7.6 Abstract Contracts using #:exists and #:∃

The contract system provides existential contracts that can protect abstractions, ensuring that clients of your module cannot depend on the precise representation choices you make for your data structures.

You can type #:exists instead of #:∃ if you cannot easily type unicode characters; in DrRacket, typing \exists followed by either alt-\ or control-\ (depending on your platform) will produce .

The contract-out form allows you to write

#:∃ name-of-a-new-contract

as one of its clauses. This declaration introduces the variable name-of-a-new-contract, binding it to a new contract that hides information about the values it protects.

As an example, consider this (simple) implementation of a queue datastructure:
#lang racket
(define empty '())
(define (enq top queue) (append queue (list top)))
(define (next queue) (car queue))
(define (deq queue) (cdr queue))
(define (empty? queue) (null? queue))
  [empty (listof integer?)]
  [enq (-> integer? (listof integer?) (listof integer?))]
  [next (-> (listof integer?) integer?)]
  [deq (-> (listof integer?) (listof integer?))]
  [empty? (-> (listof integer?) boolean?)]))
This code implements a queue purely in terms of lists, meaning that clients of this data structure might use car and cdr directly on the data structure (perhaps accidentally) and thus any change in the representation (say to a more efficient representation that supports amortized constant time enqueue and dequeue operations) might break client code.

To ensure that the queue representation is abstract, we can use #:∃ in the contract-out expression, like this:
  #:∃ queue
  [empty queue]
  [enq (-> integer? queue queue)]
  [next (-> queue integer?)]
  [deq (-> queue queue)]
  [empty? (-> queue boolean?)]))

Now, if clients of the data structure try to use car and cdr, they receive an error, rather than mucking about with the internals of the queues.

See also Exists Contracts and Predicates.