nixpulvis

## Racket Contracts With Blame 2369 words drafted on February 18, 2018.

The idea of a contract isn’t all that different from a type, since both are used to describe the shape of data. However, due to the dynamic nature of contracts they can describe much more than just shape. The three main differences are that:

1. Contracts are dynamic, telling you what went wrong at run-time.
2. Contracts are opt-in. Without getting into gradual type systems, this is generally not the case with type systems.
3. In general, a contract system is a system of predicate checks with smart errors.

I strongly recommend following along with these examples either in DrRacket, or the racket REPL.

In learning to program Racket you may not write a single contract, but you will definetly use them. This is because most of the functions (and data) you’ll build with have contracts, and when something goes wrong it’s the contracts that will tell you where. This is because contracts in Racket know how to blame the correct party, providing you with very helpful error messages. Consider the following, where I try to add one to a string:

(add1 "foo")


I get a run-time error, much like a type error.

; add1: contract violation
;   expected: number?
;   given: "hi"


This is because add1 has the following contract assigned to it:

(-> number? number?)


This looks like a more normal type if you remember that Racket is a prefix notation language. If it helps you, think of that contract as number? -> number?. In the rest of this post, I want to dive into contracts in more depth.

### Defining Data with a Contract

Typically contracts are attached at module bounderies. A module in Racket can provide an item for use in other modules, and attach a contract to each item in the process. However, it is also posible to create data with contracts within a module. These are contracts with nested contract bounderies. We’ll be using these in this post, to avoid talking about modules too much.

We’ll be using define/contract to define an item with a contract directly. We can define items just like with define but with an additional contract-expr as it’s 2nd argument. For example:

; Define add2 with a contract of it's own.
(-> number? number?)
(+ n 2))

2

;   expected: number?
;   given: "foo"
;   in: the 1st argument of
;       (-> number? number?)
;   blaming: top-level
;    (assuming the contract is correct)


Compared to a define implementation of add2:

; Define a plain old add2 without it's own contract.
(+ n 2))

2

; +: contract violation
;   expected: number?
;   given: "foo"
;   argument position: 1st


As you can see, both definitions of add2 correctly operate on 0, and both definitions correctly error when given "foo", the important difference is which party is blamed. In the define example there is no new contract, and it’s the contract of + which detects the error. In our definition with define/contract it’s the attached (-> number? number?) contract which catches our error.

### Flat Contracts

Before we look at function contracts any more, let’s first start by looking at the simplest kind of contract. A flat contract is one of:

• Symbols, booleans, keywords, null.
• Strings, Characters.
• Numbers
• Regular Expressions
• Predicate functions, i.e. (-> any/c boolean?).

These are the trival cases of contracts. Let’s take a quick look at creating data using flat contracts.

(define/contract happy? #t (or #t #f))
happy?
#t

(define/contract happy? #t (and #t #f))
; happy?: broke its own contract
;   promised: #t
;   produced: #f
;   in: #t
;   contract from: (definition happy?)
;   blaming: (definition happy?)
;    (assuming the contract is correct)


As you can see, the contract system caught us when we tried to say that happy? was contractually obligated to be #t, but we assigned (and #t #f). Strings, numbers, and regexs all work as you’d expect. Predicate functions are also pretty straightforward, and provide an easy way to check whatever condition you’d like.

; Define our own contract predicate.
(define (natural+? n) (> n 0))

(define/contract one natural+? 1)
(define/contract zero natural+? 0)
; zero: broke its own contract
;   promised: natural+?
;   produced: 0
;   in: natural+?
;   contract from: (definition zero)
;   blaming: (definition zero)
;    (assuming the contract is correct)


Pretty simple, and it’s nice to be able to talk about our assumptions in code.

### Chaperone and Impersonator Contracts

The most important kind of contract left out of the flat contracts is ->. This form of contract is also known as a contract combinator, since it takes many contracts as arguments and returns a new contract. Any contract created with -> (for example (-> number? number?)) is a chaperone contract.

#### Immutable and Mutable Wrappers

Before I get into chaperone and impersonator contracts, first let me explain impersonators and chaperones beifly. Both are a way to wrap data, where a chaperone is allowed to view the data, and an impersonator is allowed to modify it.

(define impersonated-add1
(lambda (n) 41)))

; Notice how we update the value that gets passed to add1.
42

(lambda (n) 41)))

; A chaperone is not allowed to modify the input to add1.
; procedure chaperone: non-chaperone result;
;  received a argument that is not a chaperone of the original argument
;   original: 0


An important fact about these kinds of wrappers is that they are equal? to thier wrapped functions, whereas most functions aren’t equal? to anything else.

(equal? (lambda (x) x) (lambda (x) x))
#f
#t
#t


Below I create a chaperone of the add1 function that prints it’s inputs and outputs (taken from the Racket documentation).

(define (post-wrap n)
(printf "returned: ~s\n" n) n)

(define (wrap n)
(printf "given: ~s\n" n)
(values post-wrap n))



As you can see chaperone-procedure can wrap both before and after the original function is called. This pattern is perfect for creating a contract on functions (and other kinds of composite data), since a contract for a function must check the contracts for it’s arguments and results.

#### Back to Contracts

So we’ve seen what impersonators and chaperones are, but where do they show up as contracts?

(define contracts
(number?
,(-> number? number?)
,(let ([a (new-∀/c #f)])
(-> a a))))

(map flat-contract? contracts)
'(#t #f #f)
(map chaperone-contract? contracts)
'(#t #t #f)
(map impersonator-contract? contracts)
'(#f #f #t)


As you can see function contracts (->) are chaperones and polymorphic contracts are impersonators. There are a few other examples of each, but this is a good start. I’m going to skip over the polymorphic contracts new-∀/c and new-∃/c for now.

As we’ve already seen in the first section, we can attched -> contracts to functions to protect their domain, and range. But now I want to look at this a bit more carefully. One aspect of contracts we’ve glossed over a bit is blame, which we will now come to understand better.

Let’s start by defining a function with a partially broken implementation (i.e. fails it’s contract under some inputs).

(define/contract (broken x y)
(-> (>=/c 10)
(>=/c 5)
(>/c 15))
(+ x y))

(broken 0 0)
; broken: contract violation
;   expected: (>=/c 10)
;   given: 0
;   in: the 1st argument of
;       (-> (>=/c 10) (>=/c 5) (>/c 15))
;   contract from: (function broken)
;   blaming: top-level
;    (assuming the contract is correct)

(broken 10 5)
; broken: broke its own contract
;   promised: a number strictly greater than 15
;   produced: 15
;   in: the range of
;       (-> (>=/c 10) (>=/c 5) (>/c 15))
;   contract from: (function broken)
;   blaming: (function broken)
;    (assuming the contract is correct)


As you can see, (broken 0 0) didn’t supply valid arguments, and the contract violation tells us that, and blames the top level (the REPL in this case), since it was the fault of mine when I tried to supply 0 as arguements. However, when I provided valid arguments in (broken 10 5) the function performed the (+ 10 5) arithmatic, and broke it’s own contract. This is clearly the fault of the function, not the top level, and the violation tell us that as well.

Things can get a little confusing when we remember functions are first class in Racket, and we can pass them around as data.

; Filters a list given a predicate function.
(define/contract (filter f l)
(parametric->/c [X]
(-> (-> X boolean?)
(listof X)
(listof X)))
(foldr (lambda (a bs) (if (f a) (cons a bs) bs))
'()
l))

(filter (lambda (x) (> x 1)) '(0 1 2 3))
'(2 3)
(filter odd? '(0 1 2 3))
'(1 3)


But what who’s fault is it when I pass + as the predicate function to filter? Mine! of course. More specifically, it’d be the top level in the following example:

(filter + '(0 1 2 3))
; filter: contract violation
;   expected: boolean?
;   given: 3
;   in: the range of
;       the 1st argument of
;       (parametric->/c
;        (X)
;        (-> (-> X boolean?) (listof X) (listof X)))
;   contract from: (function filter)
;   blaming: top-level
;    (assuming the contract is correct)


Racket’s contract system is smart enough to know that even though the predicate function failed within our filter function, it was passed into the filter function as an argument, and therefor it’s still the caller’s fault.

Before we dig into the internals of the contract system a bit I thought I’d show of one of Racket’s coolest type of contract, the ->i function contract. In short, this contract combinator allows you to write a contract where each argument and the result can depend on each other. Let’s look at another example from the Racket reference.

(->i ([x number?]
[y (x) (>=/c x)])
[result (x y) (>=/c (+ x y))])


This is a contract which ensures y is greater than x and that the result is always the sum of the two. This is very powerful, and comes at the cost of delaying execution of the contracts until the function itself returns.

TODO…