Defining racket contracts with a custom predicate

Question

I'm just starting to learn about contracts (via exercism.io) and so I have made a contract that is:

[step1 (-> (and/c number?
                  less-than-one-hundred?)
            string?)]

What I think I'm saying is the function will take a number less than one hundred (which is a function defined as:

(define (less-than-one-hundred? n)
  (< n 100))

But when I call the function like this:

(step1 100)

No contract violation. What am I doing wrong?

Answer 1

Here's a concrete example of what Soegaard's answer is saying:

def-step1.rkt

#lang racket

(provide (contract-out
          [step1 (-> (and/c number?
                            less-than-one-hundred?)
                     string?)]))

(define (less-than-one-hundred? n)
  (< n 100))

(define (step1 x) "")

use-step1.rkt

#lang racket

(require "def-step1.rkt")

(step1 100)

This produces a contract violation like you expect, and in particular, it blames use-step1.rkt, a different "contract party" than def-step1.rkt where the contract came from:

step1: contract violation
  expected: less-than-one-hundred?
  given: 100
  in: an and/c case of
      the 1st argument of
      (->
       (and/c number? less-than-one-hundred?)
       string?)
  contract from: .../def-step1.rkt
  blaming: .../use-step1.rkt
   (assuming the contract is correct)