This is derived from a CPSed interpreter.
If you understand so called 2-level lambda notations (in Olivier Danvy’s old papers), then it’s trivial.
(define cps
(λ (expr C)
(match expr
[(? symbol? x) (C x)]
[`(λ (,x) ,body)
(C `(λ (,x k) ,(cps body (λ (v) `(k ,v)))))]
[`(,rator ,rand)
(cps rator
(λ (v₀)
(cps rand
(λ (v₁)
(let ([v (gensym 'v)])
`(,v₀ ,v₁
(λ (,v) ,(C v))))))))])))