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

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global typed declaration ***

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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. - 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].

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

category

objects

sizes

files

268

characters

407502

nodes

1213911

sizes

files

212

characters

213959

nodes

1057531

propositions

theorems

lemmas

826

total

909

propositions

theorems

lemmas

741

total

803

concepts

declared

defined

total

125

concepts

declared

defined

total

109

Stage "B"

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

Stage "A2": "Extending the Applicability Condition"

+ 2017 October 17. + Exclusion binder in local environments. + Syntactic component updated: + syntax, relocation, s_transition, s_computation, static, i_static. +

+ 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). +

- 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"

- 2013 August 7. + 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 extended Î²-reduction + 2013 July 27. + Reaxiomatized Î²-reductum as in rt-reduction.

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

- 2013 April 16. + 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. - 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	local env. ref. for stratified native validity	lsubsv ( ? â¢ ? Â¡â[?,?] ? )	lsubsv_ldrop lsubsv_lsubd lsubsv_lsuba lsubsv_lsstas lsubsv_cpds lsubsv_cpcs lsubsv_snv	- -	- -
- -	stratified native validity	snv ( â¦?,?â¦ â¢ ? Â¡[?,?] )	snv_lift snv_da_lpr snv_aaa snv_lsstas snv_lsstas_lpr snv_lpr snv_cpcs	- -	+	component	plane	files
equivalence	decomposed extended equivalence	cpes ( â¦?,?â¦ â¢ ? â¢â¬[?,?] ? )	cpes_cpds	- -	- -	rt-transition	counted context-sensitive rt-transition	cpg ( â¦?,?â¦ â¢ ? â¬[?,?] ? )	cpg_simple cpg_drops cpg_lsubr
- -	context-sensitive equivalence	cpcs ( â¦?,?â¦ â¢ ? â¬* ? )	cpcs_aaa cpcs_cprs cpcs_cpcs	- -	- -
conversion	context-sensitive conversion	cpc ( â¦?,?â¦ â¢ ? â¬ ? )	cpc_cpc	- -	- -
computation	context-sensitive extended evaluation	cpxe ( â¦?,?â¦ â¢ â¡*[?,?] ðâ¦?â¦ )	- -	- -	- -
- -	context-sensitive evaluation	cpre ( â¦?,?â¦ â¢ â¡* ðâ¦?â¦ )	cpre_cpre	- -	- -
- -	strongly normalizing computation	csx_vector ( â¦?,?â¦ â¢ â¬*[?,?] ? )	csx_tstc_vector csx_aaa	- -	- -
- -	- -	csx ( â¦?,?â¦ â¢ â¬*[?,?] ? )	csx_alt ( â¦?,?â¦ â¢ â¬â¬*[?,?] ? )	csx_lift csx_lpx	- -	iterated static typing	iterated extension on referred entries	tc_lfxs ( ? â¦»**[?,?] ? )	tc_lfxs_length tc_lfxs_drops tc_lfxs_fqup tc_lfxs_tc_lfxs
- -	"big tree" parallel computation	fpbg ( â¦?,?,?â¦ >[?,?] â¦?,?,?â¦ )	fpbg_lift fpbg_fpbg	- -	- -	static typing	generic reducibility	lsubc ( ? â¢ ? â«[?] ? )	lsubc_drops lsubc_lsubr lsubc_lsuba
+		- -	fpbs ( â¦?,?,?â¦ â¥[?,?] â¦?,?,?â¦ )	fpbs_alt ( â¦?,?,?â¦ â¥â¥[?,?] â¦?,?,?â¦ )	fpbs_lift fpbs_fpbs	+		gcp_cr ( â¦?,?,?â¦ Ïµ[?] ã?ã )	gcp_aaa
+		decomposed extended computation	cpds ( â¦?,?â¦ â¢ ? â¢â¡[?,?] ? )	cpds_lift cpds_aaa cpds_cpds	+		+	gcp
- -	context-sensitive extended computation	lpxs ( â¦?,?â¦ â¢ â¡*[?,?] ? )	lpxs_alt ( â¦?,?â¦ â¢ â¡â¡*[?,?] ? )	lpxs_ldrop lpxs_aaa lpxs_cpxs lpxs_lpxs	+		atomic arity assignment	lsuba ( ? â¢ ? â«â ? )	lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba
- -	- -	cpxs ( â¦?,?â¦ â¢ ? â¡*[?,?] ? )	cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_aaa cpxs_cpxs	+		+		aaa ( â¦?,?â¦ â¢ ? â ? )	aaa_drops aaa_fqus aaa_lfdeq aaa_aaa
- -	context-sensitive computation	lprs ( â¦?,?â¦ â¢ â¡* ? )	lprs_alt ( â¦?,?â¦ â¢ â¡â¡* ? )	lprs_ldrop lprs_cprs lprs_lprs	+		degree-based equivalence on referred entries	ffdeq ( â¦?,?,?â¦ â¡[?,?] â¦?,?,?â¦ )	ffdeq_fqup ffdeq_ffdeq
- -	+		cprs ( â¦?,?â¦ â¢ ? â¡* ?)	cprs_lift cprs_cprs	- -	+		lfdeq ( ? â¡[?,?,?] ? )	lfdeq_length lfdeq_drops lfdeq_fqup lfdeq_fqus lfdeq_lfdeq
- -	local env. ref. for abstract candidates of reducibility	lsubc ( ? â¢ ? â[?] ? )	lsubc_ldrop lsubc_ldrops lsubc_lsuba	- -	+		generic extension on referred entries	lfxs ( ? â¦»*[?,?] ? )	lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs
- -	support for abstract computation properties	acp	acp_cr ( â¦?,?,?â¦ Ïµ[?] ã?ã )	acp_aaa	+		context-sensitive free variables	lsubf ( â¦?,?â¦ â«ð* â¦?,?â¦ )	lsubf_lsubr lsubf_frees lsubf_lsubf
reduction	"big tree" parallel reduction	fpbc ( â¦?,?,?â¦ â»[?,?] â¦?,?,?â¦ )	fpbc_lift	+		+		frees ( ? â¢ ð*â¦?â¦ â¡ ? )	frees_drops frees_fqup frees_frees
- -	- -	fpb ( â¦?,?,?â¦ â½[?,?] â¦?,?,?â¦ )	fpb_lift	- -	+		restricted ref. for local env.	lsubr ( ? â« ? )	lsubr_length lsubr_drops lsubr_lsubr
- -	context-sensitive extended normal forms	cnx ( â¦?,?â¦ â¢ ð[?,?]â¦?â¦ )	cnx_lift cnx_crx cnx_cix	- -	- -	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-sensitive extended reduction	lpx ( â¦?,?â¦ â¢ â¡[?,?] ? )	lpx_ldrop lpx_aaa	+		+		fqup ( â¦?,?,?â¦ â+[?] â¦?,?,?â¦ ) ( â¦?,?,?â¦ â+ â¦?,?,?â¦ )	fqup_weight fqup_drops fqup_fqup
- -	- -	cpx ( â¦?,?â¦ â¢ ? â¡[?,?] ? )	cpx_lift cpx_cix	- -	- -	s-transition	structural successor for closures	fquq ( â¦?,?,?â¦ ââ¸®[?] â¦?,?,?â¦ ) ( â¦?,?,?â¦ ââ¸® â¦?,?,?â¦ )	fquq_length fquq_weight
- -	context-sensitive extended irreducible forms	cix ( â¦?,?â¦ â¢ ð[?,?]â¦?â¦ )	cix_append cix_lift	+		+		fqu ( â¦?,?,?â¦ â[?] â¦?,?,?â¦ ) ( â¦?,?,?â¦ â â¦?,?,?â¦ )	fqu_length fqu_weight
- -	context-sensitive extended reducible forms	crx ( â¦?,?â¦ â¢ ð[?,?]â¦?â¦ )	crx_append crx_lift	- -	+	relocation	generic slicing for local environments	drops_vector ( â¬[?,?] ? â¡ ? ) ( â¬[?] ? â¡ ? )
- -	context-sensitive normal forms	cnr ( â¦?,?â¦ â¢ ðâ¦?â¦ )	cnr_lift cnr_crr cnr_cir	+		+		drops ( â¬[?,?] ? â¡ ? ) ( â¬[?] ? â¡ ? )	drops_lstar drops_weight drops_length drops_ext2 drops_lexs drops_lreq drops_drops
- -	context-sensitive reduction	lpr ( â¦?,?â¦ â¢ â¡ ? )	lpr_ldrop lpr_lpr	- -	+		generic relocation	lifts_bind ( â¬*[?] ? â¡ ? )	lifts_weight_bind lifts_lifts_bind
- -	- -	cpr ( â¦?,?â¦ â¢ ? â¡ ? )	cpr_lift cpr_cir	+		+		lifts_vector ( â¬*[?] ? â¡ ? )	lifts_lifts_vector
- -	context-sensitive irreducible forms	cir ( â¦?,?â¦ â¢ ðâ¦?â¦ )	cir_append cir_lift	+		+		lifts ( â¬*[?] ? â¡ ? )	lifts_simple lifts_weight lifts_tdeq lifts_lifts
- -	context-sensitive reducible forms	crr ( â¦?,?â¦ â¢ ðâ¦?â¦ )	crr_append crr_lift	- -	+		ranged equivalence for local environments	lreq ( ? â¡[?] ? )	lreq_length lreq_lreq
unfold	unfold	unfold ( â¦?,?â¦ â¢ ? â§«* ? )	- -	- -	+		generic entrywise extension	lexs ( ? â¦»*[?,?,?] ? )	lexs_length lexs_lexs
- -	iterated static type assignment	lsstas ( â¦?,?â¦ â¢ ? â¢*[?,?,?] ? )	lsstas_alt ( â¦?,?â¦ â¢ ? â¢â¢*[?,?,?] ? )	lsstas_lift lsstas_aaa lsstas_lsstas	- -	syntax	append for local environments	append ( ? @@ ? )	append_length
static typing	local env. ref. for atomic arity assignment	lsuba ( ? â¢ ? ââ ? )	lsuba_ldrop lsuba_aaa lsuba_lsuba	- -	+		head equivalence for terms	theq ( ? â©³[?,?] ? )	theq_simple theq_tdeq theq_theq theq_simple_vector
+		atomic arity assignment	aaa ( â¦?,?â¦ â¢ ? â ? )	aaa_lift aaa_lifts aaa_da aaa_ssta aaa_aaa	- -	+	degree-based equivalence	tdeq_ext ( ? â¡[?,?] ? )
+		stratified static type assignment	ssta ( â¦?,?â¦ â¢ ? â¢[?,?] ? )	ssta_lift ssta_ssta	- -	+		tdeq ( ? â¡[?,?] ? )	tdeq_tdeq
- -	local env. ref. for degree assignment	lsubd ( ? â¢ ? âªâ ? )	lsubd_da lsubd_lsubd	- -	- -
- -	degree assignment	da ( â¦?,?â¦ â¢ ? âª[?,?] ? )	da_lift da_da	+		+	closures	cl_weight ( â¯{?,?,?} )
+		parameters	sh	sd	+		+	cl_restricted_weight ( â¯{?,?} )
substitution	restricted local env. ref.	lsubr ( ? â ? )	lsubr_lsubr	+		+	global environments	genv
+		iterated structural successor for closures	fqus ( â¦?,?,?â¦ â* â¦?,?,?â¦ )	fqus_fqus	- -	+	local environments	lenv_ext2
+		+		fqup ( â¦?,?,?â¦ â+ â¦?,?,?â¦ )	fqup_fqup	- -	+	lenv_length ( \|?\| )
+		generic local env. slicing	ldrops ( â©*[?] ? â¡ ? )	ldrops_ldrop ldrops_ldrops	+		+	lenv_weight ( â¯{?} )
+		generic term relocation	lifts_vector ( â§*[?] ? â¡ ? )	lifts_lift_vector	+		+	lenv
- -	- -	lifts ( â§*[?] ? â¡ ? )	lifts_lift lifts_lifts	- -	+		binders for local environments	ext2	ext2_ext2
+		support for generic relocation	gr2 ( @â¦?,?â¦ â¡ ? )	gr2_plus ( ? + ? )	gr2_minus ( ? â ? â¡ ? )	gr2_gr2
relocation	structural successor for closures	fqu ( â¦?,?,?â¦ â â¦?,?,?â¦ )	fquq ( â¦?,?,?â¦ ââ¸® â¦?,?,?â¦ )	fquq_alt ( â¦?,?,?â¦ âââ¸® â¦?,?,?â¦ )	+		bind	bind_weight
+		global env. slicing	gdrop ( â©[?] ? â¡ ? )	gdrop_gdrop	- -	+	terms	term_vector ( â¶?.? )
+		basic local env. slicing	ldrop ( â©[?,?] ? â¡ ? )	ldrop_append ldrop_lpx_sn ldrop_ldrop	+		+	term_simple ( ðâ¦?â¦ )
+		basic term relocation	lift_vector ( â§[?,?] ? â¡ ? )	lift_lift_vector	+		+	term_weight ( â¯{?} )
+		+		lift ( â§[?,?] ? â¡ ? )	lift_lift	- -	+	term
grammar	pointwise extension of a relation	lpx_sn	lpx_sn_tc lpx_sn_lpx_sn	+		+	items	item_sd
+		same top term constructor	tstc ( ? â ? )	tstc_tstc tstc_vector	+		+	item_sh
+		closures	cl_shift ( ? @@ ? )	cl_weight ( â¯{?,?,?} )	+		+	item
- -	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	- -	- -	+	atomic arities	aarity

- -

Physical Structure of the Specification

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

+ $\lambda\delta rainbow rule$

@@ -1150,6 +844,6 @@

Last update: Sat, 12 Oct 2013 19:38:34 +0200

- +

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