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 ***

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+ 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 ****

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+ citations +

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(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

328

characters

565577

nodes

1606912

sizes

files

138

characters

109280

nodes

546141

propositions

theorems

105

lemmas

1109

total

1214

propositions

theorems

lemmas

395

total

440

concepts

declared

defined

total

128

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). +

+ 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. +

- In progress. - Closure of context-sensitive extended computation - for native validity. + 2014 October 28. + Î»Î´ version 2A1 is released.

- 2014 January 20. - Parametrized slicing for local environments + 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. + 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	- -	- -	+	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	+	rt-transition	counted context-sensitive rt-transition	cpg ( â¦?,?â¦ â¢ ? â¡[?,?] ? )	cpg_simple cpg_drops cpg_lsubr		+
equivalence	decomposed extended equivalence	cpes ( â¦?,?â¦ â¢ ? â¢â¬[?,?] ? )	cpes_cpds	+	static typing	parameters	sh	sd		+
- -	context-sensitive equivalence	cpcs ( â¦?,?â¦ â¢ ? â¬* ? )	cpcs_aaa cpcs_cprs cpcs_cpcs	+		+	restricted ref. for atomic arity assignment	lsuba ( ? â¢ ? â«â ? )	lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba
conversion	context-sensitive conversion	cpc ( â¦?,?â¦ â¢ ? â¬ ? )	cpc_cpc	- -	+
computation	evaluation for context-sensitive extended reduction	cpxe ( â¦?,?â¦ â¢ â¡*[?,?] ðâ¦?â¦ )	+		+	atomic arity assignment	aaa ( â¦?,?â¦ â¢ ? â ? )	aaa_drops aaa_fqus aaa_lfeq aaa_aaa		+
- -	evaluation for context-sensitive reduction	cpre ( â¦?,?â¦ â¢ â¡* ðâ¦?â¦ )	cpre_cpre	+		+	restricted ref. for local env.	lsubr ( ? â« ? )	lsubr_length lsubr_drops lsubr_lsubr
- -	strongly normalizing "big tree" computation	fsb ( â¦?,?â¦ â¢ â¦¥[?,?] ? )	fsb_alt ( â¦?,?â¦ â¢ â¦¥â¦¥[?,?] ? )	fsb_aaa fsb_csx	+
+		strongly normalizing extended computation	lcosx ( ? â¢ â§¤â¬*[?,?,?] ? )	lcosx_cpxs	+	equivalence for closures on referred entries	ffeq ( â¦?,?,?â¦ â¡ â¦?,?,?â¦ )	ffeq_freq		+
- -	+		lsx ( ? â¢ ââ¬*[?,?,?,?] ? )	lsx_ldrop lsx_cpxs lsx_csx	+	equivalence for local environments on referred entries	lfeq ( ? â¡[?] ? )	lfeq_length lfeq_lreq lfeq_fqup lfeq_lfeq		+
+		+	generic extension on referred entries	lfxs ( ? â¦»*[?,?] ? )	lfxs_length lfxs_fqup lfxs_lfxs		csx_vector ( â¦?,?â¦ â¢ â¬*[?,?] ? )	csx_tstc_vector csx_aaa	- -	+
+		+	context-sensitive free variables	frees ( ? â¢ ð*â¦?â¦ â¡ ? )	frees_weight frees_lreq frees_frees		csx ( â¦?,?â¦ â¢ â¬*[?,?] ? )	csx_alt ( â¦?,?â¦ â¢ â¬â¬*[?,?] ? )	csx_lift csx_lpx csx_lpxs csx_fpbs	+
- -	"big tree" parallel computation	fpbg ( â¦?,?,?â¦ >â[?,?] â¦?,?,?â¦ )	fpbg_lift fpbg_fpns fpbg_fpbg	+	s-computation	iterated structural successor for closures	fqus ( â¦?,?,?â¦ â* â¦?,?,?â¦ )	fqus_weight fqus_drops fqus_fqup fqus_fqus		+
+		+		fpbc ( â¦?,?,?â¦ â»â[?,?] â¦?,?,?â¦ )	fpbc_fpns fpbc_fpbs	+	fqup ( â¦?,?,?â¦ â+ â¦?,?,?â¦ )	fqup_weight fqup_drops fqup_fqup		+
- -	+	s-transition	structural successor for closures	fquq ( â¦?,?,?â¦ ââ¸® â¦?,?,?â¦ )	fquq_length fquq_weight		fpbu ( â¦?,?,?â¦ â»[?,?] â¦?,?,?â¦ )	fpbu_lift fpbu_fpns	- -	+
- -	+		fpbs ( â¦?,?,?â¦ â¥[?,?] â¦?,?,?â¦ )	fpbs_alt ( â¦?,?,?â¦ â¥â¥[?,?] â¦?,?,?â¦ )	fpbs_lift fpbs_aaa fpbs_fpns fpbs_fpbs	+
+	fqu ( â¦?,?,?â¦ â â¦?,?,?â¦ )	fqu_length fqu_weight		parallel computation for "big tree" normal forms	fpns ( â¦?,?,?â¦ â¢ ââ¡*[?,?] â¦?,?,?â¦ )	fpns_fpns	- -	- -
- -	decomposed extended computation	cpds ( â¦?,?â¦ â¢ ? â¢â¡[?,?] ? )	cpds_lift cpds_aaa cpds_cpds	- -	- -
- -	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	- -
- -	- -	cpxs ( â¦?,?â¦ â¢ ? â¡*[?,?] ? )	cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_cpys cpxs_lleq cpxs_aaa cpxs_cpxs	- -	- -
- -	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	- -	- -
- -	local env. ref. for abstract candidates of reducibility	lsubc ( ? â¢ ? â[?] ? )	lsubc_ldrop lsubc_ldrops lsubc_lsuba	- -	+
- -	support for abstract computation properties	acp	acp_cr ( â¦?,?,?â¦ Ïµ[?] ã?ã )	acp_aaa	+	relocation	generic slicing for local environments	drops_vector ( â¬*[?,?] ? â¡ ? )
reduction	"big tree" parallel reduction	fpb ( â¦?,?,?â¦ â½[?,?] â¦?,?,?â¦ )	fpb_lift fpb_aaa	+		+
+		normal forms for context-sensitive extended reduction	cnx ( â¦?,?â¦ â¢ â¡[?,?] ðâ¦?â¦ )	cnx_lift cnx_crx cnx_cix	- -	- -
+		context-sensitive extended reduction	lpx ( â¦?,?â¦ â¢ â¡[?,?] ? )	lpx_ldrop lpx_cpys lpx_lleq lpx_aaa	+	drops ( â¬*[?,?] ? â¡ ? )	drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops		+
+		+	generic relocation for terms	lifts_vector ( â¬*[?] ? â¡ ? )	lifts_lifts_vector		cpx ( â¦?,?â¦ â¢ ? â¡[?,?] ? )	cpx_lift cpx_cpys cpx_lleq cpx_cix	- -	+
- -	irreducible forms for context-sensitive extended reduction	cix ( â¦?,?â¦ â¢ â¡[?,?] ðâ¦?â¦ )	cix_lift	- -	+
+		reducible forms for context-sensitive extended reduction	crx ( â¦?,?â¦ â¢ â¡[?,?] ðâ¦?â¦ )	crx_lift	+	lifts ( â¬*[?] ? â¡ ? )	lifts_simple lifts_weight lifts_lifts		+
+		normal forms for context-sensitive reduction	cnr ( â¦?,?â¦ â¢ â¡ ðâ¦?â¦ )	cnr_lift cnr_crr cnr_cir	+	ranged equivalence for local environments	lreq ( ? â¡[?] ? )	lreq_length lreq_lreq		+
+		context-sensitive reduction	lpr ( â¦?,?â¦ â¢ â¡ ? )	lpr_ldrop lpr_lpr	+	generic entrywise extension	lexs ( ? â¦»*[?,?,?] ? )	lexs_length lexs_lexs		+
- -	- -	cpr ( â¦?,?â¦ â¢ ? â¡ ? )	cpr_lift cpr_cir	+	grammar	append for local environments	append ( ? @@ ? )	append_length		+
+		irreducible forms for context-sensitive reduction	cir ( â¦?,?â¦ â¢ â¡ ðâ¦?â¦ )	cir_lift	+	context-sensitive equivalences for terms	ceq	ceq_ceq		+
+		reducible forms for context-sensitive reduction	crr ( â¦?,?â¦ â¢ â¡ ðâ¦?â¦ )	crr_lift	+	same top term structure	tsts ( ? â ? )	tsts_tsts tsts_vector		+
unfold	unfold	unfold ( â¦?,?â¦ â¢ ? â§«* ? )	+		+	closures	cl_weight ( â¯{?,?,?} )	cl_restricted_weight ( â¯{?,?} )		+
+		iterated static type assignment	lsstas ( â¦?,?â¦ â¢ ? â¢*[?,?,?] ? )	lsstas_alt ( â¦?,?â¦ â¢ ? â¢â¢*[?,?,?] ? )	lsstas_lift lsstas_aaa lsstas_lsstas	+	internal syntax	genv
static typing	local env. ref. for atomic arity assignment	lsuba ( ? â¢ ? ââ ? )	lsuba_ldrop lsuba_aaa lsuba_lsuba	- -	- -
- -	atomic arity assignment	aaa ( â¦?,?â¦ â¢ ? â ? )	aaa_lift aaa_lifts aaa_fqus aaa_da aaa_ssta aaa_aaa	+		+
+		stratified static type assignment	ssta ( â¦?,?â¦ â¢ ? â¢[?,?] ? )	ssta_lift ssta_ssta	+		+	lenv	lenv_weight ( â¯{?} )	lenv_length ( \|?\| )
- -	local env. ref. for degree assignment	lsubd ( ? â¢ ? âªâ ? )	lsubd_da lsubd_lsubd	+		+		term	term_weight ( â¯{?} )	term_simple ( ðâ¦?â¦ )	term_vector ( â¶?.? )
+		degree assignment	da ( â¦?,?â¦ â¢ ? âª[?,?] ? )	da_lift da_da	+		+	item
- -	parameters	sh	sd	- -	+
substitution	lazy equivalence for local environments	lleq ( ? â[?,?] ? )	lleq_alt ( ? ââ[?,?] ? )	lleq_ldrop lleq_fqus lleq_lleq lleq_ext	+
- -	contxt-sensitive extended multiple substitution	cpys ( â¦?,?â¦ â¢ ? â¶*[?,?] ? )	cpys_alt ( â¦?,?â¦ â¢ ? â¶â¶*[?,?] ? )	cpys_lift cpys_cpys	+
+	external syntax	aarity		iterated structural successor for closures	fqus ( â¦?,?,?â¦ â* â¦?,?,?â¦ )	fqus_alt fqus_fqus	+		- -
- -	- -	fqup ( â¦?,?,?â¦ â+ â¦?,?,?â¦ )	fqup_fqup	- -	- -
- -	iterated 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¦?,?â¦ â¡ ? )	gr2_plus ( ? + ? )	gr2_minus ( ? â ? â¡ ? )	gr2_gr2
relocation	contxt-sensitive extended ordinary substitution	cpy ( â¦?,?â¦ â¢ ? â¶[?,?] ? )	cpy_lift cpy_cpy	- -	- -
- -	restricted local env. ref.	lsubr ( ? â ? )	lsubr_lsubr	- -	- -
- -	local env. ref. for extended substitution	lsuby ( ? âÃ[?,?] ? )	lsuby_lsuby	- -	- -
- -	structural successor for closures	fquq ( â¦?,?,?â¦ ââ¸® â¦?,?,?â¦ )	fquq_alt ( â¦?,?,?â¦ âââ¸® â¦?,?,?â¦ )	- -	- -
- -	- -	fqu ( â¦?,?,?â¦ â â¦?,?,?â¦ )	- -	- -	- -
- -	global env. slicing	gdrop ( â©[?] ? â¡ ? )	gdrop_gdrop	- -	- -
- -	basic local env. slicing	ldrop ( â©[?,?,?] ? â¡ ? )	ldrop_lpx_sn ldrop_leq ldrop_ldrop	- -	- -
- -	basic term relocation	lift_vector ( â§[?,?] ? â¡ ? )	lift_lift_vector	- -	- -
- -	- -	lift ( â§[?,?] ? â¡ ? )	lift_lift	- -	- -
grammar	equivalence for local environments	leq ( ? â[?,?] ? )	leq_leq	- -	- -
- -	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_weight ( â¯{?,?,?} )	cl_restricted_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. -

+ $\lambda\delta rainbow rule$

@@ -1318,6 +781,6 @@

Last update: Sat, 22 Feb 2014 12:36:18 +0100

- +

Last update: Thu, 19 May 2016 12:17:40 +0200