lambdadelta version 2

+
+

- - - - - - - - - - - - - - - - - - - - - - - - - - - - + + - - - - - - - - - - - - - - - - - - - - - - - - - - - + + - - - - - - - + + + + - - - - - - + + + - - - - - - - + + + + + + + +

domain

block

leader

applicator (with âÎ¸)*

reduction

âÎ¶ *

reference *

{X | Î â¢ X : W}

local typed abstraction *

Î â¢ +Î»W

âV

âÎ²

-
+

+ home

local typed declaration **

Î â¢ -Î»W

âV

âÎ²

+ news +

+ specification +

global typed declaration ***

Î â¢ pÎ»W

native type annotation *

Î â¢ âW

yes

{X | Î â¢ X = V}

local abbreviation *

Î â¢ +Î´V

local âÎ´

yes

+ documentation +

+ implementation +

local definition **

Î â¢ -Î´V

local âÎ´

+ foreword +

+ milestones +

+ version 2 +

(background - core - applications)

global definition ***

Î â¢ pÎ´V

global âÎ´

+ version 2 +

+ helena +

+ Open Symbolic Notation (OSN) +

sort ****

Î â¢ âk

+ citations +

+ visibility +

+ version 1 +

(background - core)

(static HELM directory)

+ version 1 +

+ library +

(static LDDL directory)

* In terms only. + +

Summary of the Specification $\lambda\delta butterfly$ +

Here is a numerical account of the specification's contents and its timeline.

- - - + + - - - - - - - - - - - + + + + + + + - - - - - - - + + + + + + + - - - - - - - + + + + + + +

category

objects

sizes

files

198

characters

414004

nodes

1213218

sizes

files

177

characters

181483

nodes

952913

propositions

theorems

lemmas

877

total

966

propositions

theorems

lemmas

633

total

682

concepts

declared

defined

total

124

concepts

declared

defined

total

Stage "B"

- In progress. + Ongoing. Context-sensitive subject equivalence for native type assignment.

Stage "A2": "Extending the Applicability Condition"

+ 2017 January 17. + Confluence for parallel r-transition on referred entries of local environments. +

+ 2016 September 15. + Confluence for context-sensitive parallel r-transition on terms. +

+ 2016 April 16. + Grammatical component reconstructed: + grammar, relocation, s_transition, s_computation, static + (anniversary milestone). +

+ 2016 March 25. + Relocation with reference transforming maps (rtmap). +

- In progress. - Closure of context-sensitive extended computation - for native validity. + 2015 October 9. + Î»Î´ version 2A2 is started.

Stage "A1": "Extending the Applicability Condition"

- In progress. - Reaxiomatized Î²-reductum as in extended Î²-reduction + 2015 August 27. + Î»Î´ version 2A1 appears too complex and is dismissed.

- 2013 July 20. - Context-sensitive extended strong normalization + 2014 October 28. + Î»Î´ version 2A1 is released. +

+ 2014 September 9. + Iterated static type assignment defined (more elegantly) + as a primitive notion. +

+ 2014 June 18. + Preservation of stratified native validity + for context-sensitive computation on terms. +

+ 2014 June 9. + Strong qrst-normalization for simply typed terms.

+ 2014 April 16. + Lazy equivalence on local environments + added as q-step to rst-computation on closures + (anniversary milestone). +

+ 2014 January 20. + Parametrized slicing of local environments + comprises both versions of this operation + (one from basic_1, the other used in basic_2 till now). +

- 2013 April 16. - Reaxiomatized substitution and reduction + 2013 August 7. + Passive support for global environments. +

+ 2013 July 27. + Reaxiomatized Î²-reductum as in rt-reduction. +

+ 2013 July 20. + Context-sensitive strong rt-normalization + for simply typed terms. +

+ 2013 April 16. + Reaxiomatized substitution and reduction commute with respect to subclosure (anniversary milestone).

- 2013 March 16. + 2013 March 16. Mutual recursive preservation of stratified native validity - for hyper computation on closures. + for rst-computation on closures.

- 2012 October 16. + 2012 October 16. Confluence for context-free parallel reduction on closures.

- 2012 July 26. - Term binders polarized to control Î¶-reduction. + 2012 July 26. + Term binders polarized to control Î¶-reduction (not released).

- 2012 April 16. + 2012 April 16. Context-sensitive subject equivalence for atomic arity assignment (anniversary milestone).

- 2012 March 15. + 2012 March 15. Context-sensitive strong normalization for simply typed terms.

- 2012 January 27. + 2012 January 27. Support for abstract candidates of reducibility.

- 2011 September 21. + 2011 September 21. Confluence for context-sensitive parallel reduction on terms.

- 2011 September 6. + 2011 September 6. Confluence for context-free parallel reduction on terms.

- 2011 April 17. - Specification starts. + 2011 April 17. + Î»Î´ version 2 is started.

Logical Structure of the Specification

The source files are grouped in planes and components - 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 (? are placeholders). +

Logical Structure of the Specification $\lambda\delta butterfly$ +

This table reports the specification's components and their planes.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + - - - - - - - + + + + - - - - - - - - - - - + + - - - - - - - - - - + + - - - - - - - - - - + + + - - - - - - - - - - - - - + + - - - - - - - - - - - - - - + + + - - - - - - - - - - + + + + - - - - - - + + + - - - - - - + + + - - - - - - + + + - - - - - - + + + - - - - - - + + + - - - - - - + + + - - - - - - + + + - - - + + + - - - - - - - - - + + + + - - - - - - - + + - - - - - - - - - - - - - + + + + - - - - - - + + - - + + + - - - - - - - - - - - - - - - - - - + + - - - - - - + + + - - - - - - - - - - - - - - + + - - - + + + - - - - - - - - - + + + - - - - - - + + + + - - - + + + - - - - - - - - - + + + - - - - - - + + + - - - - - - + + - - - - - - - - - - - - - - - - - - - - - - - + + + - - - - - - + + + + - - - - - - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + - -

component	plane	files	- -	- -	- -
dynamic typing	"big tree" parallel computation	yprs ( ? â¢ â¦?,?â¦ â¥[g] â¦?,?â¦ )	yprs_yprs	ygt ( ? â¢ â¦?,?â¦ >[g] â¦?,?â¦ )	ygt_ygt
- -	"big tree" parallel reduction	ypr ( ? â¢ â¦?,?â¦ â½[g] â¦?,?â¦ )	ysc ( ? â¢ â¦?,?â¦ â»[g] â¦?,?â¦ )	- -	- -
- -	local env. ref. for stratified native validity	lsubsv ( ? â¢ ? Â¡â[?] ? )	lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv	- -	- -
- -	stratified native validity	snv ( â¦?,?â¦ â¢ ? Â¡[?] )	snv_lift snv_lpss snv_aaa snv_ssta snv_sstas snv_ssta_lpr snv_lpr snv_cpcs	- -	- -
equivalence	local env. ref. for stratified static type assignment	lsubss ( ? â¢â[?] ? )	lsubss_ldrop lsubss_ssta lsubss_cpcs	- -	- -
- -	context-sensitive equivalence	cpcs ( ? â¢ ? â¬* ? )	cpcs_lpss cpcs_aaa cpcs_cprs cpcs_cpcs	- -	- -
conversion	context-sensitive conversion	cpc ( ? â¢ ? â¬ ? )	cpc_cpc	- -	- -
computation	context-sensitive extended evaluation	cpxe ( â¦?,?â¦ â¢ â¡*[?] ðâ¦?â¦ )	+	component	plane	files		+		+
- -	context-sensitive evaluation	cpre ( ? â¢ â¡* ðâ¦?â¦ )	cpre_cpre	+	rt-transition	t-bound context-sensitive rt-transition	lfpr ( â¦?,?â¦ â¢ â¡[?,?] ? )	lfpr_length lfpr_drops lfpr_fqup lfpr_frees lfpr_aaa lfpr_lfpx lfpr_lfpr		+
- -	strongly normalizing computation	csn_vector ( ? â¢ â¬* ? )	csn_tstc_vector csn_aaa	+		- -
+		+	cpr ( â¦?,?â¦ â¢ ? â¡[?] ? )	cpr_drops		csn ( ? â¢ â¬* ? )	csn_alt ( ? â¢ â¬â¬* ? )	csn_lift csn_lpx	+
+		decomposed extended computation	dxprs ( â¦?,?â¦ â¢ ? â¢â¡[?] ? )	dxprs_lift dxprs_lpss dxprs_aaa dxprs_dxprs	+		+	cpm ( â¦?,?â¦ â¢ ? â¡[?,?] ? )	cpm_simple cpm_drops cpm_lsubr cpm_cpx
- -	context-sensitive extended computation	lpxs ( â¦?,?â¦ â¢ â¡*[?] ? )	lpxs_alt ( â¦?,?â¦ â¢ â¡â¡*[?] ? )	lpxs_ldrop lpxs_aaa lpxs_cpxs lpxs_lpxs	+
+		+	uncounted context-sensitive rt-transition	lfpx ( â¦?,?â¦ â¢ â¬[?,?] ? )	lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_aaa		cpxs ( â¦?,?â¦ â¢ ? â¡*[?] ? )	cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_aaa cpxs_cpxs	- -	+
+		context-sensitive computation	lprs ( ? â¢ â¡* ? )	lprs_alt ( ? â¢ â¡â¡* ? )	lprs_ldrop lprs_lpss lprs_cprs lprs_lprs	+
+	cpx ( â¦?,?â¦ â¢ ? â¬[?] ? )	cpx_simple cpx_drops cpx_lsubr		- -	cprs ( ? â¢ ? â¡* ?)	cprs_lift cprs_lpss cprs_cprs	- -	+
- -	local env. ref. for abstract candidates of reducibility	lsubc ( ? â[?] ? )	lsubc_ldrop lsubc_ldrops lsubc_lsuba	- -	+
+	counted context-sensitive rt-transition	cpg ( â¦?,?â¦ â¢ ? â¬[?,?] ? )	cpg_simple cpg_drops cpg_lsubr		support for abstract computation properties	acp	acp_cr ( â¦?,?â¦ Ïµ[?] ã?ã )	acp_aaa	+
reduction	context-sensitive extended normal forms	cnx ( â¦?,?â¦ â¢ ð[?]â¦?â¦ )	cnx_lift cnx_crx cnx_cix	+	static typing	parameters	sh	sd		+
+		context-sensitive extended reduction	lpx ( â¦?,?â¦ â¢ â¡[?] ? )	lpx_ldrop lpx_aaa	+	restricted ref. for atomic arity assignment	lsuba ( ? â¢ ? â«â ? )	lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba		+
- -	+		cpx ( â¦?,?â¦ â¢ ? â¡[?] ? )	cpx_lift cpx_cix	+	atomic arity assignment	aaa ( â¦?,?â¦ â¢ ? â ? )	aaa_drops aaa_fqus aaa_lfeq aaa_aaa		+
+		context-sensitive extended irreducible forms	cix ( â¦?,?â¦ â¢ ð[?]â¦?â¦ )	cix_append cix_lift	+	equivalence for closures on referred entries	ffeq ( â¦?,?,?â¦ â¡ â¦?,?,?â¦ )	ffeq_freq		+
+		context-sensitive extended reducible forms	crx ( â¦?,?â¦ â¢ ð[?]â¦?â¦ )	crx_append crx_lift	+	equivalence for local environments on referred entries	lfeq ( ? â¡[?] ? )	lfeq_length lfeq_lreq lfeq_fqup lfeq_lfeq		+
+		local env. ref. for extended reduction	lsubx ( ? ââ ? )	lsubx_lsubx	+	generic extension on referred entries	lfxs ( ? â¦»*[?,?] ? )	lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs		+
+		context-sensitive normal forms	cnr ( ? â¢ ðâ¦?â¦ )	cnr_lift cnr_crr cnr_cir	+	restricted ref. for context-sensitive free variables	lsubf ( â¦?,?â¦ â«ð* â¦?,?â¦ )	lsubf_frees		+
+		context-sensitive reduction	lpr ( ? â¢ â¡ ? )	lpr_ldrop lpr_lpss lpr_lpr	+	context-sensitive free variables	frees ( ? â¢ ð*â¦?â¦ â¡ ? )	frees_weight frees_lreq frees_drops frees_fqup frees_frees		+
+		+	restricted ref. for local env.	lsubr ( ? â« ? )	lsubr_length lsubr_drops lsubr_lsubr		cpr ( ? â¢ ? â¡ ? )	cpr_lift cpr_cir	- -	+
- -	context-sensitive irreducible forms	cir ( ? â¢ ðâ¦?â¦ )	cir_append cir_lift	+	s-computation	iterated structural successor for closures	fqus ( â¦?,?,?â¦ â* â¦?,?,?â¦ )	fqus_weight fqus_drops fqus_fqup fqus_fqus		+
+		context-sensitive reducible forms	crr ( ? â¢ ðâ¦?â¦ )	crr_append crr_lift	+		+	fqup ( â¦?,?,?â¦ â+ â¦?,?,?â¦ )	fqup_weight fqup_drops fqup_fqup
unfold	restricted parallel computation	lpqs ( ? â¢ â¤* ? )	lpqs_ldrop lpqs_cpqs lpqs_lpqs	- -	+
- -	- -	cpqs ( ? â¢ ? â¤* ? )	cpqs_lift	+	s-transition	structural successor for closures	fquq ( â¦?,?,?â¦ ââ¸® â¦?,?,?â¦ )	fquq_length fquq_weight		+
+		unfold	unfold ( ? â¢ ? â§«* ? )	+		+	fqu ( â¦?,?,?â¦ â â¦?,?,?â¦ )	fqu_length fqu_weight		+
+	relocation	generic slicing for local environments	drops_vector ( â¬[?,?] ? â¡ ? ) ( â¬[?] ? â¡ ? )		iterated stratified static type assignment	sstas ( â¦?,?â¦ â¢ ? â¢*[?] ? )	sstas_lift sstas_lpss sstas_aaa sstas_sstas	+		+
static typing	stratified static type assignment	ssta ( â¦?,?â¦ â¢ ? â¢[?,?] ? )	ssta_lift ssta_lpss ssta_aaa ssta_ssta	+		+
- -	local env. ref. for atomic arity assignment	lsuba ( ? ââ ? )	lsuba_ldrop lsuba_aaa lsuba_lsuba	+	drops ( â¬[?,?] ? â¡ ? ) ( â¬[?] ? â¡ ? )	drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops		+
+		atomic arity assignment	aaa ( ? â¢ ? â ? )	aaa_lift aaa_lifts aaa_lpss aaa_aaa	+	generic relocation for terms	lifts_vector ( â¬*[?] ? â¡ ? )	lifts_lifts_vector		+
+		parameters	sh	sd	+		- -
substitution	parallel substitution	lpss ( ? â¢ â¶* ? )	lpss_ldrop lpss_cpss lpss_lpss	+	lifts ( â¬*[?] ? â¡ ? )	lifts_simple lifts_weight lifts_lifts		+
+		+	ranged equivalence for local environments	lreq ( ? â¡[?] ? )	lreq_length lreq_lreq		cpss ( ? â¢ ? â¶* ? )	cpss_lift	- -	+
+		local env. ref. for substitution	lsubr ( ? â ? )	lsubr_lsubr	+	generic entrywise extension	lexs ( ? â¦»*[?,?,?] ? )	lexs_length lexs_lexs		+
- -	iterated structural successor for closures	fsups ( â¦?,?â¦ â* â¦?,?â¦ )	fsups_fsups	+	grammar	append for local environments	append ( ? @@ ? )	append_length		+
+		+	context-sensitive equivalences for terms	ceq	ceq_ceq		fsupp ( â¦?,?â¦ â+ â¦?,?â¦ )	fsupp_fsupp	- -	+
+		generic local env. slicing	ldrops ( â©*[?] ? â¡ ? )	ldrops_ldrop ldrops_ldrops	+	same top term structure	tsts ( ? â ? )	tsts_tsts tsts_vector		+
+		generic term relocation	lifts_vector ( â§*[?] ? â¡ ? )	lifts_lift_vector	+	closures	cl_weight ( â¯{?,?,?} )	cl_restricted_weight ( â¯{?,?} )		+
- -	+		lifts ( â§*[?] ? â¡ ? )	lifts_lift lifts_lifts	+	internal syntax	genv		+
- -	support for generic relocation	gr2 ( @â¦?,?â¦ â¡ ? )	gr2_plus ( ? + ? )	gr2_minus ( ? â ? â¡ ? )	gr2_gr2
relocation	structural successor for closures	fsup ( â¦?,?â¦ â â¦?,?â¦ )	fsupq ( â¦?,?â¦ ââ¸® â¦?,?â¦ )	fsupq_alt	+
+		global env. slicing	gdrop ( â©[?] ? â¡ ? )	gdrop_gdrop	+		+	lenv	lenv_weight ( â¯{?} )	lenv_length ( \|?\| )
- -	basic local env. slicing	ldrop ( â©[?,?] ? â¡ ? )	ldrop_append ldrop_lpx_sn ldrop_ldrop	+		+		term	term_weight ( â¯{?} )	term_simple ( ðâ¦?â¦ )	term_vector ( â¶?.? )
+		basic term relocation	lift_vector ( â§[?,?] ? â¡ ? )	lift_lift_vector	+		+	item
- -	- -	lift ( â§[?,?] ? â¡ ? )	lift_lift	- -	- -
grammar	pointwise extension of a relation	lpx_sn	lpx_sn_tc lpx_sn_lpx_sn	- -	- -
- -	same top term constructor	tstc ( ? â ? )	tstc_tstc tstc_vector	- -	- -
- -	closures	cl_shift ( ? @@ ? )	cl_weight ( â¯{?,?} )	- -	- -
- -	internal syntax	genv	- -	- -	- -
- -	- -	lenv	lenv_weight ( â¯{?} )	lenv_length ( \|?\| )	lenv_append ( ? @@ ? )
- -	- -	term	term_weight ( â¯{?} )	term_simple ( ðâ¦?â¦ )	term_vector
+		- -	item	- -	- -	+
+		external syntax	aarity	+	external syntax	aarity		+		+

- -

Physical Structure of the Specification

The source files are grouped in directories, - one for each component. -

+ $\lambda\delta rainbow rule$

@@ -1154,6 +883,6 @@

Last update: Sun, 21 Jul 2013 00:11:48 +0200

- +

Last update: Sat, 21 Jan 2017 15:35:26 +0100