ⊢ X : W}</td>
- <td class="snns plane wine">local typed abstraction *</td>
- <td class="snns text wine">Γ ⊢ +λW</td>
- <td class="snns text wine">ⓐV</td>
- <td class="snns text wine">→β</td>
- <td class="snns text wine">no</td>
- <td class="ssns text wine">#i</td>
- </tr>
- <tr>
- <td class="nnns text">
- <br />
- </td>
- <td class="snns plane magenta">local typed declaration **</td>
- <td class="snns text magenta">Γ ⊢ -λW</td>
- <td class="snns text magenta">ⓐV</td>
- <td class="snns text magenta">→β</td>
- <td class="snns text magenta">no</td>
- <td class="ssns text magenta">#i</td>
- </tr>
- <tr>
- <td class="nnns text">
- <br />
- </td>
- <td class="snns plane prune">global typed declaration ***</td>
- <td class="snns text prune">Γ ⊢ pλW</td>
- <td class="snns text prune">no</td>
- <td class="snns text prune">no</td>
- <td class="snns text prune">no</td>
- <td class="ssns text prune">$p</td>
- </tr>
- <tr>
- <td class="nnns text">
- <br />
- </td>
- <td class="snns plane blue">native type annotation *</td>
- <td class="snns text blue">Γ ⊢ ⓝW</td>
- <td class="snns text blue">no</td>
- <td class="snns text blue">no</td>
- <td class="snns text blue">yes</td>
- <td class="ssns text blue">no</td>
- </tr>
- <tr>
- <td class="snns text">{X | Γ ⊢ X = V}</td>
- <td class="snns plane sky">local abbreviation *</td>
- <td class="snns text sky">Γ ⊢ +δV</td>
- <td class="snns text sky">no</td>
- <td class="snns text sky">local →δ</td>
- <td class="snns text sky">yes</td>
- <td class="ssns text sky">#i</td>
- </tr>
- <tr>
- <td class="nnns text">
- <br />
- </td>
- <td class="snns plane cyan">local definition **</td>
- <td class="snns text cyan">Γ ⊢ -δV</td>
- <td class="snns text cyan">no</td>
- <td class="snns text cyan">local →δ</td>
- <td class="snns text cyan">no</td>
- <td class="ssns text cyan">#i</td>
- </tr>
- <tr>
- <td class="nnns text">
- <br />
- </td>
- <td class="snns plane water">global definition ***</td>
- <td class="snns text water">Γ ⊢ pδV</td>
- <td class="snns text water">no</td>
- <td class="snns text water">global →δ</td>
- <td class="snns text water">no</td>
- <td class="ssns text water">$p</td>
- </tr>
- <tr>
- <td class="snss text">no</td>
- <td class="snss plane green">sort ****</td>
- <td class="snss text green">Γ ⊢ ⋆k</td>
- <td class="snss text green">no</td>
- <td class="snss text green">no</td>
- <td class="snss text green">no</td>
- <td class="ssss text green">no</td>
- </tr>
- </tbody>
- </table>
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="text">* In terms only.
- ** In terms and local environments only.
- *** In global environments only.
- **** Sort level k in terms only.
- </div>
- <div xmlns:ld="http://lambdadelta.info/" class="head2">Summary of the Specification</div>
+
+ <div xmlns:ld="http://lambdadelta.info/" class="head2sn" id="">Summary of the Specification</div>
<div xmlns:ld="http://lambdadelta.info/" class="text">Here is a numerical acount of the specification's contents
and its timeline.
+ Nodes are counted according to the "intrinsinc complexity measure"
+ [F. Guidi: "Procedural Representation of CIC Proof Terms"
+ Journal of Automated Reasoning 44(1-2), Springer (February 2010),
+ pp. 53-78].
</div>
<div xmlns:ld="http://lambdadelta.info/" class="text">
<table cellpadding="4" cellspacing="0">
<tbody>
<tr>
- <td class="snns component grey">category</td>
- <td class="snns plane grey">objects</td>
- <td class="snnn number grey">
+ <td class="snns component gray">category</td>
+ <td class="snns plane gray">objects</td>
+ <td class="snnn number gray">
<br />
</td>
- <td class="snnn plane grey">
+ <td class="snnn plane gray">
<br />
</td>
- <td class="snnn number grey">
+ <td class="snnn number gray">
<br />
</td>
- <td class="snnn plane grey">
+ <td class="snnn plane gray">
<br />
</td>
- <td class="ssnn number grey">
+ <td class="ssnn number gray">
<br />
</td>
</tr>
<tr>
<td class="snns component cyan">sizes</td>
<td class="snns plane cyan">files</td>
- <td class="snnn number cyan">173 </td>
+ <td class="snnn number cyan">367</td>
<td class="snns plane cyan">characters</td>
- <td class="snnn number cyan">363812</td>
+ <td class="snnn number cyan">431873</td>
<td class="snns plane cyan">nodes</td>
- <td class="ssnn number cyan">1057233</td>
+ <td class="ssnn number cyan">1830977</td>
</tr>
<tr>
<td class="snns component green">propositions</td>
<td class="snns plane green">theorems</td>
- <td class="snnn number green">75</td>
+ <td class="snnn number green">128</td>
<td class="snns plane green">lemmas</td>
- <td class="snnn number green">750</td>
+ <td class="snnn number green">1302</td>
<td class="snns plane green">total</td>
- <td class="ssnn number green">825</td>
+ <td class="ssnn number green">1430</td>
</tr>
<tr>
<td class="snss component yellow">concepts</td>
<td class="snss plane yellow">declared</td>
- <td class="snsn number yellow">43</td>
+ <td class="snsn number yellow">55</td>
<td class="snss plane yellow">defined</td>
- <td class="snsn number yellow">68</td>
+ <td class="snsn number yellow">82</td>
<td class="snss plane yellow">total</td>
- <td class="sssn number yellow">111</td>
+ <td class="sssn number yellow">137</td>
</tr>
</tbody>
</table>
</ul>
<ul xmlns:ld="http://lambdadelta.info/">
<li>
- <span class="date">In progress.</span>
- Closure of extended context-sensitive computation
- for native validity.
+ <span class="date">2014 June 18.</span>
+ Preservation of stratified native validity
+ for context-sensitive computation on terms.
</li>
</ul>
<ul xmlns:ld="http://lambdadelta.info/">
<li>
- <span class="date">In progress.</span>
- Extended context-sensitive strong normalization
+ <span class="date">2014 June 9.</span>
+ "Big tree" strong normalization
+ for simply typed terms.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="date">2014 April 16.</span>
+ lazy equivalence on local environments
+ serves as irrelevant step in "big tree" computation on closures
+ (anniversary milestone).
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="date">2014 January 20.</span>
+ Parametrized slicing for local environments
+ comprises both versions of this operation
+ (one from basic_1, the other used in basic_2 till now).
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="date">2013 August 7.</span>
+ Passive support for global environments.
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="date">2013 July 27.</span>
+ Reaxiomatized β-reductum as in extended β-reduction
+ </li>
+ </ul>
+ <ul xmlns:ld="http://lambdadelta.info/">
+ <li>
+ <span class="date">2013 July 20.</span>
+ Context-sensitive extended strong normalization
for simply typed terms.
</li>
</ul>
<ul xmlns:ld="http://lambdadelta.info/">
<li>
<span class="date">2013 April 16.</span>
- Reaxiomatized substitution and reduction
+ Reaxiomatized substitution and reduction
commute with respect to subclosure
(anniversary milestone).
</li>
<li>
<span class="date">2013 March 16.</span>
Mutual recursive preservation of stratified native validity
- for hyper computation on closures.
+ for "big tree" computation on closures.
</li>
</ul>
<ul xmlns:ld="http://lambdadelta.info/">
<ul xmlns:ld="http://lambdadelta.info/">
<li>
<span class="date">2012 July 26.</span>
- Term binders polarized to control ζ reduction.
+ Term binders polarized to control ζ-reduction (not released).
</li>
</ul>
<ul xmlns:ld="http://lambdadelta.info/">
</li>
</ul>
- <div xmlns:ld="http://lambdadelta.info/" class="head2">Logical Structure of the Specification</div>
+ <div xmlns:ld="http://lambdadelta.info/" class="head2sn" id="">Logical Structure of the Specification</div>
<div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in planes and components
according to the following table.
- A notation file covering the whole specification is provided.
+ Notation files covering the whole specification are provided.
The notation for the relations or functions introduced in each file
is shown in parentheses (? are placeholders).
</div>
<table cellpadding="4" cellspacing="0">
<tbody>
<tr>
- <td class="snns component grey">component</td>
- <td class="snns plane grey">plane</td>
- <td class="snns file grey">files</td>
- <td class="snnn file grey">
+ <td class="snns component gray">component</td>
+ <td class="snns plane gray">plane</td>
+ <td class="snns file gray">files</td>
+ <td class="snnn file gray">
<br />
</td>
- <td class="snnn file grey">
+ <td class="snnn file gray">
<br />
</td>
- <td class="ssnn file grey">
+ <td class="ssnn file gray">
<br />
</td>
</tr>
<tr>
- <td class="snns component prune">dynamic typing</td>
- <td class="snns plane prune">"big tree" parallel computation</td>
- <td class="snns file prune">yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )</td>
- <td class="snnn file prune">yprs_yprs</td>
- <td class="snnn file prune">ygt ( ? ⊢ ⦃?,?⦄ >[g] ⦃?,?⦄ )</td>
- <td class="ssnn file prune">ygt_ygt</td>
+ <td class="snns component wine">examples</td>
+ <td class="snns plane wine">terms with special features</td>
+ <td class="snns file wine">ex_cpr_omega</td>
+ <td class="snnn file wine">
+ <br />
+ </td>
+ <td class="snnn file wine">
+ <br />
+ </td>
+ <td class="ssnn file wine">
+ <br />
+ </td>
</tr>
<tr>
- <td class="nnns component prune">
+ <td class="snns component magenta" />
+ <td class="snns plane magenta" />
+ <td class="snns file magenta" />
+ <td class="snnn file magenta">
+ <br />
+ </td>
+ <td class="snnn file magenta">
+ <br />
+ </td>
+ <td class="ssnn file magenta">
<br />
</td>
- <td class="snns plane prune">"big tree" parallel reduction</td>
- <td class="snns file prune">ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )</td>
- <td class="snnn file prune">ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )</td>
+ </tr>
+ <tr>
+ <td class="snns component prune">dynamic typing</td>
+ <td class="snns plane prune">local env. ref. for stratified native validity</td>
+ <td class="snns file prune">lsubsv ( ? ⊢ ? ⫃¡[?,?] ? )</td>
+ <td class="snnn file prune">lsubsv_lsuba lsubsv_lsubd lsubsv_lstas lsubsv_cpds lsubsv_cpcs lsubsv_snv</td>
<td class="snnn file prune">
<br />
</td>
<td class="nnns component prune">
<br />
</td>
- <td class="snns plane prune">local env. ref. for stratified native validity</td>
- <td class="snns file prune">lsubsv ( ? ⊢ ? ¡⊑[?] ? )</td>
- <td class="snnn file prune">lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv</td>
+ <td class="snns plane prune">stratified native validity</td>
+ <td class="snns file prune">hsnv ( ⦃?,?⦄ ⊢ ? ¡[?,?,?] )</td>
+ <td class="snnn file prune">hsnv_aaa</td>
<td class="snnn file prune">
<br />
</td>
<td class="nnns component prune">
<br />
</td>
- <td class="snns plane prune">stratified native validity</td>
- <td class="snns file prune">snv ( ⦃?,?⦄ ⊢ ? ¡[?] )</td>
- <td class="snnn file prune">snv_lift snv_lpss snv_aaa snv_ssta snv_sstas snv_ssta_lpr snv_lpr snv_cpcs</td>
+ <td class="nnns plane prune">
+ <br />
+ </td>
+ <td class="snns file prune">snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )</td>
+ <td class="snnn file prune">snv_lift snv_aaa snv_da_lpr snv_lstas snv_lstas_lpr snv_lpr snv_cpes snv_preserve</td>
<td class="snnn file prune">
<br />
</td>
</tr>
<tr>
<td class="snns component blue">equivalence</td>
- <td class="snns plane blue">local env. ref. for stratified static type assignment</td>
- <td class="snns file blue">lsubss ( ? •⊑[?] ? )</td>
- <td class="snnn file blue">lsubss_ldrop lsubss_ssta lsubss_cpcs</td>
+ <td class="snns plane blue">decomposed extended equivalence</td>
+ <td class="snns file blue">cpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?,?,?] ? )</td>
+ <td class="snnn file blue">cpes_aaa cpes_cpcs cpes_cpes</td>
<td class="snnn file blue">
<br />
</td>
<br />
</td>
<td class="snns plane blue">context-sensitive equivalence</td>
- <td class="snns file blue">cpcs ( ? ⊢ ? ⬌* ? )</td>
- <td class="snnn file blue">cpcs_lpss cpcs_aaa cpcs_cprs cpcs_cpcs</td>
+ <td class="snns file blue">cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )</td>
+ <td class="snnn file blue">cpcs_aaa cpcs_cprs cpcs_cpcs</td>
<td class="snnn file blue">
<br />
</td>
<tr>
<td class="snns component sky">conversion</td>
<td class="snns plane sky">context-sensitive conversion</td>
- <td class="snns file sky">cpc ( ? ⊢ ? ⬌ ? )</td>
+ <td class="snns file sky">cpc ( ⦃?,?⦄ ⊢ ? ⬌ ? )</td>
<td class="snnn file sky">cpc_cpc</td>
<td class="snnn file sky">
<br />
</tr>
<tr>
<td class="snns component cyan">computation</td>
- <td class="snns plane cyan">decomposed extended computation</td>
- <td class="snns file cyan">dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )</td>
- <td class="snnn file cyan">dxprs_lift dxprs_lpss dxprs_aaa dxprs_dxprs</td>
+ <td class="snns plane cyan">evaluation for context-sensitive extended reduction</td>
+ <td class="snns file cyan">cpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ )</td>
+ <td class="snnn file cyan">
+ <br />
+ </td>
+ <td class="snnn file cyan">
+ <br />
+ </td>
+ <td class="ssnn file cyan">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component cyan">
+ <br />
+ </td>
+ <td class="snns plane cyan">evaluation for context-sensitive reduction</td>
+ <td class="snns file cyan">cpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )</td>
+ <td class="snnn file cyan">cpre_cpre</td>
+ <td class="snnn file cyan">
+ <br />
+ </td>
+ <td class="ssnn file cyan">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component cyan">
+ <br />
+ </td>
+ <td class="snns plane cyan">strongly normalizing "big tree" computation</td>
+ <td class="snns file cyan">fsb ( ⦃?,?⦄ ⊢ ⦥[?,?] ? )</td>
+ <td class="snnn file cyan">fsb_alt ( ⦃?,?⦄ ⊢ ⦥⦥[?,?] ? )</td>
+ <td class="snnn file cyan">fsb_aaa fsb_csx</td>
+ <td class="ssnn file cyan">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component cyan">
+ <br />
+ </td>
+ <td class="snns plane cyan">strongly normalizing extended computation</td>
+ <td class="snns file cyan">lcosx ( ? ⊢ ~⬊*[?,?,?] ? )</td>
+ <td class="snnn file cyan">lcosx_cpx</td>
+ <td class="snnn file cyan">
+ <br />
+ </td>
+ <td class="ssnn file cyan">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component cyan">
+ <br />
+ </td>
+ <td class="nnns plane cyan">
+ <br />
+ </td>
+ <td class="snns file cyan">lsx ( ? ⊢ ⬊*[?,?,?,?] ? )</td>
+ <td class="snnn file cyan">lsx_alt ( ? ⊢ ⬊⬊*[?,?,?,?] ? )</td>
+ <td class="snnn file cyan">lsx_drop lsx_lpx lsx_lpxs llsx_csx</td>
+ <td class="ssnn file cyan">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component cyan">
+ <br />
+ </td>
+ <td class="nnns plane cyan">
+ <br />
+ </td>
+ <td class="snns file cyan">csx_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )</td>
+ <td class="snnn file cyan">csx_tstc_vector csx_aaa</td>
+ <td class="snnn file cyan">
+ <br />
+ </td>
+ <td class="ssnn file cyan">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component cyan">
+ <br />
+ </td>
+ <td class="nnns plane cyan">
+ <br />
+ </td>
+ <td class="snns file cyan">csx ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )</td>
+ <td class="snnn file cyan">csx_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )</td>
+ <td class="snnn file cyan">csx_lift csx_lleq csx_lpx csx_lpxs csx_fpbs</td>
+ <td class="ssnn file cyan">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component cyan">
+ <br />
+ </td>
+ <td class="snns plane cyan">"big tree" parallel computation</td>
+ <td class="snns file cyan">fpbg ( ⦃?,?,?⦄ >≡[?,?] ⦃?,?,?⦄ )</td>
+ <td class="snnn file cyan">fpbg_lift fpbg_fleq fpbg_fpbg</td>
+ <td class="snnn file cyan">
+ <br />
+ </td>
+ <td class="ssnn file cyan">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component cyan">
+ <br />
+ </td>
+ <td class="nnns plane cyan">
+ <br />
+ </td>
+ <td class="snns file cyan">fpbc ( ⦃?,?,?⦄ ≻≡[?,?] ⦃?,?,?⦄ )</td>
+ <td class="snnn file cyan">fpbc_fleq fpbc_fpbs</td>
<td class="snnn file cyan">
<br />
</td>
<td class="nnns component cyan">
<br />
</td>
- <td class="snns plane cyan">weakly normalizing computation</td>
- <td class="snns file cyan">cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )</td>
- <td class="snnn file cyan">cpe_cpe</td>
+ <td class="nnns plane cyan">
+ <br />
+ </td>
+ <td class="snns file cyan">fpbu ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )</td>
+ <td class="snnn file cyan">fpbu_lift fpbu_lleq</td>
+ <td class="snnn file cyan">fpbu_fleq</td>
+ <td class="ssnn file cyan">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component cyan">
+ <br />
+ </td>
+ <td class="nnns plane cyan">
+ <br />
+ </td>
+ <td class="snns file cyan">fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )</td>
+ <td class="snnn file cyan">fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )</td>
+ <td class="snnn file cyan">fpbs_lift fpbs_fleq fpbs_aaa fpbs_fpbs fpbs_ext</td>
+ <td class="ssnn file cyan">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component cyan">
+ <br />
+ </td>
+ <td class="snns plane cyan">decomposed extended computation</td>
+ <td class="snns file cyan">cpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?,?] ? )</td>
+ <td class="snnn file cyan">cpds_lift cpds_aaa cpds_cpds</td>
<td class="snnn file cyan">
<br />
</td>
<td class="nnns component cyan">
<br />
</td>
- <td class="snns plane cyan">strongly normalizing computation</td>
- <td class="snns file cyan">csn_vector ( ? ⊢ ⬊* ? )</td>
- <td class="snnn file cyan">csn_tstc_vector csn_aaa</td>
+ <td class="snns plane cyan">context-sensitive extended computation</td>
+ <td class="snns file cyan">lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )</td>
+ <td class="snnn file cyan">lpxs_drop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs</td>
<td class="snnn file cyan">
<br />
</td>
<td class="nnns plane cyan">
<br />
</td>
- <td class="snns file cyan">csn ( ? ⊢ ⬊* ? )</td>
- <td class="snnn file cyan">csn_alt ( ? ⊢ ⬊⬊* ? )</td>
- <td class="snnn file cyan">csn_lift csn_lpr</td>
+ <td class="snns file cyan">cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )</td>
+ <td class="snnn file cyan">cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs</td>
+ <td class="snnn file cyan">
+ <br />
+ </td>
<td class="ssnn file cyan">
<br />
</td>
<br />
</td>
<td class="snns plane cyan">context-sensitive computation</td>
- <td class="snns file cyan">lprs ( ? ⊢ ➡* ? )</td>
- <td class="snnn file cyan">lprs_alt ( ? ⊢ ➡➡* ? )</td>
- <td class="snnn file cyan">lprs_ldrop lprs_lpss lprs_aaa lprs_cprs lprs_lprs</td>
+ <td class="snns file cyan">lprs ( ⦃?,?⦄ ⊢ ➡* ? )</td>
+ <td class="snnn file cyan">lprs_drop lprs_cprs lprs_lprs</td>
+ <td class="snnn file cyan">
+ <br />
+ </td>
<td class="ssnn file cyan">
<br />
</td>
<td class="nnns plane cyan">
<br />
</td>
- <td class="snns file cyan">cprs ( ? ⊢ ? ➡* ?)</td>
- <td class="snnn file cyan">cprs_tstc cprs_tstc_vector cprs_lift cprs_lpss cprs_aaa cprs_cprs</td>
+ <td class="snns file cyan">cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)</td>
+ <td class="snnn file cyan">cprs_lift cprs_cprs</td>
<td class="snnn file cyan">
<br />
</td>
<br />
</td>
<td class="snns plane cyan">local env. ref. for abstract candidates of reducibility</td>
- <td class="snns file cyan">lsubc ( ? â\8a\91[?] ? )</td>
- <td class="snnn file cyan">lsubc_ldrop lsubc_ldrops lsubc_lsuba</td>
+ <td class="snns file cyan">lsubc ( ? â\8a¢ ? â«\83[?] ? )</td>
+ <td class="snnn file cyan">lsubc_drop lsubc_drops lsubc_lsuba</td>
<td class="snnn file cyan">
<br />
</td>
</td>
<td class="snns plane cyan">support for abstract computation properties</td>
<td class="snns file cyan">acp</td>
- <td class="snnn file cyan">acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )</td>
+ <td class="snnn file cyan">acp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
<td class="snnn file cyan">acp_aaa</td>
<td class="ssnn file cyan">
<br />
</tr>
<tr>
<td class="snns component water">reduction</td>
- <td class="snns plane water">context-sensitive extended reduction</td>
- <td class="snns file water">lpx ( ⦃?,?⦄ ⊢ ➡[?] ? )</td>
- <td class="snnn file water">lpx_ldrop lpx_aaa</td>
+ <td class="snns plane water">"big tree" parallel reduction</td>
+ <td class="snns file water">fpb ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )</td>
+ <td class="snnn file water">fpb_lift fpb_aaa</td>
+ <td class="snnn file water">
+ <br />
+ </td>
+ <td class="ssnn file water">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component water">
+ <br />
+ </td>
+ <td class="snns plane water">normal forms for context-sensitive extended reduction</td>
+ <td class="snns file water">cnx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐍⦃?⦄ )</td>
+ <td class="snnn file water">cnx_lift cnx_crx cnx_cix</td>
<td class="snnn file water">
<br />
</td>
<br />
</td>
</tr>
+ <tr>
+ <td class="nnns component water">
+ <br />
+ </td>
+ <td class="snns plane water">context-sensitive extended reduction</td>
+ <td class="snns file water">lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
+ <td class="snnn file water">lpx_drop lpx_frees</td>
+ <td class="snnn file water">lpx_lleq lpx_aaa</td>
+ <td class="ssnn file water">
+ <br />
+ </td>
+ </tr>
<tr>
<td class="nnns component water">
<br />
<td class="nnns plane water">
<br />
</td>
- <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
- <td class="snnn file water">cpx_lift</td>
+ <td class="snns file water">cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
+ <td class="snnn file water">cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix</td>
+ <td class="snnn file water">
+ <br />
+ </td>
+ <td class="ssnn file water">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component water">
+ <br />
+ </td>
+ <td class="snns plane water">irreducible forms for context-sensitive extended reduction</td>
+ <td class="snns file water">cix ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐈⦃?⦄ )</td>
+ <td class="snnn file water">cix_lift</td>
+ <td class="snnn file water">
+ <br />
+ </td>
+ <td class="ssnn file water">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component water">
+ <br />
+ </td>
+ <td class="snns plane water">reducible forms for context-sensitive extended reduction</td>
+ <td class="snns file water">crx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐑⦃?⦄ )</td>
+ <td class="snnn file water">crx_lift</td>
<td class="snnn file water">
<br />
</td>
<td class="nnns component water">
<br />
</td>
- <td class="snns plane water">context-sensitive normal forms</td>
- <td class="snns file water">cnf ( ? ⊢ 𝐍⦃?⦄ )</td>
- <td class="snnn file water">cnf_liftt cnf_crf cnf_cif</td>
+ <td class="snns plane water">normal forms for context-sensitive reduction</td>
+ <td class="snns file water">cnr ( ⦃?,?⦄ ⊢ ➡ 𝐍⦃?⦄ )</td>
+ <td class="snnn file water">cnr_lift cnr_crr cnr_cir</td>
<td class="snnn file water">
<br />
</td>
<br />
</td>
<td class="snns plane water">context-sensitive reduction</td>
- <td class="snns file water">lpr ( ? ⊢ ➡ ? )</td>
- <td class="snnn file water">lpr_ldrop lpr_lpss lpr_lpr</td>
+ <td class="snns file water">lpr ( ⦃?,?⦄ ⊢ ➡ ? )</td>
+ <td class="snnn file water">lpr_drop lpr_lpr</td>
<td class="snnn file water">
<br />
</td>
<td class="nnns plane water">
<br />
</td>
- <td class="snns file water">cpr ( ? ⊢ ? ➡ ? )</td>
- <td class="snnn file water">cpr_lift cpr_cif</td>
+ <td class="snns file water">cpr ( ⦃?,?⦄ ⊢ ? ➡ ? )</td>
+ <td class="snnn file water">cpr_lift cpr_llpx_sn cpr_cir</td>
+ <td class="snnn file water">
+ <br />
+ </td>
+ <td class="ssnn file water">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component water">
+ <br />
+ </td>
+ <td class="snns plane water">irreducible forms for context-sensitive reduction</td>
+ <td class="snns file water">cir ( ⦃?,?⦄ ⊢ ➡ 𝐈⦃?⦄ )</td>
+ <td class="snnn file water">cir_lift</td>
<td class="snnn file water">
<br />
</td>
<td class="nnns component water">
<br />
</td>
- <td class="snns plane water">context-sensitive reducible forms</td>
- <td class="snns file water">crf ( ? ⊢ 𝐑⦃?⦄ )</td>
- <td class="snnn file water">crf_append</td>
- <td class="snnn file water">cif ( ? ⊢ 𝐈⦃?⦄ )</td>
- <td class="ssnn file water">cif_append</td>
+ <td class="snns plane water">reducible forms for context-sensitive reduction</td>
+ <td class="snns file water">crr ( ⦃?,?⦄ ⊢ ➡ 𝐑⦃?⦄ )</td>
+ <td class="snnn file water">crr_lift</td>
+ <td class="snnn file water">
+ <br />
+ </td>
+ <td class="ssnn file water">
+ <br />
+ </td>
</tr>
<tr>
<td class="snns component green">unfold</td>
- <td class="snns plane green">restricted parallel computation</td>
- <td class="snns file green">lpqs ( ? ⊢ ➤* ? )</td>
- <td class="snnn file green">lpqs_ldrop lpqs_cpqs lpqs_lpqs</td>
+ <td class="snns plane green">unfold</td>
+ <td class="snns file green">unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )</td>
+ <td class="snnn file green">
+ <br />
+ </td>
<td class="snnn file green">
<br />
</td>
<td class="nnns component green">
<br />
</td>
- <td class="nnns plane green">
+ <td class="snns plane green">iterated static type assignment</td>
+ <td class="snns file green">lstas ( ⦃?,?⦄ ⊢ ? •*[?,?] ? )</td>
+ <td class="snnn file green">lstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?] ? )</td>
+ <td class="snnn file green">lstas_lift lstas_aaa lstas_da lstas_lstas</td>
+ <td class="ssnn file green">
<br />
</td>
- <td class="snns file green">cpqs ( ? ⊢ ? ➤* ? )</td>
- <td class="snnn file green">cpqs_lift</td>
- <td class="snnn file green">
+ </tr>
+ <tr>
+ <td class="snns component grass">static typing</td>
+ <td class="snns plane grass">local env. ref. for degree assignment</td>
+ <td class="snns file grass">lsubd ( ? ⊢ ? ⫃▪[?,?] ? )</td>
+ <td class="snnn file grass">lsubd_da lsubd_lsubd</td>
+ <td class="snnn file grass">
<br />
</td>
- <td class="ssnn file green">
+ <td class="ssnn file grass">
<br />
</td>
</tr>
<tr>
- <td class="nnns component green">
- <br />
- </td>
- <td class="snns plane green">unfold</td>
- <td class="snns file green">unfold ( ? ⊢ ? ⧫* ? )</td>
- <td class="snnn file green">
+ <td class="nnns component grass">
<br />
</td>
- <td class="snnn file green">
+ <td class="snns plane grass">degree assignment</td>
+ <td class="snns file grass">da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )</td>
+ <td class="snnn file grass">da_lift da_aaa da_sta da_da</td>
+ <td class="snnn file grass">
<br />
</td>
- <td class="ssnn file green">
+ <td class="ssnn file grass">
<br />
</td>
</tr>
<tr>
- <td class="nnns component green">
+ <td class="nnns component grass">
<br />
</td>
- <td class="snns plane green">iterated stratified static type assignment</td>
- <td class="snns file green">sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )</td>
- <td class="snnn file green">sstas_lift sstas_lpss sstas_aaa sstas_sstas</td>
- <td class="snnn file green">
+ <td class="snns plane grass">static type assignment</td>
+ <td class="snns file grass">sta ( ⦃?,?⦄ ⊢ ? •[?] ? )</td>
+ <td class="snnn file grass">sta_lift sta_lpx_sn sta_aaa sta_sta</td>
+ <td class="snnn file grass">
<br />
</td>
- <td class="ssnn file green">
+ <td class="ssnn file grass">
<br />
</td>
</tr>
<tr>
- <td class="snns component grass">static typing</td>
- <td class="snns plane grass">stratified static type assignment</td>
- <td class="snns file grass">ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )</td>
- <td class="snnn file grass">ssta_lift ssta_lpss ssta_aaa ssta_ssta</td>
+ <td class="nnns component grass">
+ <br />
+ </td>
+ <td class="snns plane grass">parameters</td>
+ <td class="snns file grass">sh</td>
+ <td class="snnn file grass">sd</td>
<td class="snnn file grass">
<br />
</td>
<br />
</td>
<td class="snns plane grass">local env. ref. for atomic arity assignment</td>
- <td class="snns file grass">lsuba ( ? â\81\9dâ\8a\91 ? )</td>
- <td class="snnn file grass">lsuba_ldrop lsuba_aaa lsuba_lsuba</td>
+ <td class="snns file grass">lsuba ( ? â\8a¢ ? â«\83â\81\9d ? )</td>
+ <td class="snnn file grass">lsuba_aaa lsuba_lsuba</td>
<td class="snnn file grass">
<br />
</td>
<br />
</td>
<td class="snns plane grass">atomic arity assignment</td>
- <td class="snns file grass">aaa ( ? ⊢ ? ⁝ ? )</td>
- <td class="snnn file grass">aaa_lift aaa_lifts aaa_lpss aaa_aaa</td>
+ <td class="snns file grass">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
+ <td class="snnn file grass">aaa_lift aaa_lifts aaa_fqus aaa_lleq aaa_aaa</td>
<td class="snnn file grass">
<br />
</td>
<td class="nnns component grass">
<br />
</td>
- <td class="snns plane grass">parameters</td>
- <td class="snns file grass">sh</td>
- <td class="snnn file grass">sd</td>
+ <td class="snns plane grass">restricted local env. ref.</td>
+ <td class="snns file grass">lsubr ( ? ⫃ ? )</td>
+ <td class="snnn file grass">lsubr_lsubr</td>
<td class="snnn file grass">
<br />
</td>
</td>
</tr>
<tr>
- <td class="snns component yellow">substitution</td>
- <td class="snns plane yellow">parallel substitution</td>
- <td class="snns file yellow">lpss ( ? ⊢ ▶* ? )</td>
- <td class="snnn file yellow">lpss_ldrop lpss_cpss lpss_lpss</td>
+ <td class="snns component yellow">multiple substitution</td>
+ <td class="snns plane yellow">lazy equivalence</td>
+ <td class="snns file yellow">fleq ( ⦃?,?,?⦄ ≡[?] ⦃?,?,?⦄ )</td>
+ <td class="snnn file yellow">fleq_fleq</td>
<td class="snnn file yellow">
<br />
</td>
<td class="nnns plane yellow">
<br />
</td>
- <td class="snns file yellow">cpss ( ? ⊢ ? ▶* ? )</td>
- <td class="snnn file yellow">cpss_lift</td>
+ <td class="snns file yellow">lleq ( ? ≡[?,?] ? )</td>
+ <td class="snnn file yellow">lleq_alt lleq_alt_rec lleq_leq lleq_drop lleq_fqus lleq_llor lleq_lleq</td>
+ <td class="snnn file yellow">
+ <br />
+ </td>
+ <td class="ssnn file yellow">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component yellow">
+ <br />
+ </td>
+ <td class="snns plane yellow">lazy pointwise extension of a relation</td>
+ <td class="snns file yellow">llpx_sn</td>
+ <td class="snnn file yellow">llpx_sn_alt llpx_sn_alt_rec llpx_sn_tc llpx_sn_leq llpx_sn_drop llpx_sn_lpx_sn llpx_sn_frees llpx_sn_llor</td>
+ <td class="snnn file yellow">
+ <br />
+ </td>
+ <td class="ssnn file yellow">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component yellow">
+ <br />
+ </td>
+ <td class="snns plane yellow">pointwise union for local environments</td>
+ <td class="snns file yellow">llor ( ? ⩖[?,?] ? ≡ ? )</td>
+ <td class="snnn file yellow">llor_alt llor_drop</td>
<td class="snnn file yellow">
<br />
</td>
<td class="nnns component yellow">
<br />
</td>
- <td class="snns plane yellow">local env. ref. for substitution</td>
- <td class="snns file yellow">lsubr ( ? ⊑ ? )</td>
- <td class="snnn file yellow">lsubr_lsubr</td>
+ <td class="snns plane yellow">context-sensitive exclusion from free variables</td>
+ <td class="snns file yellow">frees ( ? ⊢ ? ϵ 𝐅*[?]⦃?⦄ )</td>
+ <td class="snnn file yellow">frees_append frees_leq frees_lift</td>
<td class="snnn file yellow">
<br />
</td>
<br />
</td>
</tr>
+ <tr>
+ <td class="nnns component yellow">
+ <br />
+ </td>
+ <td class="snns plane yellow">contxt-sensitive extended multiple substitution</td>
+ <td class="snns file yellow">cpys ( ⦃?,?⦄ ⊢ ? ▶*[?,?] ? )</td>
+ <td class="snnn file yellow">cpys_alt ( ⦃?,?⦄ ⊢ ? ▶▶*[?,?] ? )</td>
+ <td class="snnn file yellow">cpys_lift cpys_cpys</td>
+ <td class="ssnn file yellow">
+ <br />
+ </td>
+ </tr>
<tr>
<td class="nnns component yellow">
<br />
</td>
<td class="snns plane yellow">iterated structural successor for closures</td>
- <td class="snns file yellow">fsups ( ⦃?,?⦄ ⊃* ⦃?,?⦄ )</td>
- <td class="snnn file yellow">fsups_fsups</td>
+ <td class="snns file yellow">fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
+ <td class="snnn file yellow">fqus_alt fqus_fqus</td>
<td class="snnn file yellow">
<br />
</td>
<td class="nnns plane yellow">
<br />
</td>
- <td class="snns file yellow">fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )</td>
- <td class="snnn file yellow">fsupp_fsupp</td>
+ <td class="snns file yellow">fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
+ <td class="snnn file yellow">fqup_fqup</td>
<td class="snnn file yellow">
<br />
</td>
<td class="nnns component yellow">
<br />
</td>
- <td class="snns plane yellow">generic local env. slicing</td>
- <td class="snns file yellow">ldrops ( ⇩*[?] ? ≡ ? )</td>
- <td class="snnn file yellow">ldrops_ldrop ldrops_ldrops</td>
+ <td class="snns plane yellow">iterated local env. slicing</td>
+ <td class="snns file yellow">drops ( ⇩*[?,?] ? ≡ ? )</td>
+ <td class="snnn file yellow">drops_drop drops_drops</td>
<td class="snnn file yellow">
<br />
</td>
<td class="ssnn file yellow">gr2_gr2</td>
</tr>
<tr>
- <td class="snns component orange">relocation</td>
+ <td class="snns component orange">substitution</td>
<td class="snns plane orange">structural successor for closures</td>
- <td class="snns file orange">fsup ( ⦃?,?⦄ ⊃ ⦃?,?⦄ )</td>
- <td class="snnn file orange">fsupq ( ⦃?,?⦄ ⊃⸮ ⦃?,?⦄ )</td>
+ <td class="snns file orange">fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
+ <td class="snnn file orange">fquq_alt ( ⦃?,?,?⦄ ⊐⊐⸮ ⦃?,?,?⦄ )</td>
+ <td class="snnn file orange">
+ <br />
+ </td>
+ <td class="ssnn file orange">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component orange">
+ <br />
+ </td>
+ <td class="nnns plane orange">
+ <br />
+ </td>
+ <td class="snns file orange">fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
+ <td class="snnn file orange">
+ <br />
+ </td>
<td class="snnn file orange">
<br />
</td>
<br />
</td>
<td class="snns plane orange">global env. slicing</td>
- <td class="snns file orange">gdrop ( ⇩[?] ? ≡ ? )</td>
- <td class="snnn file orange">gdrop_gdrop</td>
+ <td class="snns file orange">gget ( ⇩[?] ? ≡ ? )</td>
+ <td class="snnn file orange">gget_gget</td>
+ <td class="snnn file orange">
+ <br />
+ </td>
+ <td class="ssnn file orange">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component orange">
+ <br />
+ </td>
+ <td class="snns plane orange">contxt-sensitive extended ordinary substitution</td>
+ <td class="snns file orange">cpy ( ⦃?,?⦄ ⊢ ? ▶[?,?] ? )</td>
+ <td class="snnn file orange">cpy_lift cpy_nlift cpy_cpy</td>
+ <td class="snnn file orange">
+ <br />
+ </td>
+ <td class="ssnn file orange">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component orange">
+ <br />
+ </td>
+ <td class="snns plane orange">local env. ref. for extended substitution</td>
+ <td class="snns file orange">lsuby ( ? ⊆[?,?] ? )</td>
+ <td class="snnn file orange">lsuby_lsuby</td>
+ <td class="snnn file orange">
+ <br />
+ </td>
+ <td class="ssnn file orange">
+ <br />
+ </td>
+ </tr>
+ <tr>
+ <td class="nnns component orange">
+ <br />
+ </td>
+ <td class="snns plane orange">pointwise extension of a relation</td>
+ <td class="snns file orange">lpx_sn</td>
+ <td class="snnn file orange">lpx_sn_alt lpx_sn_tc lpx_sn_drop lpx_sn_lpx_sn</td>
<td class="snnn file orange">
<br />
</td>
<br />
</td>
<td class="snns plane orange">basic local env. slicing</td>
- <td class="snns file orange">ldrop ( ⇩[?,?] ? ≡ ? )</td>
- <td class="snnn file orange">ldrop_append ldrop_lpx_sn ldrop_ldrop</td>
+ <td class="snns file orange">drop ( ⇩[?,?,?] ? ≡ ? )</td>
+ <td class="snnn file orange">drop_append drop_leq drop_drop</td>
<td class="snnn file orange">
<br />
</td>
<br />
</td>
<td class="snns file orange">lift ( ⇧[?,?] ? ≡ ? )</td>
- <td class="snnn file orange">lift_lift</td>
+ <td class="snnn file orange">lift_neq lift_lift</td>
<td class="snnn file orange">
<br />
</td>
</tr>
<tr>
<td class="snns component red">grammar</td>
- <td class="snns plane red">pointwise extension of a relation</td>
- <td class="snns file red">lpx_sn</td>
- <td class="snnn file red">lpx_sn_tc lpx_sn_lpx_sn</td>
+ <td class="snns plane red">equivalence for local environments</td>
+ <td class="snns file red">leq ( ? ⩬[?,?] ? )</td>
+ <td class="snnn file red">leq_leq</td>
<td class="snnn file red">
<br />
</td>
<br />
</td>
<td class="snns plane red">same top term constructor</td>
- <td class="snns file red">tstc ( ? â\89\83 ? )</td>
+ <td class="snns file red">tstc ( ? â\89\82 ? )</td>
<td class="snnn file red">tstc_tstc tstc_vector</td>
<td class="snnn file red">
<br />
<br />
</td>
<td class="snns plane red">closures</td>
- <td class="snns file red">cl_shift ( ? @@ ? )</td>
- <td class="snnn file red">cl_weight ( ♯{?,?} )</td>
+ <td class="snns file red">cl_weight ( ♯{?,?,?} )</td>
+ <td class="snnn file red">cl_restricted_weight ( ♯{?,?} )</td>
<td class="snnn file red">
<br />
</td>
</table>
</div>
- <div xmlns:ld="http://lambdadelta.info/" class="head2">Physical Structure of the Specification</div>
+ <div xmlns:ld="http://lambdadelta.info/" class="head2sn" id="">Physical Structure of the Specification</div>
<div xmlns:ld="http://lambdadelta.info/" class="text">The source files are grouped in directories,
one for each component.
</div>
<div xmlns:ld="http://lambdadelta.info/" class="spacer">
<br />
</div>
- <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sat, 08 Jun 2013 22:22:33 +0200</div>
+ <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Tue, 05 Aug 2014 23:07:40 +0200</div>
</body>
</html>