List/Parigot.bruijn

# MIT License, Copyright (c) 2024 Marvin Borner
# see "on the representation of data in lambda-calculus" (Parigot 1989)
# constant append/snoc

# empty list element
empty [0] ⧗ (Parigot a)

# prepends an element to a list
cons [[[[0 3 (2 1)]]]] ⧗ a → (Parigot a) → (Parigot a)

…:… cons

# returns the head of a list or k
head [0 [0] [[1]]] ⧗ (Parigot a) → a

:test (head ('a' : ('b' : ('c' : empty)))) ('a')
:test (head empty) ([[1]])

# returns the tail of a list or &ki
tail [[1 0 [[0]]]] ⧗ (Parigot a) → (Parigot a)

:test (tail ('a' : ('b' : ('c' : empty)))) ('b' : ('c' : empty))
:test (tail empty) ([0 [[0]]])

# appends two lists
append [[[2 (1 0)]]] ⧗ (Parigot a) → (Parigot a) → (Parigot a)

…++… append

:test (append ('a' : ('b' : empty)) ('c' : ('d' : empty))) ('a' : ('b' : ('c' : ('d' : empty))))

# appends an element to a list
snoc [[[2 [0 2 1]]]] ⧗ (Parigot a) → a → (Parigot a)

…;… snoc

:test (snoc ('a' : ('b' : empty)) 'c') ('a' : ('b' : ('c' : empty)))

iter [[[0 ι ρ ρ]]]
	ρ [[3 (1 0 0)]]
	ι [[4]]