lambdadelta version 2

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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 ****

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+ 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

250

characters

484782

nodes

1304867

sizes

files

212

characters

213959

nodes

1057531

propositions

theorems

lemmas

1112

total

1196

propositions

theorems

lemmas

741

total

803

concepts

declared

defined

total

128

concepts

declared

defined

total

109

Stage "B"

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

Stage "A2": "Extending the Applicability Condition"

- In progress. - Closure of extended context-sensitive computation - for native validity. + 2017 October 17. + Exclusion binder in local environments. + Syntactic component updated: + syntax, relocation, s_transition, s_computation, static, i_static.

- In progress. - Extended context-sensitive strong normalization + 2017 April 16. + Strong rt-normalization + for simply typed terms + (anniversary milestone). +

+ 2017 March 16. + First behavioral component reconstructed: + rt_transition. +

+ 2017 February 19. + Generic candidates of reducibility. +

+ 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. + Syntactic component reconstructed: + syntax, relocation, s_transition, s_computation, static + (anniversary milestone). +

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

+ 2015 October 9. + Î»Î´ version 2A2 is started. +

Stage "A1": "Extending the Applicability Condition"

+ 2015 August 27. + Î»Î´ version 2A1 appears too complex and is dismissed. +

+ 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 on local environments + comprises both versions of this operation + (one from basic_1, the other used in basic_2 till now). +

+ 2013 August 7. + Passive support for global environments. +

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

- 2013 March 16. + 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. 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. - Support for abstract candidates of reducibility. + 2012 January 27. + Generic 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© ? :[?] )	snv_lift snv_ltpss_dx snv_ltpss_sn snv_aaa snv_ssta snv_sstas snv_ssta_ltpr snv_ltpr snv_cpcs	- -	- -	- -
equivalence	focalized equivalence	lfpcs ( â¦?â¦ â¬* â¦?â¦ )	lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs	- -	- -	- -
- -	- -	fpcs ( â¦?,?â¦ â¬* â¦?,?â¦ )	fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs	- -	- -	- -
- -	local env. ref. for stratified static type assignment	lsubss ( ? â¢â[?] ? )	lsubss_ldrop lsubss_ssta lsubss_cpcs	- -	- -	- -
- -	context-sensitive equivalence	cpcs ( ? â¢ ? â¬* ? )	cpcs_ltpss_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs	- -	- -	- -
conversion	focalized conversion	lfpc ( â¦?â¦ â¬ â¦?â¦ )	lfpc_lfpc	- -	- -	- -
- -	- -	fpc ( â¦?,?â¦ â¬ â¦?,?â¦ )	fpc_fpc	- -	- -	- -
- -	context-sensitive conversion	cpc ( ? â¢ ? â¬ ? )	cpc_cpc	- -	- -	- -
computation	focalized computation	lfprs ( â¦?â¦ â¡* â¦?â¦ )	lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs	- -	- -	- -
- -	- -	fprs ( â¦?,?â¦ â¡* â¦?,?â¦ )	fprs_aaa fprs_fprs	- -	- -	- -
- -	decomposed extended computation	dxprs ( â¦?,?â¦ â¢ ? â¢â¡[?] ? )	dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn dxprs_aaa dxprs_dxprs	- -	- -	+	component	plane	files
- -	weakly normalizing computation	cpe ( ? â¢ â¡* ðâ¦?â¦ )	cpe_cpe	- -	- -	- -	rt-transition	counted context-sensitive rt-transition	cpg ( â¦?,?â¦ â¢ ? â¬[?,?] ? )	cpg_simple cpg_drops cpg_lsubr
- -	strongly normalizing computation	csn_vector ( ? â¢ â¬* ? )	csn_cpr_vector csn_tstc_vector csn_aaa	- -	- -	- -	iterated static typing	iterated extension on referred entries	tc_lfxs ( ? â¦»**[?,?] ? )	tc_lfxs_length tc_lfxs_drops tc_lfxs_fqup tc_lfxs_tc_lfxs
- -	- -	csn ( ? â¢ â¬* ? )	csn_alt ( ? â¢ â¬â¬* ? )	csn_lift csn_cpr csn_lfpr	- -	- -	static typing	generic reducibility	lsubc ( ? â¢ ? â«[?] ? )	lsubc_drops lsubc_lsubr lsubc_lsuba
- -	context-sensitive computation	cprs (? â¢ ? â¡* ?)	cprs_lift cprs_tpss cprs_ltpss_dx cprs_ltpss_sn cprs_delift cprs_aaa cprs_ltpr cprs_lfpr cprs_cprs cprs_lfprs cprs_tstc cprs_tstc_vector	- -	+		+		gcp_cr ( â¦?,?,?â¦ Ïµ[?] ã?ã )	gcp_aaa
+		context-free computation	ltprs ( ? â¡* ? )	ltprs_alt ( ? â¡â¡* ? )	ltprs_ldrop ltprs_ltprs	+		+	gcp
- -	- -	tprs ( ? â¡* ?)	tprs_lift tprs_tprs	- -	- -	+		atomic arity assignment	lsuba ( ? â¢ ? â«â ? )	lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba
- -	local env. ref. for abstract candidates of reducibility	lsubc ( ? â[?] ? )	lsubc_ldrop lsubc_ldrops lsubc_lsuba	+		- -	+		aaa ( â¦?,?â¦ â¢ ? â ? )	aaa_drops aaa_fqus aaa_lfdeq aaa_aaa
- -	support for abstract computation properties	acp	acp_cr ( â¦?,?â¦ Ïµ[?] ã?ã )	acp_aaa	- -	+		degree-based equivalence on referred entries	ffdeq ( â¦?,?,?â¦ â¡[?,?] â¦?,?,?â¦ )	ffdeq_fqup ffdeq_ffdeq
reducibility	context-sensitive focalized reduction	cfpr ( ? â¢ â¦?,?â¦ â¡ â¦?,?â¦ )	cnfpr_ltpss cfpr_aaa cfpr_cpr cfpr_cfpr	- -	+		+		lfdeq ( ? â¡[?,?,?] ? )	lfdeq_length lfdeq_drops lfdeq_fqup lfdeq_fqus lfdeq_lfdeq
- -	context-free focalized reduction	lfpr ( â¦?â¦ â¡ â¦?â¦ )	lfpr_alt ( â¦?â¦ â¡â¡ â¦?â¦ )	lfpr_aaa lfpr_cpr lfpr_fpr lfpr_lfpr	- -	+		generic extension on referred entries	lfxs ( ? â¦»*[?,?] ? )	lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs
- -	- -	fpr ( â¦?,?â¦ â¡ â¦?,?â¦ )	fpr_cpr fpr_fpr	- -	- -	+		context-sensitive free variables	lsubf ( â¦?,?â¦ â«ð* â¦?,?â¦ )	lsubf_lsubr lsubf_frees lsubf_lsubf
- -	context-sensitive normal forms	cnf ( ? â¢ ðâ¦?â¦ )	cnf_lift cnf_cif	+		- -	+		frees ( ? â¢ ð*â¦?â¦ â¡ ? )	frees_drops frees_fqup frees_frees
- -	context-sensitive reduction	cpr ( ? â¢ ? â¡ ? )	cpr_lift cpr_tpss cpr_ltpss_dx cpr_ltpss_sn cpr_delift cpr_aaa cpr_ltpr cpr_cpr	- -	- -	+		restricted ref. for local env.	lsubr ( ? â« ? )	lsubr_length lsubr_drops lsubr_lsubr
- -	context-sensitive reducible forms	crf ( ? â¢ ðâ¦?â¦ )	crf_append	cif ( ? â¢ ðâ¦?â¦ )	cif_append	- -	s-computation	iterated structural successor for closures	fqus ( â¦?,?,?â¦ â[?] â¦?,?,?â¦ ) ( â¦?,?,?â¦ â â¦?,?,?â¦ )	fqus_weight fqus_drops fqus_fqup fqus_fqus
- -	context-free normal forms	thnf ( ððâ¦?â¦ )	+		- -	- -	+		fqup ( â¦?,?,?â¦ â+[?] â¦?,?,?â¦ ) ( â¦?,?,?â¦ â+ â¦?,?,?â¦ )	fqup_weight fqup_drops fqup_fqup
- -	context-free reduction	ltpr ( ? â¡ ? )	ltpr_ldrop ltpr_tps ltpr_ltpss_dx ltpr_ltpss_sn ltpr_aaa ltpr_ltpr	- -	- -	- -
- -	- -	tpr ( ? â¡ ? )	tpr_lift tpr_tps tpr_tpss tpr_delift tpr_tpr	- -	- -	- -
unwind	iterated stratified static type assignment	sstas ( â¦?,?â¦ â¢ ? â¢*[?] ? )	sstas_lift sstas_ltpss_dx sstas_ltpss_sn sstas_aaa sstas_sstas	- -	- -	- -	s-transition	structural successor for closures	fquq ( â¦?,?,?â¦ ââ¸®[?] â¦?,?,?â¦ ) ( â¦?,?,?â¦ ââ¸® â¦?,?,?â¦ )	fquq_length fquq_weight
static typing	stratified static type assignment	ssta ( â¦?,?â¦ â¢ ? â¢[?,?] ? )	ssta_lift ssta_ltpss_dx ssta_ltpss_sn ssta_aaa ssta_ssta	+		- -	+		fqu ( â¦?,?,?â¦ â[?] â¦?,?,?â¦ ) ( â¦?,?,?â¦ â â¦?,?,?â¦ )	fqu_length fqu_weight
- -	local env. ref. for atomic arity assignment	lsuba ( ? ââ ? )	lsuba_ldrop lsuba_aaa lsuba_lsuba	- -	- -	+	relocation	generic slicing for local environments	drops_vector ( â¬[?,?] ? â¡ ? ) ( â¬[?] ? â¡ ? )
- -	atomic arity assignment	aaa ( ? â¢ ? â ? )	aaa_lift aaa_lifts aaa_ltpss_dx aaa_ltpss_sn aaa_aaa	+		- -	+		drops ( â¬[?,?] ? â¡ ? ) ( â¬[?] ? â¡ ? )	drops_lstar drops_weight drops_length drops_ext2 drops_lexs drops_lreq drops_drops
- -	parameters	sh	sd	- -	- -	+		generic relocation	lifts_bind ( â¬*[?] ? â¡ ? )	lifts_weight_bind lifts_lifts_bind
unfold	basic local env. thinning	thin ( ? â¼*[?,?] â¡ ? )	thin_ldrop thin_delift	+		- -	+		lifts_vector ( â¬*[?] ? â¡ ? )	lifts_lifts_vector
- -	inverse basic term relocation	delift ( ? â¢ ? â¼*[?,?] â¡ ? )	delift_alt ( ? â¢ ? â¼â¼*[?,?] â¡ ? )	delift_lift delift_tpss delift_ltpss delift_delift	+		+		lifts ( â¬*[?] ? â¡ ? )	lifts_simple lifts_weight lifts_tdeq lifts_lifts
- -	partial unfold	ltpss_sn ( ? â¢ â¶*[?,?] ? )	ltpss_sn_alt ( ? â¢ â¶â¶*[?,?] ? )	ltpss_sn_ldrop ltpss_sn_tps ltpss_sn_tpss ltpss_sn_ltpss_sn	- -	+		ranged equivalence for local environments	lreq ( ? â¡[?] ? )	lreq_length lreq_lreq
- -	- -	ltpss_dx ( ? â¶*[?,?] ? )	ltpss_dx_ldrop ltpss_dx_tps ltpss_dx_tpss ltpss_dx_ltpss_dx	- -	- -	+		generic entrywise extension	lexs ( ? â¦»*[?,?,?] ? )	lexs_length lexs_lexs
- -	- -	tpss ( ? â¢ ? â¶*[?,?] ? )	tpss_alt ( ? â¢ ? â¶â¶*[?,?] ? )	tpss_lift	tpss_tpss	- -	syntax	append for local environments	append ( ? @@ ? )	append_length
- -	generic local env. slicing	ldrops ( â©*[?] ? â¡ ? )	ldrops_ldrop ldrops_ldrops	- -	- -	+		head equivalence for terms	theq ( ? â©³[?,?] ? )	theq_simple theq_tdeq theq_theq theq_simple_vector
+		iterated restricted structural predecessor for closures	frsups ( â¦?,?â¦ â§* â¦?,?â¦ )	frsups_frsups	- -	- -	+	degree-based equivalence	tdeq_ext ( ? â¡[?,?] ? )
- -	- -	frsupp ( â¦?,?â¦ â§+ â¦?,?â¦ )	frsupp_frsupp	+		- -	+		tdeq ( ? â¡[?,?] ? )	tdeq_tdeq
- -	generic term relocation	lifts_vector ( â§*[?] ? â¡ ? )	lifts_lift_vector	+		- -	+	closures	cl_weight ( â¯{?,?,?} )
+		+		lifts ( â§*[?] ? â¡ ? )	lifts_lift lifts_lifts	- -	- -	+	cl_restricted_weight ( â¯{?,?} )
+		support for generic relocation	gr2 ( @â¦?,?â¦ â¡ ? )	gr2_plus ( ? + ? )	gr2_minus ( ? â ? â¡ ? )	gr2_gr2	+	global environments	genv
substitution	parallel substitution	tps ( ? â¢ ? â¶[?,?] ? )	tps_lift tps_tps	- -	+		+	local environments	lenv_ext2
- -	global env. slicing	gdrop ( â©[?] ? â¡ ? )	gdrop_gdrop	+		+		+	lenv_length ( \|?\| )
+		basic local env. slicing	ldrop ( â©[?,?] ? â¡ ? )	ldrop_append ldrop_lpx ldrop_sfr ldrop_ldrop	+		- -	+	lenv_weight ( â¯{?} )
+		local env. ref. for substitution	lsubs ( ? â¼[?,?] ? )	(lsubs_lsubs)	lsubs_sfr ( â½[?,?] ? )	+		+	lenv
- -	restricted structural predecessor for closures	frsup ( â¦?,?â¦ â§ â¦?,?â¦ )	- -	- -	- -	+		binders for local environments	ext2	ext2_ext2
- -	basic term relocation	lift_vector ( â§[?,?] ? â¡ ? )	lift_lift_vector	+		- -	+		bind	bind_weight
- -	- -	lift ( â§[?,?] ? â¡ ? )	lift_lift	+		- -	+	terms	term_vector ( â¶?.? )
grammar	same head term form	tshf ( ? â ? )	(tshf_tshf)	+		+		+	term_simple ( ðâ¦?â¦ )
- -	same top term constructor	tstc ( ? â ? )	tstc_tstc tstc_vector	+		+		+	term_weight ( â¯{?} )
+		closures	cl_shift ( ? @@ ? )	cl_weight ( â¯{?,?} )	+		- -	- -
- -	internal syntax	genv	- -	- -	- -	+	term
+		+	items	item_sd		lenv	lenv_weight ( â¯{?} )	lenv_length ( \|?\| )	lenv_append ( ? @@ ? )	lenv_px lenv_px_bi
+		+		term	term_weight ( â¯{?} )	term_simple ( ðâ¦?â¦ )	term_vector	+	item_sh
+		+		item	- -	- -	- -	+	item
- -	external syntax	aarity	- -	+		- -	+	atomic arities	aarity

- -

Physical Structure of the Specification

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

+ $\lambda\delta rainbow rule$

@@ -1361,6 +844,6 @@

Last update: Sat, 16 Mar 2013 23:25:31 +0100

- +

Last update: Tue, 17 Oct 2017 20:34:24 +0200