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7.2.1 Parametric Contracts
parametric->/ c

7.2 Function Contracts

A function contract wraps a procedure to delay checks for its arguments and results. There are three primary function contract combinators that have increasing amounts of expressiveness and increasing additional overheads. The first -> is the cheapest. It generates wrapper functions that can call the original function directly. Contracts built with ->* require packaging up arguments as lists in the wrapper function and then using either keyword-apply or apply. Finally, ->i is the most expensive (along with ->d), because it requires delaying the evaluation of the contract expressions for the domain and range until the function itself is called or returns.

The case-> contract is a specialized contract, designed to match case-lambda and unconstrained-domain-> allows range checking without requiring that the domain have any particular shape (see below for an example use).

(-> dom ... range)
dom = dom-expr
  | keyword dom-expr
range = range-expr
  | (values range-expr ...)
  | any
Produces a contract for a function that accepts a fixed number of arguments and returns either a fixed number of results or completely unspecified results (the latter when any is specified).

Each dom-expr is a contract on an argument to a function, and each range-expr is a contract on a result of the function.

Using a -> between two whitespace-delimited .s is the same as putting the -> right after the enclosing opening parenthesis. See Lists and Racket Syntax or Reading Pairs and Lists for more information.

For example,

(integer? boolean? . -> . integer?)

produces a contract on functions of two arguments. The first argument must be an integer, and the second argument must be a boolean. The function must produce an integer.

A domain specification may include a keyword. If so, the function must accept corresponding (mandatory) keyword arguments, and the values for the keyword arguments must match the corresponding contracts. For example:

(integer? #:x boolean? . -> . integer?)

is a contract on a function that accepts a by-position argument that is an integer and a #:x argument that is a boolean.

If any is used as the last sub-form for ->, no contract checking is performed on the result of the function, and thus any number of values is legal (even different numbers on different invocations of the function).

If (values range-expr ...) is used as the last sub-form of ->, the function must produce a result for each contract, and each value must match its respective contract.

(->* (mandatory-dom ...) optional-doms rest pre range post)
mandatory-dom = dom-expr
  | keyword dom-expr
optional-doms = 
  | (optional-dom ...)
optional-dom = dom-expr
  | keyword dom-expr
rest = 
  | #:rest rest-expr
pre = 
  | #:pre pre-cond-expr
range = range-expr
  | (values range-expr ...)
  | any
post = 
  | #:post post-cond-expr
The ->* contract combinator produces contracts for functions that accept optional arguments (either keyword or positional) and/or arbitrarily many arguments. The first clause of a ->* contract describes the mandatory arguments, and is similar to the argument description of a -> contract. The second clause describes the optional arguments. The range of description can either be any or a sequence of contracts, indicating that the function must return multiple values. If present, the rest-expr contract governs the arguments in the rest parameter. The pre-cond-expr and post-cond-expr expressions are checked as the function is called and returns, respectively, and allow checking of the environment without an explicit connection to an argument (or a result).

As an example, the contract

(->* () (boolean? #:x integer?) #:rest (listof symbol?) symbol?)

matches functions that optionally accept a boolean, an integer keyword argument #:x and arbitrarily more symbols, and that return a symbol.

(->i (mandatory-dependent-dom ...)
(->i (mandatory-dependent-dom ...)
     (optional-dependent-dom ...)
mandatory-dependent-dom = id+ctc
  | keyword id+ctc
optional-dependent-dom = id+ctc
  | keyword id+ctc
dependent-rest = 
  | #:rest id+ctc
pre-condition = 
  | #:pre (id ...) boolean-expr pre-condition
  | #:pre/name (id ...) string boolean-expr pre-condition
dependent-range = any
  | id+ctc
  | un+ctc
  | (values id+ctc ...)
  | (values un+ctc ...)
post-condition = 
  | #:post (id ...) boolean-expr post-condition
  | #:post/name (id ...) string boolean-expr post-condition
id+ctc = [id contract-expr]
  | [id (id ...) contract-expr]
un+ctc = [_ contract-expr]
  | [_ (id ...) contract-expr]
The ->i contract combinator differs from the ->* combinator in that the support pre- and post-condition clauses and in that each argument and result is named. These names can then be used in the subcontracts and in the pre-/post-condition clauses. In short, contracts now express dependencies among arguments and results.

The first sub-form of a ->i contract covers the mandatory and the second sub-form covers the optional arguments. Following that is an optional rest-args contract, and an optional pre-condition. The pre-condition is introduced with the #:pre keyword followed by the list of names on which it depends. If the #:pre/name keyword is used, the string supplied is used as part of the error message; similarly with #:post/name.

The dep-range non-terminal specifies the possible result contracts. If it is any, then any value is allowed. Otherwise, the result contract pairs a name and a contract or a multiple values return with names and contracts. In the last two cases, the range contract may be optionally followed by a post-condition; the post-condition expression is not allowed if the range contract is any. Like the pre-condition, the post-condition must specify the variables on which it depends.

Consider this sample contract:
(->i ([x number?]
      [y (x) (>=/c x)])
     [result (x y) (and/c number? (>=/c (+ x y)))])
It specifies a function of two arguments, both numbers. The contract on the second argument (y) demands that it is greater than the first argument. The result contract promises a number that is greater than the sum of the two arguments. While the dependency specification for y signals that the argument contract depends on the value of the first argument, the dependency sequence for result indicates that the contract depends on both argument values. In general, an empty sequence is (nearly) equivalent to not adding a sequence at all except that the former is more expensive than the latter. Since the contract for x does not depend on anything else, it does not come with any dependency sequence, not even ().

The contract expressions are not always evaluated in order. First, if there is no dependency for a given contract expression, the contract expression is evaluated at the time that the ->i expression is evaluated rather than the time when the function is called or returns. These dependency-free contract expressions are evaluated in the order in which they are listed. Second, the dependent contract sub-expressions are evaluated when the contracted function is called or returns in some order that satisfies the dependencies. That is, if a contract for an argument depends on the value of some other contract, the former is evaluated first (so that the argument, with its contract checked, is available for the other). When there is no dependency between two arguments (or the result and an argument), then the contract that appears earlier in the source text is evaluated first.

Finally, if all of the identifier positions of the range contract are _s (underscores), then the range contract expressions are evaluated when the function is called and the underscore is not bound in the range, after the argument contracts are evaluated and checked. Otherwise, the range expressions are evaluated when the function returns.

If there are optional arguments that are not supplied, then the corresponding variables will be bound to a special value called the-unsupplied-arg value.

(->d (mandatory-dependent-dom ...)
(->d (mandatory-dependent-dom ...)
     (optional-dependent-dom ...)
mandatory-dependent-dom = [id dom-expr]
  | keyword [id dom-expr]
optional-dependent-dom = [id dom-expr]
  | keyword [id dom-expr]
dependent-rest = 
  | #:rest id rest-expr
pre-condition = 
  | #:pre boolean-expr
  | #:pre-cond boolean-expr
dependent-range = any
  | [_ range-expr]
  | (values [_ range-expr] ...)
  | [id range-expr]
  | (values [id range-expr] ...)
post-condition = 
  | #:post-cond boolean-expr
This contract is here for backwards compatibility; any new code should use ->i instead.

This contract is similar to ->i, but is “lax”, meaning that it does not enforce contracts internally. For example, using this contract
(->d ([f (-> integer? integer?)])
     (zero? (f #f))
will allow f to be called with #f, trigger whatever bad behavior the author of f was trying to prohibit by insisting that f’s contract accept only integers.

The #:pre-cond and #:post-cond keywords are aliases for #:pre and #:post and are provided for backwards compatibility.

(case-> (-> dom-expr ... rest range) ...)
rest = 
  | #:rest rest-expr
range = range-expr
  | (values range-expr ...)
  | any
This contract form is designed to match case-lambda. Each argument to case-> is a contract that governs a clause in the case-lambda. If the #:rest keyword is present, the corresponding clause must accept an arbitrary number of arguments. The range specification is just like that for -> and ->*.

(unconstrained-domain-> range-expr ...)
Constructs a contract that accepts a function, but makes no constraint on the function’s domain. The range-exprs determine the number of results and the contract for each result.

Generally, this contract must be combined with another contract to ensure that the domain is actually known to be able to safely call the function itself.

For example, the contract

 [f (->d ([size natural-number/c]
          [proc (and/c (unconstrained-domain-> number?)
                       (lambda (p)
                         (procedure-arity-includes? p size)))])

says that the function f accepts a natural number and a function. The domain of the function that f accepts must include a case for size arguments, meaning that f can safely supply size arguments to its input.

For example, the following is a definition of f that cannot be blamed using the above contract:

(define (f i g)
  (apply g (build-list i add1)))

Used by ->i (and ->d) to bind optional arguments that are not supplied by a call site.

(unsupplied-arg? v)  boolean?
  v : any/c
A predicate to determine whether v is the-unsupplied-arg.

7.2.1 Parametric Contracts

(parametric->/c (x ...) c)
Creates a contract for parametric polymorphic functions. Each function is protected by c, where each x is bound in c and refers to a polymorphic type that is instantiated each time the function is applied.

At each application of a function, the parametric->/c contract constructs a new opaque wrapper for each x; values flowing into the polymorphic function (i.e. values protected by some x in negative position with respect to parametric->/c) are wrapped in the corresponding opaque wrapper. Values flowing out of the polymorphic function (i.e. values protected by some x in positive position with respect to parametric->/c) are checked for the appropriate wrapper. If they have it, they are unwrapped; if they do not, a contract violation is signaled.


> (define/contract (check x y)
    (parametric->/c [X] (boolean? X . -> . X))
    (if (or (not x) (equal? y 'surprise))
> (check #t 'ok)


> (check #f 'ignored)

self-contract violation: expected a(n) X; got: 'invalid

  contract on check from (function check), blaming

(function check)

  contract: (parametric->/c (X) ...)

        at: eval:2.0

> (check #t 'surprise)