System's Syntax and Behavior
+ This is a summary of the "block structure"
+ of the System's syntactic items and reductions.
+
+ domain | block | leader | applicator (with âθ)* | reduction | âζ * | reference * |
{X | Π⢠X : W} | typed abstraction ** | Π⢠λW | âV | âβ | no | #i |
typed declaration *** | Π⢠pλW | no | no | no | $p | |
native type annotation * | Π⢠â£W | no | no | yes | no | |
{X | Π⢠X = V} | local abbreviation ** | Π⢠δV | no | local âδ | yes | #i |
global abbreviation *** | Π⢠pδV | no | global âδ | no | $p | |
no | sort **** | Π⢠âk | no | no | no | no |
* In terms only.
+ ** In terms and local environments only.
+ *** In global environments only.
+ **** Sort level k in terms only.
- category | objects | |||
propositions | theorems | 39 | lemmas | 333 |
concepts | declared | 33 | defined | 46 |
Logical structure of the contribution
+ Summary of the Specification
+ Here is a numerical acount of the specification's contents
+ and its timeline.
+
+ category | objects | |||||
propositions | theorems | 43 | lemmas | 409 | total | 452 |
concepts | declared | 32 | defined | 35 | total | 67 |
- In progress. + Context-sensitive strong normalization of simply typed terms. +
- 2012 January 27. + Support for abstract candidates of reducibility closed. +
- 2011 September 21. + Confluence of context-sensitive parallel reduction closed. +
- 2011 September 6. + Confluence of context-free parallel reduction closed. +
- 2011 April 17. + Specification started. +
Logical Structure of the Specification
The source files are grouped in planes and components
- according to the following table.
- The notation for the relations or functions introduced in each file
- is shown in parentheses.
+ according to the following table.
+ A notation file covering the whole specification is provided.
+ The notation for the relations or functions introduced in each file
+ is shown in parentheses.
- component | plane | files | |||
functional | reduction and type machine | rtm | rtm_step ( ? ⨠? ) | ||
unfold | lift ( â[?,?] ? ) | subst ( [?â?] ? ) | |||
examples | |||||
native typing | nty | ||||
conversion | context-sensitive conversion | cpcs ( ? ⢠? â¬* ? ) | |||
computation | strongly normalizing computation | csn ( â¬* ? ) | csn_cr | csn_aaa | |
context-sensitive computation | cprs (? ⢠? â¡* ?) | ||||
local env. ref. for abstract candidates of reducibility | lsubc ( ? [?] â ? ) | lsubc_ldrop | lsubc_ldrops | lsubc_lsuba | |
support for abstract computation properties | acp | acp_cr ( â¦?,?⦠ϵ ã?ã ) | acp_aaa | ||
reducibility | context-sensitive reduction | lcpr ( ? ⢠⡠? ) | |||
cpr ( ? ⢠? ⡠? ) | cpr_lift | cpr_ltpr | cpr_cpr | ||
context-free normal forms | twhnf ( ððð[?] ) | tnf ( ð[?] ) | tnf_tif | ||
context-free reduction | ltpr ( ? â¡ ? ) | ltpr_ldrop | |||
tpr ( ? â¡ ? ) | tpr_lift | tpr_tpss | tpr_tpr | ||
context-free reducible forms | trf ( ð[?] ) | tif ( ð[?] ) | |||
static typing | static type assignment | sty | sty_lift | sty_sty | |
local env. ref. for atomic arity assignment | lsuba ( ? ։ ? ) | lsuba_ldrop | lsuba_aaa | lsuba_lsuba | |
atomic arity assignment | aaa ( ? ⢠? ÷ ? ) | aaa_lift | aaa_lifts | aaa_aaa | |
parameters | sh | ||||
unfold | term inverse relocation | delift ( ? ⢠? [?,?] ⡠? ) | delift_lift | ||
partial unfold | ltpss ( ? [?,?] â¶* ? ) | ltpss_ldrop | ltpss_tps | ltpss_ltpss | |
tpss ( ? ⢠? [?,?] â¶* ? ) | tpss_lift | tpss_tpss | tpss_ltps | ||
generic local env. slicing | ldrops ( â©*[?] ? â¡ ? ) | ldrops_ldrop | ldrops_ldrops | ||
generic term relocation | lifts_vector ( â§*[?] ? â¡ ? ) | lifts_lift_vector | |||
lifts ( â§*[?] ? â¡ ? ) | lifts_lift | lifts_lifts | |||
support for generic relocation | gr2 ( @ [ ? ] ? â¡ ? ) | gr2_plus ( ? + ? ) | gr2_minus ( ? â ? â¡ ? ) | gr2_gr2 | |
substitution | parallel substitution | ltps ( ? [?,?] ⶠ? ) | ltps_ldrop | ltps_tps | ltps_ltps |
tps ( ? ⢠? [?,?] ⶠ? ) | tps_lift | tps_tps | |||
global env. slicing | gdrop ( â©[?] ? â¡ ? ) | gdrop_gdrop | |||
basic local env. slicing | ldrop ( â©[?,?] ? â¡ ? ) | ldrop_ldrop | |||
basic term relocation | lift_vector ( â§[?,?] ? â¡ ? ) | lift_lift_vector | |||
lift ( â§[?,?] ? â¡ ? ) | lift_lift | ||||
grammar | local env. ref. for substitution | lsubs ( ? [?,?] â¼ ? ) | lsubs_lsubs | ||
term hom. | thom | thom_thom | |||
closures | cl_shift ( ? @ ? ) | cl_weight ( #[?,?] ) | |||
internal syntax | genv | ||||
lenv | lenv_weight ( #[?] ) | lenv_length ( |?| ) | |||
term | term_weight ( #[?] ) | term_simple ( ð[?] ) | term_vector | ||
item | |||||
external syntax | aarity |
Physical structure of the contribution
- The source files are grouped in directories, one for each
- component.
+
+
+ ![lambda_delta rainbow rule [Spacer]](http://lambda-delta.info/images/rainbow.png)
![lambda_delta rainbow rule [Spacer]](http://lambda-delta.info/images/rainbow.png)
component | plane | files | ||||
examples | ||||||
native typing | nty | |||||
conversion | context-sensitive conversion | cpcs ( ? ⢠? â¬* ? ) | ||||
computation | strongly normalizing computation | csn_vector ( â¬* ? ) | csn_lcpr_vector | csn_aaa | ||
csn ( â¬* ? ) | csn_lift | csn_cpr | csn_cprs ( â¬** ? ) | csn_lcpr | ||
context-sensitive computation | cprs (? ⢠? â¡* ?) | cprs_lcpr | cprs_cprs | cprs_tstc | cprs_tstc_vector | |
local env. ref. for abstract candidates of reducibility | lsubc ( ? [?] â ? ) | lsubc_ldrop | lsubc_ldrops | lsubc_lsuba | ||
support for abstract computation properties | acp | acp_cr ( â¦?,?⦠ϵ ã?ã ) | acp_aaa | |||
reducibility | context-sensitive normal forms | cnf ( ? ⢠ð[?] ) | cnf_lift | |||
context-sensitive reduction | lcpr ( ? ⢠⡠? ) | lcpr_cpr | ||||
cpr ( ? ⢠? ⡠? ) | cpr_lift | cpr_ltpss | cpr_ltpr | cpr_cpr | ||
context-free normal forms | twhnf ( ððð[?] ) | tnf ( ð[?] ) | tnf_tif | |||
context-free reduction | ltpr ( ? â¡ ? ) | ltpr_ldrop | ltpr_tps | |||
tpr ( ? â¡ ? ) | tpr_lift | tpr_tpss | tpr_tpr | |||
context-free reducible forms | trf ( ð[?] ) | tif ( ð[?] ) | ||||
static typing | static type assignment | sty | sty_lift | sty_sty | ||
local env. ref. for atomic arity assignment | lsuba ( ? ։ ? ) | lsuba_ldrop | lsuba_aaa | lsuba_lsuba | ||
atomic arity assignment | aaa ( ? ⢠? ÷ ? ) | aaa_lift | aaa_lifts | aaa_aaa | ||
parameters | sh | |||||
unfold | term inverse relocation | delift ( ? ⢠? [?,?] ⡠? ) | delift_lift | |||
partial unfold | ltpss ( ? [?,?] â¶* ? ) | ltpss_ldrop | ltpss_tps | ltpss_ltpss | ||
tpss ( ? ⢠? [?,?] â¶* ? ) | tpss_lift | tpss_tpss | tpss_ltps | |||
generic local env. slicing | ldrops ( â©*[?] ? â¡ ? ) | ldrops_ldrop | ldrops_ldrops | |||
generic term relocation | lifts_vector ( â§*[?] ? â¡ ? ) | lifts_lift_vector | ||||
lifts ( â§*[?] ? â¡ ? ) | lifts_lift | lifts_lifts | ||||
support for generic relocation | gr2 ( @ [ ? ] ? â¡ ? ) | gr2_plus ( ? + ? ) | gr2_minus ( ? â ? â¡ ? ) | gr2_gr2 | ||
substitution | parallel substitution | ltps ( ? [?,?] ⶠ? ) | ltps_ldrop | ltps_tps | ltps_ltps | |
tps ( ? ⢠? [?,?] ⶠ? ) | tps_lift | tps_tps | ||||
global env. slicing | gdrop ( â©[?] ? â¡ ? ) | gdrop_gdrop | ||||
basic local env. slicing | ldrop ( â©[?,?] ? â¡ ? ) | ldrop_ldrop | ||||
basic term relocation | lift_vector ( â§[?,?] ? â¡ ? ) | lift_lift_vector | ||||
lift ( â§[?,?] ? â¡ ? ) | lift_lift | |||||
grammar | local env. ref. for substitution | lsubs ( ? [?,?] â¼ ? ) | lsubs_lsubs | |||
same head term form | tshf ( ? â ? ) | tshf_tshf | ||||
same top term constructor | tstc ( ? â ? ) | tstc_tstc | ||||
closures | cl_shift ( ? @ ? ) | cl_weight ( #[?,?] ) | ||||
internal syntax | genv | |||||
lenv | lenv_weight ( #[?] ) | lenv_length ( |?| ) | ||||
term | term_weight ( #[?] ) | term_simple ( ð[?] ) | term_vector | |||
item | ||||||
external syntax | aarity |
Physical Structure of the Specification
+ The source files are grouped in directories,
+ one for each component.
- ![lambda_delta rainbow rule [Spacer]](http://lambda-delta.info/images/rainbow.png)
Last update: 2012-02-01+01:00
+ ![lambda_delta rainbow rule [Spacer]](http://lambda-delta.info/images/rainbow.png)
Last update: 2012-02-24+01:00