Steps

Sample programs

Pluck the 4th element from the arguments

delve 3 ^A ^B ^C ^D ^E ^F

Pick abstraction with Church booleans

if not or true false (^A) (^B)

Add 2 and 1 as Church numerals

add 2 1

Add 3 to first element of pair ("first" to get it out)

map-pair (add 3) pair 1 2

Side-effect 6 times for testing

apply 6 (tally)

Duplicate all inputs on right

apply Y (copy under (apply) swap) ^A ^B ^C

Count forever

apply Y (under (apply swap) copy add 1 swap) 0

Count forever (bind)

apply Y (bind (f) (bind (y) (y apply f y) add 1)) 0

Fibonacci sequence

apply Y (bind (f) (bind (x) (bind (y) (bind (z) (x apply f z x) add x y)))) 1 0

Factorials (up to 24 at step limit 1000)

apply Y (bind (f) (bind (x) (bind (y) (bind (z) (z apply f z add 1 y) mul x y)))) 1 1

Predefined named terms