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1. Overview

QCheck is a library for automatic unit testing of Standard ML modules. You provide specifications (in the form of ML code) of the properties that your module's functions should satisfy, and ask QCheck to exercise the module with randomly-chosen test cases. It will show how many cases passed the test, and print counter-examples in case of failure. Actually, random testing is just one possibility; QCheck can pull test cases from any kind of stream (disk file, data structure, etc.)

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1.1 Simple properties of integers

The best way to demonstrate the capabilities of QCheck is with a simple example. Let's begin by writing a few tiny functions on integers: successor, even, and odd:

fun succ x = x+1
fun even x = x mod 2 = 0
fun odd x = x mod 2 = 1
 › val succ = fn : int → intval even = fn : int → boolval odd = fn : int → bool

Now we need to think of a property that we expect to hold for this implementation. Here is a trivial one: every integer is either even or odd. That is, for any x exactly one of the functions even or odd returns true; the other returns false. One way to specify this in ML is to use <> (not equal), which amounts to an exclusive OR when applied to boolean values.

fun even_xor_odd x = even x <> odd x
 › val even_xor_odd = fn : int → bool

We now call upon QCheck to test this property on a bunch of randomly chosen integers. QCheck checkers are polymorphic. To test integers, we'll have to specify two things: a generator that produces integers, and a printer that can convert integers to strings (in case there are counter-examples to be printed).

open QCheck infix ==>
val int = (Gen.Int.int, SOME Int.toString)
 › val int = (fn,SOME fn) : int Gen.gen * (int → string) option

Finally, we call checkGen with the int spec, a string to identify the test, and the property we are testing.

checkGen int ("even<>odd", pred even_xor_odd);
 › even<>odd..............ok      (100 passed)        val it = () : unit

The output indicates that QCheck tested the property on 100 random integers, and all of them succeeded. (The number of cases required to complete the test is configurable. See section Settings.)

For the next example, we will demonstrate a conditional property: the successor of any even number should be odd.

val succ_even_odd = even ==> odd o succ
 › val succ_even_odd = - : int prop
checkGen int ("even+1=odd", succ_even_odd);
 › even+1=odd.............ok      (100 passed)        val it = () : unit

In this example, the 100 test cases that passed were all ones that met the condition: they were all even. Odd numbers trivially satisfy the property (by falsifying the condition) and are not counted.

Now, let's try the inverse property: the successor of an odd number should be even:

checkGen int ("odd+1=even", odd ==> even o succ);
 › odd+1=even.............FAILED  (99/100 passed)           counter-examples:       1073741823val it = () : unit

Oops! QCheck found a counter-example: the maximum 31-bit integer. It is odd, but since its successor is undefined, the property does not hold. (We were not extraordinarily lucky to generate maxInt this time around; in fact, the generator is biased so that zero, minInt, and maxInt are chosen more frequently than other integers, precisely because they are often “boundary conditions.” See section Generating test cases.)

At any rate, what is broken here is not really our implementation, but rather the specification of the property. We need to limit it to odd integers that are less than maxInt.

fun odd_not_max x = odd x andalso x < valOf(Int.maxInt);
 › val odd_not_max = fn : int → bool
checkGen int ("odd+1=even", odd_not_max ==> even o succ)
 › odd+1=even.............ok      (100 passed)        val it = () : unit

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1.2 Generating pairs of integers

Other properties involve pairs of integers. For example, the sum of two odd numbers is even.

fun both_odd(x,y) = odd x andalso odd y
fun sum_even(x,y) = even (x+y)
fun show_pair(x,y) = Int.toString x ^","^ Int.toString y
 › val both_odd = fn : int * int → boolval sum_even = fn : int * int → boolval show_pair = fn : int * int → string

QCheck includes not only generators for most primitive and aggregate data types, but also functions for combining them in various ways. To generate random pairs of integers, we “zip” together two integer generators.

checkGen (Gen.zip(Gen.Int.int, Gen.Int.int), SOME show_pair)
         ("odd+odd=even", both_odd ==> sum_even)
 › odd+odd=even...........FAILED  (93/96 passed)            counter-examples:       4919,1073741823                              995224081,1073741823                              1073741823,561val it = () : unit

All of the counter-examples overflow the sum computation. I'll leave fixing this specification as an exercise for the reader.

Test cases need not be randomly generated. Here is an example where the pairs will be taken from a list, but they could just as easily be read from a file. See section Specifying test cases.

check (List.getItem, SOME show_pair)
      ("sum_odds_even[]", both_odd ==> sum_even)
      [(1,1), (3,5), (3,4), (* this one won't count! *)
       (~1,1), (21,21), (7,13)]
 › sum_odds_even[]........ok      (5 passed)          val it = () : unit

I provided 6 pairs in the list, but only 5 counted because (3,4) did not meet the precondition of the property.

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1.3 The QCheck structure

The examples in the preceding sections used several top-level functions from the QCheck structure. Here, we will examine the signature of QCheck, beginning with its sub-structures.

structure Gen : GENERATOR_SIG      
structure Files : FILES_SIG    
structure Settings : SETTINGS_SIG

The Gen structure contains random value generators for all the basis types, including aggregates like vectors and lists. It also contains a rich library of combinators such as zip, map, and filter. See section Generating test cases.

Files is provided to make it easy to use lines in a file or files in a directory as test cases. See section Specifying test cases. Settings contains various user-customizable settings, including user-definable output styles. See section Settings.


This signature contains functions for specifying properties and observing the distribution of test cases. In preceding sections, we met two of its members: pred converts a predicate (boolean function) on a given type to a property, and ==> creates a conditional property. A property over a given type t has type t prop. See section Properties.

Two types are useful for discussing the parameters of the various check functions:

type ('a,'b) reader = 'b → ('a * 'b) option  
type 'a rep = ('a → string) option           

An ('a,'b) reader pulls objects of type 'a from a stream of type 'b. In this case, the objects are test cases of some type. (This is defined the same way as StringCvt.reader.) The type 'a rep is an (optional) method for rendering test cases as strings. It is used in case there are counter-examples to be printed.

Now, the most general function for invoking QCheck is called check. It takes 3 (curried) parameters:

val check : ('a,'b) reader * 'a rep →   
            string * 'a prop → 
            'b → unit
  1. The first parameter is a reader and representation pair. It contains everything the checker needs to know about the type of the test cases, and the same pair can be reused to check additional properties of the same type.
  2. Next is the property name and specification. This parameter will be different for each property checked. The name is just a string used to distinguish the results of this test in the output.
  3. Finally, you provide a stream of test cases. The source of the test cases is arbitrary, as long as a matching reader is provided. They could be randomly generated, read from a data structure, extracted from the file system, etc.

We provide two specializations of check that are useful in particular circumstances. First, checkGen is for checking randomly generated test cases. The random number stream is implicit, and the reader is always a generator from the Gen module.

val checkGen : 'a Gen.gen * 'a rep →     
               string * 'a prop → unit

Second, if we just want to check one particular test case, the reader is trivial (and therefore omitted), and the `stream' is just the test case itself:

val checkOne : 'a rep → string * 'a prop → 'a → unit

Finally, the Qcheck structure includes a pair version that can be useful in determining the version of QCheck you are using. The context contains expanded version information that can be used by darcs to reconstruct this precise configuration of QCheck.

val version : int * int   
val context : string      

The version information currently reported by QCheck.version is:

 › val it = (1,1) : int * int

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This document was generated by Chris League on April, 14 2008 using texi2html 1.78.