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}	typed abstraction **	Γ ⊢ λW	ⓐV	→β	no	#i
	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
	global abbreviation ***	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	158	bytes	591982
propositions	theorems	60	lemmas	650	total	710
concepts	declared	37	defined	47	total	84

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
examples
dynamic typing	local env. ref. for native type assignment	lsubn ( ? ⊢ ? :⊑ ? )	lsubn_ldrop	lsubn_cpcs	lsubn_nta
	native type assignment	nta ( ⦃?,?⦄ ⊢ ? : ? )	nta_alt ( ⦃?,?⦄ ⊢ ? :: ? )	nta_lift	nta_ltpss	nta_thin	nta_sta	nta_nta
equivalence	context-sensitive equivalence	lcpcs ( ? ⊢ ⬌* ? )	lcpcs_aaa	lcpcs_lcprs	lcpcs_lcpcs
		cpcs ( ? ⊢ ? ⬌* ? )	cpcs_ltpss	cpcs_delift	cpcs_ltpr	cpcs_cprs	cpcs_cpcs
conversion	context-sensitive conversion	lcpc ( ? ⊢ ⬌ ? )	lcpc_lcpc
		cpc ( ? ⊢ ? ⬌ ? )	cpc_cpc
computation	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_lcpr
	context-sensitive computation	lcprs ( ? ⊢ ➡* ? )	lcprs_aaa	lcprs_cprs	lcprs_lcprs
		cprs (? ⊢ ? ➡* ?)	cprs_lift	cprs_delift	cprs_ltpr	cprs_lcpr	cprs_cprs	cprs_lcprs	cprs_tstc	cprs_tstc_vector
	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	context-sensitive normal forms	cnf ( ? ⊢ 𝐍⦃?⦄ )	cnf_lift
	context-sensitive reduction	lcpr ( ? ⊢ ➡ ? )	lcpr_aaa	lcpr_cpr	lcpr_lcpr
		cpr ( ? ⊢ ? ➡ ? )	cpr_lift	cpr_ltpss	cpr_delift	cpr_ltpr	cpr_cpr
	context-free normal forms	twhnf ( 𝐖𝐇𝐍⦃?⦄ )	tnf ( 𝐍⦃?⦄ )	tnf_tif
	context-free reduction	ltpr ( ? ➡ ? )	ltpr_ldrop	ltpr_tps	ltpr_ltpss	ltpr_aaa	ltpr_ltpr
		tpr ( ? ➡ ? )	tpr_lift	tpr_tpss	tpr_delift	tpr_tpr
	context-free reducible forms	trf ( 𝐑⦃?⦄ )	tif ( 𝐈⦃?⦄ )
static typing	static type assignment	sta ( ⦃?,?⦄ ⊢ ? • ? )	sta_lift	sta_sta
	local env. ref. for atomic arity assignment	lsuba ( ? ⁝⊑ ? )	lsuba_ldrop	lsuba_aaa	lsuba_lsuba
	atomic arity assignment	aaa ( ? ⊢ ? ⁝ ? )	aaa_lift	aaa_lifts	aaa_ltpss	aaa_aaa
	parameters	sh
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 ( ? ▶*[?,?] ? )	ltpss_ldrop	ltpss_tps	ltpss_tpss	ltpss_ltpss
		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_ldrop	ldrop_sfr
	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 ( \|?\| )
		term	term_weight ( #[?] )	term_simple ( 𝐒⦃?⦄ )	term_vector
		item
	external syntax	aarity

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