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 +

+ news +

+ specification +

local typed declaration **

Î â¢ -Î»W

âV

âÎ²

global typed declaration ***

Î â¢ pÎ»W

+ documentation +

+ implementation +

native type annotation *

Î â¢ âW

yes

{X | Î â¢ X = V}

local abbreviation *

Î â¢ +Î´V

local âÎ´

yes

+ foreword +

+ milestones +

+ version 2 +

(background - core - applications)

local definition **

Î â¢ -Î´V

local âÎ´

+ version 2 +

+ helena +

global definition ***

Î â¢ pÎ´V

global âÎ´

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. - 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

301

characters

474902

nodes

1399948

sizes

files

143

characters

116151

nodes

604153

propositions

theorems

lemmas

917

total

1006

propositions

theorems

lemmas

428

total

473

concepts

declared

defined

total

123

concepts

declared

defined

total

Stage "B"

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

Stage "A2": "Extending the Applicability Condition"

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

- In progress. - Closure of context-sensitive extended computation - for native validity. + 2016 March 25. + Relocation with reference transforming maps (rtmap).

- 2013 August 7. + 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 of 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 "big tree" 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. - 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). +

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	- -	- -
equivalence	decomposed extended equivalence	cpes ( â¦?,?â¦ â¢ ? â¢â¬[?,?] ? )	cpes_cpds	- -	- -
- -	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 "big tree" computation	fsb ( â¦?,?â¦ â¢ â¦¥[?,?] ? )	fsb_alt ( â¦?,?â¦ â¢ â¦¥â¦¥[?,?] ? )	fsb_fleq fsb_csx	- -
- -	strongly normalizing extended 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	- -
- -	parallel computation for "big tree" normal forms	fpns ( â¦?,?,?â¦ â¢ ââ¡*[?,?] â¦?,?,?â¦ )	fpns_fpns	- -	- -
- -	"big tree" parallel computation	fpbr ( â¦?,?,?â¦ ââ¥[?,?] â¦?,?,?â¦ )	fpbr_fpbr	- -	- -
- -	- -	fpbg ( â¦?,?,?â¦ >[?,?] â¦?,?,?â¦ )	fpbg_lift fpbg_fpbg	- -	- -
- -	- -	fpbs ( â¦?,?,?â¦ â¥[?,?] â¦?,?,?â¦ )	fpbs_alt ( â¦?,?,?â¦ â¥â¥[?,?] â¦?,?,?â¦ )	fpbs_lift fpbs_fleq fpbs_fpbs	- -
+	component	plane	files		decomposed extended computation	cpds ( â¦?,?â¦ â¢ ? â¢â¡[?,?] ? )	cpds_lift cpds_aaa cpds_cpds	+		+
+	rt-transition	uncounted context-sensitive rt-transition	cpx ( â¦?,?â¦ â¢ ? â¡[?] ? )	cpx_simple cpx_drops cpx_lsubr		context-sensitive extended computation	lpxs ( â¦?,?â¦ â¢ â¡*[?,?] ? )	lpxs_alt ( â¦?,?â¦ â¢ â¡â¡*[?,?] ? )	lpxs_ldrop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs	+
+		+	counted context-sensitive rt-transition	cpg ( â¦?,?â¦ â¢ ? â¡[?,?] ? )	cpg_simple cpg_drops cpg_lsubr		cpxs ( â¦?,?â¦ â¢ ? â¡*[?,?] ? )	cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs	- -	+
+	static typing	parameters	sh	sd		context-sensitive computation	lprs ( â¦?,?â¦ â¢ â¡* ? )	lprs_alt ( â¦?,?â¦ â¢ â¡â¡* ? )	lprs_ldrop lprs_cprs lprs_lprs	+
- -	+		cprs ( â¦?,?â¦ â¢ ? â¡* ?)	cprs_lift cprs_cprs	+	restricted ref. for 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¢ ? â[?] ? )	lsubc_ldrop lsubc_ldrops lsubc_lsuba	+	atomic arity assignment	aaa ( â¦?,?â¦ â¢ ? â ? )	aaa_drops aaa_fqus aaa_lfeq aaa_aaa		+
+		support for abstract computation properties	acp	acp_cr ( â¦?,?,?â¦ Ïµ[?] ã?ã )	acp_aaa	+	restricted ref. for local env.	lsubr ( ? â« ? )	lsubr_length lsubr_drops lsubr_lsubr
reduction	"big tree" parallel reduction	fpbc ( â¦?,?,?â¦ â»[?,?] â¦?,?,?â¦ )	fpbc_lift	- -	+
+		+	equivalence for closures on referred entries	ffeq ( â¦?,?,?â¦ â¡ â¦?,?,?â¦ )	ffeq_freq		fpb ( â¦?,?,?â¦ â½[?,?] â¦?,?,?â¦ )	fpb_lift	- -	+
+		context-sensitive extended normal forms	cnx ( â¦?,?â¦ â¢ ð[?,?]â¦?â¦ )	cnx_lift cnx_crx cnx_cix	+	equivalence for local environments on referred entries	lfeq ( ? â¡[?] ? )	lfeq_length lfeq_lreq lfeq_fqup lfeq_lfeq		+
+		context-sensitive extended reduction	lpx ( â¦?,?â¦ â¢ â¡[?,?] ? )	lpx_leq lpx_ldrop lpx_lleq lpx_aaa	+	generic extension on referred entries	lfxs ( ? â¦»*[?,?] ? )	lfxs_length lfxs_fqup lfxs_lfxs		+
+		+	context-sensitive free variables	frees ( ? â¢ ð*â¦?â¦ â¡ ? )	frees_weight frees_lreq frees_frees		cpx ( â¦?,?â¦ â¢ ? â¡[?,?] ? )	cpx_leq cpx_lift cpx_cix	- -	+
- -	context-sensitive extended irreducible forms	cix ( â¦?,?â¦ â¢ ð[?,?]â¦?â¦ )	cix_append cix_lift	+	s-computation	iterated structural successor for closures	fqus ( â¦?,?,?â¦ â* â¦?,?,?â¦ )	fqus_weight fqus_drops fqus_fqup fqus_fqus		+
+		context-sensitive extended reducible forms	crx ( â¦?,?â¦ â¢ ð[?,?]â¦?â¦ )	crx_append crx_lift	+		+	fqup ( â¦?,?,?â¦ â+ â¦?,?,?â¦ )	fqup_weight fqup_drops fqup_fqup
- -	context-sensitive normal forms	cnr ( â¦?,?â¦ â¢ ðâ¦?â¦ )	cnr_lift cnr_crr cnr_cir	- -	+
- -	context-sensitive reduction	lpr ( â¦?,?â¦ â¢ â¡ ? )	lpr_ldrop lpr_lpr	+	s-transition	structural successor for closures	fquq ( â¦?,?,?â¦ ââ¸® â¦?,?,?â¦ )	fquq_length fquq_weight		+
+		+		cpr ( â¦?,?â¦ â¢ ? â¡ ? )	cpr_lift cpr_cir	+	fqu ( â¦?,?,?â¦ â â¦?,?,?â¦ )	fqu_length fqu_weight		+
+	relocation	generic slicing for local environments	drops_vector ( â¬*[?,?] ? â¡ ? )		context-sensitive irreducible forms	cir ( â¦?,?â¦ â¢ ðâ¦?â¦ )	cir_append cir_lift	+		+
+		context-sensitive reducible forms	crr ( â¦?,?â¦ â¢ ðâ¦?â¦ )	crr_append crr_lift	+		+	drops ( â¬*[?,?] ? â¡ ? )	drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops
unfold	unfold	unfold ( â¦?,?â¦ â¢ ? â§«* ? )	- -	- -	+
- -	iterated static type assignment	lsstas ( â¦?,?â¦ â¢ ? â¢*[?,?,?] ? )	lsstas_alt ( â¦?,?â¦ â¢ ? â¢â¢*[?,?,?] ? )	lsstas_lift lsstas_aaa lsstas_lsstas	+
static typing	local env. ref. for atomic arity assignment	lsuba ( ? â¢ ? ââ ? )	lsuba_ldrop lsuba_aaa lsuba_lsuba	+	generic relocation for terms	lifts_vector ( â¬*[?] ? â¡ ? )	lifts_lifts_vector		+
+		atomic arity assignment	aaa ( â¦?,?â¦ â¢ ? â ? )	aaa_lift aaa_lifts aaa_da aaa_ssta aaa_aaa	+		+	lifts ( â¬*[?] ? â¡ ? )	lifts_simple lifts_weight lifts_lifts
- -	stratified static type assignment	ssta ( â¦?,?â¦ â¢ ? â¢[?,?] ? )	ssta_lift ssta_ssta	- -	+
+		local env. ref. for degree assignment	lsubd ( ? â¢ ? âªâ ? )	lsubd_da lsubd_lsubd	+	ranged equivalence for local environments	lreq ( ? â¡[?] ? )	lreq_length lreq_lreq		+
+		degree assignment	da ( â¦?,?â¦ â¢ ? âª[?,?] ? )	da_lift da_da	+	generic entrywise extension	lexs ( ? â¦»*[?,?,?] ? )	lexs_length lexs_lexs		+
- -	parameters	sh	sd	- -	- -
substitution	restricted local env. ref.	lsubr ( ? â ? )	lsubr_lsubr	- -	- -
- -	iterated structural successor for closures	fqus ( â¦?,?,?â¦ â* â¦?,?,?â¦ )	fqus_alt fqus_lleq fqus_fqus	+	grammar	append for local environments	append ( ? @@ ? )	append_length		+
- -	+		fqup ( â¦?,?,?â¦ â+ â¦?,?,?â¦ )	fqup_lleq fqup_fqup	+	context-sensitive equivalences for terms	ceq	ceq_ceq		+
+		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¯{?,?} )		+
+		+	internal syntax	genv		lifts ( â§*[?] ? â¡ ? )	lifts_lift lifts_lifts	+		- -
- -	support for generic relocation	gr2 ( @â¦?,?â¦ â¡ ? )	gr2_plus ( ? + ? )	gr2_minus ( ? â ? â¡ ? )	gr2_gr2
relocation	structural successor for closures	fquq ( â¦?,?,?â¦ ââ¸® â¦?,?,?â¦ )	fquq_alt ( â¦?,?,?â¦ âââ¸® â¦?,?,?â¦ )	fquq_lleq	+
+		+		fqu ( â¦?,?,?â¦ â â¦?,?,?â¦ )	fqu_lleq	- -	+	lenv	lenv_weight ( â¯{?} )	lenv_length ( \|?\| )
+		lazy equivalence for local environments	lleq ( ? â[?,?] ? )	lleq_lleq	- -	+		term	term_weight ( â¯{?} )	term_simple ( ðâ¦?â¦ )	term_vector ( â¶?.? )
- -	global env. slicing	gdrop ( â©[?] ? â¡ ? )	gdrop_gdrop	+		+
+	item		basic local env. slicing	ldrop ( â©[?,?] ? â¡ ? )	ldrop_append ldrop_lpx_sn ldrop_leq ldrop_ldrop	+		+
+		basic term relocation	lift_vector ( â§[?,?] ? â¡ ? )	lift_lift_vector	+	external syntax	aarity		+
- -	- -	lift ( â§[?,?] ? â¡ ? )	lift_lift	- -	- -
grammar	equivalence for local environments	leq ( ? â[?,?] ? )	- -	- -	- -
- -	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	- -	- -	+

- -

Physical Structure of the Specification

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

+ $\lambda\delta rainbow rule$

@@ -1238,6 +795,6 @@

Last update: Wed, 04 Dec 2013 16:42:13 +0100

- +

Last update: Sat, 21 May 2016 22:22:39 +0200