7.2 Simple Contracts on Functions

A mathematical function has a domain and a range. The domain indicates the kind of values that the function can accept as arguments, and the range indicates the kind of values that it produces. The conventional notation for describing a function with its domain and range is

f : A -> B

where A is the domain of the function and B is the range.

Functions in a programming language have domains and ranges, too, and a contract can ensure that a function receives only values in its domain and produces only values in its range. A -> creates such a contract for a function. The forms after a -> specify contracts for the domains and finally a contract for the range.

Here is a module that might represent a bank account:

#lang racket

(provide (contract-out

[deposit (-> number? any)]

[balance (-> number?)]))

(define amount 0)

(define (deposit a) (set! amount (+ amount a)))

(define (balance) amount)

The module exports two functions:

• deposit, which accepts a number and returns some value that is not specified in the contract, and

• balance, which returns a number indicating the current balance of the account.

When a module exports a function, it establishes two channels of communication between itself as a “server” and the “client” module that imports the function. If the client module calls the function, it sends a value into the server module. Conversely, if such a function call ends and the function returns a value, the server module sends a value back to the client module. This client–server distinction is important, because when something goes wrong, one or the other of the parties is to blame.

If a client module were to apply deposit to 'millions, it would violate the contract. The contract-monitoring system would catch this violation and blame the client for breaking the contract with the above module. In contrast, if the balance function were to return 'broke, the contract-monitoring system would blame the server module.

A -> by itself is not a contract; it is a contract combinator, which combines other contracts to form a contract.

7.2.1 Styles of ->

If you are used to mathematical functions, you may prefer a contract arrow to appear between the domain and the range of a function, not at the beginning. If you have read How to Design Programs, you have seen this many times. Indeed, you may have seen contracts such as these in other people’s code:

(provide (contract-out

[deposit (number? . -> . any)]))

If a Racket S-expression contains two dots with a symbol in the middle, the reader re-arranges the S-expression and place the symbol at the front, as described in Lists and Racket Syntax. Thus,

(number? . -> . any)

is just another way of writing

(-> number? any)

7.2.2 any and any/c

The any contract used for deposit matches any kind of result, and it can only be used in the range position of a function contract. Instead of any above, we could use the more specific contract void?, which says that the function will always return the (void) value. The void? contract, however, would require the contract monitoring system to check the return value every time the function is called, even though the “client” module can’t do much with the value. In contrast, any tells the monitoring system not to check the return value, it tells a potential client that the “server” module makes no promises at all about the function’s return value, even whether it is a single value or multiple values.

The any/c contract is similar to any, in that it makes no demands on a value. Unlike any, any/c indicates a single value, and it is suitable for use as an argument contract. Using any/c as a range contract imposes a check that the function produces a single value. That is,

(-> integer? any)

describes a function that accepts an integer and returns any number of values, while

(-> integer? any/c)

describes a function that accepts an integer and produces a single result (but does not say anything more about the result). The function

(define (f x) (values (+ x 1) (- x 1)))

matches (-> integer? any), but not (-> integer? any/c).

Use any/c as a result contract when it is particularly important to promise a single result from a function. Use any when you want to promise as little as possible (and incur as little checking as possible) for a function’s result.

7.2.3 Rolling Your Own Contracts

The deposit function adds the given number to the value of amount. While the function’s contract prevents clients from applying it to non-numbers, the contract still allows them to apply the function to complex numbers, negative numbers, or inexact numbers, none of which sensibly represent amounts of money.

The contract system allows programmers to define their own contracts as functions:

#lang racket

(define (amount? a)

(and (number? a) (integer? a) (exact? a) (>= a 0)))

(provide (contract-out

; an amount is a natural number of cents

; is the given number an amount?

[deposit (-> amount? any)]

[amount? (-> any/c boolean?)]

[balance (-> amount?)]))

(define amount 0)

(define (deposit a) (set! amount (+ amount a)))

(define (balance) amount)

This module defines an amount? function and uses it as a contract within -> contracts. When a client calls the deposit function as exported with the contract (-> amount? any), it must supply an exact, nonnegative integer, otherwise the amount? function applied to the argument will return #f, which will cause the contract-monitoring system to blame the client. Similarly, the server module must provide an exact, nonnegative integer as the result of balance to remain blameless.

Of course, it makes no sense to restrict a channel of communication to values that the client doesn’t understand. Therefore the module also exports the amount? predicate itself, with a contract saying that it accepts an arbitrary value and returns a boolean.

In this case, we could also have used natural-number/c in place of amount?, since it implies exactly the same check:

(provide (contract-out

[deposit (-> natural-number/c any)]

[balance (-> natural-number/c)]))

Every function that accepts one argument can be treated as a predicate and thus used as a contract. For combining existing checks into a new one, however, contract combinators such as and/c and or/c are often useful. For example, here is yet another way to write the contracts above:

(define amount/c

(and/c number? integer? exact? (or/c positive? zero?)))

(provide (contract-out

[deposit (-> amount/c any)]

[balance (-> amount/c)]))

Other values also serve double duty as contracts. For example, if a function accepts a number or #f, (or/c number? #f) suffices. Similarly, the amount/c contract could have been written with a 0 in place of zero?. If you use a regular expression as a contract, the contract accepts strings and byte strings that match the regular expression.

Naturally, you can mix your own contract-implementing functions with combinators like and/c. Here is a module for creating strings from banking records:

If we want to strengthen the promise of the range contract for format-nat so that it admits only strings with digits and a single dot, we could write it like this:

#lang racket

(define (digit-char? x)

(member x '(#\1 #\2 #\3 #\4 #\5 #\6 #\7 #\8 #\9 #\0)))

(define (has-decimal? str)

(define L (string-length str))

(and (>= L 3)

(char=? #\. (string-ref str (- L 3)))))

(define (is-decimal-string? str)

(define L (string-length str))

(and (has-decimal? str)

(andmap digit-char?

(string->list (substring str 0 (- L 3))))

(andmap digit-char?

(string->list (substring str (- L 2) L)))))

....

(provide (contract-out

....

; convert an amount (natural number) of cents

; into a dollar-based string

[format-nat (-> natural-number/c

(and/c string?

is-decimal-string?))]))

Alternately, in this case, we could use a regular expression as a contract:

#lang racket

(provide

(contract-out

....

; convert an amount (natural number) of cents

; into a dollar-based string

[format-nat (-> natural-number/c

(and/c string? #rx"[0-9]*\\.[0-9][0-9]"))]))

7.2.4 Contracts on Higher-order Functions

Function contracts are not just restricted to having simple predicates on their domains or ranges. Any of the contract combinators discussed here, including function contracts themselves, can be used as contracts on the arguments and results of a function.

For example,

(-> integer? (-> integer? integer?))

is a contract that describes a curried function. It matches functions that accept one argument and then return another function accepting a second argument before finally returning an integer. If a server exports a function make-adder with this contract, and if make-adder returns a value other than a function, then the server is to blame. If make-adder does return a function, but the resulting function is applied to a value other than an integer, then the client is to blame.

Similarly, the contract

(-> (-> integer? integer?) integer?)

describes functions that accept other functions as its input. If a server exports a function twice with this contract and the twice is applied to a value other than a function of one argument, then the client is to blame. If twice is applied to a function of one argument and twice calls the given function on a value other than an integer, then the server is to blame.

7.2.5 Contract Messages with “???”

Several clients used your module. Others used their modules in turn. And all of a sudden one of them sees this error message:

> (require 'bank-server)

> (deposit -10)

deposit: contract violation

expected: ???

given: -10

in: the 1st argument of

(-> ??? any)

contract from: bank-server

blaming: top-level

at: eval:2.0

What is the ??? doing there? Wouldn’t it be nice if we had a name for this class of data much like we have string, number, and so on?

For this situation, Racket provides flat named contracts. The use of “contract” in this term shows that contracts are first-class values. The “flat” means that the collection of data is a subset of the built-in atomic classes of data; they are described by a predicate that consumes all Racket values and produces a boolean. The “named” part says what we want to do, which is to name the contract so that error messages become intelligible:

> (module improved-bank-server racket     (define (amount? x) (and (number? x) (integer? x) (>= x 0)))     (define amount (flat-named-contract 'amount amount?))        (provide (contract-out [deposit (amount . -> . any)]))        (define total 0)     (define (deposit a) (set! total (+ a total))))

With this little change, the error message becomes quite readable:

> (require 'improved-bank-server)

> (deposit -10)

deposit: contract violation

expected: amount

given: -10

in: the 1st argument of

(-> amount any)

contract from: improved-bank-server

blaming: top-level

at: eval:5.0

7.2.6 Dissecting a contract error message