#lang racket/base

(define lam1

(case-lambda

[(a b c) (* a b c)]

[(a b) (+ a b)]))

(displayln (procedure-arity lam1))

(define lam2

(case-lambda

[() "duh"]

[(a b c) (* a b c)]

[(a b) (+ a b)]

[v (apply + v)]))

(equal? (procedure-arity lam2) (make-arity-at-least 0))

(define lam3

(case-lambda

[() "duh"]

[(a b c) (* a b c)]

[(a b) (+ a b)]

[(a b c . d) (+ a b c (apply * d))]

[v (apply * v)]))

(equal? (procedure-arity lam3) (make-arity-at-least 0))

(define lam4

(case-lambda

[(a b c) (* a b c)]

[(a b c d e . f) (+ a b)]))

(equal? (procedure-arity lam4) (list 3 (make-arity-at-least 5)))

(define lam5

(case-lambda

[(a b c) (* a b c)]

[(a b c d e . f) (* a b c)]

[(a b c d e f g h . i) (+ a b)]))

(equal? (procedure-arity lam5) (list 3 (make-arity-at-least 5)))

(define lam6

(case-lambda

[(a b c d e f g h . i) (+ a b)]

[(a b c) (* a b c)]))

(equal? (procedure-arity lam6) (list 3 (make-arity-at-least 8)))

(define lam7

(case-lambda

[(a b c d e f g h . i) (+ a b)]

[(a b c . d) (* a b c)]))

(equal? (procedure-arity lam7) (make-arity-at-least 3))