lambda_delta version 2

This is a summary of the "block structure" of the System's syntactic items and reductions.

domain	block	leader	applicator (with →θ)*	reduction	→ζ *	reference *
{X \| Γ ⊢ X : W}	local typed abstraction *	Γ ⊢ +λW	ⓐV	→β	no	#i
	local typed declaration **	Γ ⊢ -λW	ⓐV	→β	no	#i
	global typed declaration ***	Γ ⊢ pλW	no	no	no	$p
	native type annotation *	Γ ⊢ ⓝW	no	no	yes	no
{X \| Γ ⊢ X = V}	local abbreviation *	Γ ⊢ +δV	no	local →δ	yes	#i
	local definition **	Γ ⊢ -δV	no	local →δ	no	#i
	global definition ***	Γ ⊢ pδV	no	global →δ	no	$p
no	sort ****	Γ ⊢ ⋆k	no	no	no	no

* In terms only. ** In terms and local environments only. *** In global environments only. **** Sort level k in terms only.

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

category	objects
sizes	files	204	bytes	742579
propositions	theorems	74	lemmas	889	total	963
concepts	declared	40	defined	73	total	113

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).

component	plane	files
dynamic typing	stratified native validity	snv ( ⦃?,?⦄ ⊩ ? :[?] )	snv_lift snv_aaa
equivalence	focalized equivalence	lfpcs ( ⦃?⦄ ⬌* ⦃?⦄ )	lfpcs_aaa lfpcs_lfprs lfpcs_lfpcs
	context-sensitive equivalence	cpcs ( ? ⊢ ? ⬌* ? )	cpcs_ltpss cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs
conversion	focalized conversion	lfpc ( ⦃?⦄ ⬌ ⦃?⦄ )	lfpc_lfpc
	context-sensitive conversion	cpc ( ? ⊢ ? ⬌ ? )	cpc_cpc
computation	extended computation	xprs ( ⦃?,?⦄ ⊢ ? ➸*[?] ? )	xprs_lift xprs_aaa xprs_cprs
	weakly normalizing computation	cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )	cpe_cpe
	strongly normalizing computation	csn_vector ( ? ⊢ ⬊* ? )	csn_cpr_vector csn_tstc_vector csn_aaa
		csn ( ? ⊢ ⬊* ? )	csn_alt ( ? ⊢ ⬊⬊* ? )	csn_lift csn_cpr csn_lfpr
	focalized computation	lfprs ( ⦃?⦄ ➡* ⦃?⦄ )	lfprs_aaa lfprs_cprs lfprs_lfprs
		fprs ( ⦃?,?⦄ ➡* ⦃?,?⦄ )	fprs_aaa fprs_fprs
	context-sensitive computation	cprs (? ⊢ ? ➡* ?)	cprs_lift cprs_delift cprs_aaa cprs_ltpr cprs_lfpr cprs_cprs cprs_lfprs cprs_tstc cprs_tstc_vector
	context-free computation	ltprs ( ? ➡* ? )	ltprs_alt ( ? ➡➡* ? )	ltprs_ldrop ltprs_ltprs
		tprs ( ? ➡* ?)	tprs_lift tprs_tprs
	local env. ref. for abstract candidates of reducibility	lsubc ( ? ⊑[?] ? )	lsubc_ldrop lsubc_ldrops lsubc_lsuba
	support for abstract computation properties	acp	acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )	acp_aaa
reducibility	extended reduction	xpr ( ⦃?,?⦄ ⊢ ? ➸[?] ? )	xpr_lift xpr_aaa
	context-sensitive focalized reduction	cfpr ( ? ⊢ ⦃?,?⦄ ➡ ⦃?,?⦄ )	cnfpr_ltpss cfpr_aaa cfpr_cpr cfpr_cfpr
	context-free focalized reduction	lfpr ( ⦃?⦄ ➡ ⦃?⦄ )	lfpr_alt ( ⦃?⦄ ➡➡ ⦃?⦄ )	lfpr_aaa lfpr_cpr lfpr_fpr lfpr_lfpr
		fpr ( ⦃?,?⦄ ➡ ⦃?,?⦄ )	fpr_cpr fpr_fpr
	context-sensitive normal forms	cnf ( ? ⊢ 𝐍⦃?⦄ )	cnf_lift cnf_cif
	context-sensitive reduction	cpr ( ? ⊢ ? ➡ ? )	cpr_lift cpr_tpss cpr_ltpss cpr_delift cpr_aaa cpr_ltpr cpr_cpr
	context-sensitive reducible forms	crf ( ? ⊢ 𝐑⦃?⦄ )	crf_append	cif ( ? ⊢ 𝐈⦃?⦄ )	cif_append
	context-free normal forms	thnf ( 𝐇𝐍⦃?⦄ )
	context-free reduction	ltpr ( ? ➡ ? )	ltpr_ldrop ltpr_tps ltpr_ltpss_dx ltpr_ltpss_sn ltpr_aaa ltpr_ltpr
		tpr ( ? ➡ ? )	tpr_lift tpr_tps tpr_tpss tpr_delift tpr_tpr
unwind
static typing	local env. ref. for stratified static type assignment	lsubss ( ? ⁝⊑ ? )	lsubss_ldrop lsubss_ssta lsubss_lsubss
	stratified static type assignment	ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )	ssta_lift ssta_ltpss_dx ssta_ltpss_sn ssta_aaa ssta_ssta
	local env. ref. for atomic arity assignment	lsuba ( ? ⁝⊑ ? )	lsuba_ldrop lsuba_aaa lsuba_lsuba
	atomic arity assignment	aaa ( ? ⊢ ? ⁝ ? )	aaa_lift aaa_lifts aaa_ltpss_dx aaa_ltpss_sn aaa_aaa
	parameters	sh	sd
unfold	basic local env. thinning	thin ( ? ▼*[?,?] ≡ ? )	thin_ldrop thin_delift
	inverse basic term relocation	delift ( ? ⊢ ? ▼*[?,?] ≡ ? )	delift_alt ( ? ⊢ ? ▼▼*[?,?] ≡ ? )	delift_lift delift_tpss delift_ltpss delift_delift
	partial unfold	ltpss_sn ( ? ⊢ ▶*[?,?] ? )	ltpss_sn_alt ( ? ⊢ ▶▶*[?,?] ? )	ltpss_sn_ldrop ltpss_sn_tps ltpss_sn_tpss ltpss_sn_ltpss_sn
		ltpss_dx ( ? ▶*[?,?] ? )	ltpss_dx_ldrop ltpss_dx_tps ltpss_dx_tpss ltpss_dx_ltpss_dx
		tpss ( ? ⊢ ? ▶*[?,?] ? )	tpss_alt ( ? ⊢ ? ▶▶*[?,?] ? )	tpss_lift	tpss_tpss
	generic local env. slicing	ldrops ( ⇩*[?] ? ≡ ? )	ldrops_ldrop ldrops_ldrops
	generic term relocation	lifts_vector ( ⇧*[?] ? ≡ ? )	lifts_lift_vector
		lifts ( ⇧*[?] ? ≡ ? )	lifts_lift lifts_lifts
	support for generic relocation	gr2 ( @⦃?,?⦄ ≡ ? )	gr2_plus ( ? + ? )	gr2_minus ( ? ▭ ? ≡ ? )	gr2_gr2
substitution	parallel substitution	tps ( ? ⊢ ? ▶[?,?] ? )	tps_lift tps_tps
	global env. slicing	gdrop ( ⇩[?] ? ≡ ? )	gdrop_gdrop
	basic local env. slicing	ldrop ( ⇩[?,?] ? ≡ ? )	ldrop_append ldrop_lpx ldrop_sfr ldrop_ldrop
	local env. ref. for substitution	lsubs ( ? ≼[?,?] ? )	(lsubs_lsubs)	lsubs_sfr ( ≽[?,?] ? )
	basic term relocation	lift_vector ( ⇧[?,?] ? ≡ ? )	lift_lift_vector
		lift ( ⇧[?,?] ? ≡ ? )	lift_lift
grammar	same head term form	tshf ( ? ≈ ? )	(tshf_tshf)
	same top term constructor	tstc ( ? ≃ ? )	tstc_tstc tstc_vector
	closures	cl_shift ( ? @@ ? )	cl_weight ( #{?,?} )
	internal syntax	genv
		lenv	lenv_weight ( #{?} )	lenv_length ( \|?\| )	lenv_append ( ? @@ ? )	lenv_px lenv_px_bi
		term	term_weight ( #{?} )	term_simple ( 𝐒⦃?⦄ )	term_vector
		item
	external syntax	aarity

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