R: Property testing

Huw Campbell

Hedgehog is a modern property based testing system in the spirit of QuickCheck, originally written in Haskell, but now also available in R. One of the key benefits of Hedgehog is integrated shrinking of counterexamples, which allows one to quickly find the cause of bugs, given salient examples when incorrect behaviour occurs.

Features

Example

To get a quick look of how Hedgehog feels, here's an example showing some of the properties a function which reverses a vector should have. We'll be testing the rev function from package:base.

test_that( "Reverse of reverse is identity",
 forall( gen.c( gen.element(1:100) ), function(xs) expect_equal(rev(rev(xs)), xs))
)

The property above tests that if I reverse a vector twice, the result should be the same as the vector that I began with. Hedgehog has generated 100 examples, and checked that this property holds in all of these cases.

As one can see, there is not a big step from using vanilla testthat to including hedgehog in one's process. Inside a test_that block, one can add a forall and set expectations within it.

We use the term forall (which comes from predicate logic) to say that we want the property to be true no matter what the input to the tested function is. The first argument to forall is function to generate random values (the generator); while the second is the properties we wish to test.

The property above doesn't actually completely specify that the rev function is accurate though, as one could replace revwith the identity function and still observe this result. We will therefore write one more property to thoroughly test this function.

test_that( "Reversed of concatenation is flipped concatenation of reversed",
 forall( list( as = gen.c( gen.element(1:100) )
             , bs = gen.c( gen.element(1:100) ))
       , function(as,bs) expect_equal ( rev(c(as, bs)), c(rev(bs), rev(as)))
 )
)

This is now a well tested reverse function. Notice that the property function now accepts two arguments: as and bs. A list of generators in Hedgehog is treated as a generator of lists, and shrinks all members independently. We do however do our best to make sure that properties can be specified naturally if the generator is specified in this manner as a list of generators.

Now let's look at an assertion which isn't true so we can see what our counterexamples looks like

test_that( "Reverse is identity",
 forall( gen.c( gen.element(1:100) ), function(xs) expect_equal(rev(xs), c(xs)))
)
## Error: Test failed: 'Reverse is identity'
## * Falsifiable after 2 tests, and 7 shrinks
## rev(xs) not equal to c(xs).
## 2/2 mismatches (average diff: 1)
## [1] 2 - 1 ==  1
## [2] 1 - 2 == -1
## Counterexample:
## [1] 1 2

This test says that the reverse of a vector should equal the vector, which is obviously not true for all vectors. Here, hedgehog has run this expectation with random input, and found it to not be true. Instead of reporting it directly, it has shrunk the bad test case to the smallest counterexample it could find: c(1,2). Hedgehog then reëmits this test error to testthat, which handles it as per usual and displays it to the user.

Generators

Hedgehog exports some basic generators and plenty of combinators for making new generators. Here's an example analogous to calling sample on a small list, using the hedgehog generator gen.sample:

gen.sample(1:5)
## Hedgehog generator:
## Example:
## [1] 3 2 5 1 4
## Initial shrinks:
## [1] 1 2 3 4 5
## [1] 1 2 3 5 4
## [1] 2 3 5 1 4
## [1] 1 2 5 3 4
## [1] 3 1 5 2 4
## [1] 3 2 1 5 4
## [1] 3 2 4 1 5

This generator shrinks back towards the original list ordering the user supplied. Although only a few shrinks are shown above, these are actually just the first layer of a rose tree of possible shrinks. This integrated shrinking property is a key component of hedgehog, and gives us an excellent chance of reducing to the minimum possible counterexample.

test_that( "a is less than b + 1",
   forall(list(a = gen.element(1:100), b = gen.unif(1,100, shrink.median = F))
 , function(a, b) expect_lt( a, b + 1 ))
)
## Error: Test failed: 'a is less than b + 1'
## * Falsifiable after 6 tests, and 9 shrinks
## `a` is not strictly less than b + 1. Difference: 0
## Counterexample:
## $a
## [1] 2
##
## $b
## [1] 1

The generators gen.c, gen.element, and gen.unif, are related to standard R functions: c, to create a vector; sample, to sample from a list or vector; and runif, to sample from a uniform distribution. We try to maintain a relationship to R's well known functions inside Hedgehog.

Generators are also monads, meaning that one can use the result of a generator to build a generator. An example of this is a list generator, which first randomly chooses a length, then generates a list of said length.

The gen.map function can be used to apply an arbitrary function to the output of a generator, while gen.and_then is useful in chaining the results of a generator.

In the following example, we'll create a generator which builds two lists of length n, then turn them into a data.frame with gen.with.

gen.df.of <- function ( n )
 gen.with (
   list( as = gen.c(of = n, gen.element(1:10) )
       , bs = gen.c(of = n, gen.element(10:20) )
       )
 , as.data.frame
 )

test_that( "Number of rows is 5",
 forall( gen.df.of(5), function(df) expect_equal(nrow(df), 5))
)

While this is good, but we would also like to be able to create data.frames with a varying number of rows. Here, we'll again test a property which is false in order to show how hedgehog will find the minimum shrink.

gen.df <-
 generate(for (e in gen.element(1:100)) {
   gen.df.of(e)
 })

test_that( "All data frames are of length 1",
 forall( gen.df, function(x) expect_equal(nrow(x), 1))
)
## Error: Test failed: 'All data frames are of length 1'
## * Falsifiable after 1 tests, and 9 shrinks
## nrow(x) not equal to 1.
## 1/1 mismatches
## [1] 2 - 1 == 1
## Counterexample:
##   as bs
## 1  1 10
## 2  1 10

Technically, that we can sequence generators is this way implies they are monads, and we provide a number combinators for manipulating them in this manner. Indeed, generate is simply syntactic sugar for monadic bind, sometimes referred to as "and then".

The gen.with function can be used to apply an arbitrary function to the output of a generator, while gen.and_then is useful in chaining the results of a generator.

State Machine Testing

R is a multi-paradigm programming language, while all the tests we have seen so far have tested functions which have no side effects (pure functions).

To deal with more complex situations which might arise in practice, Hedgehog also supports testing stateful system using a state machine model under random actions.

The general idea is that we can generate a model of the system, with requirements and post-conditions for every action we can take. With a random sequence of actions, we can test our model of the system against the true implementation. Hedgehog will then be able to identify inconsistencies between the true implementation and the model, from which the programmer can ask whether this is a bug in the model or a true bug in the system.

John Hughes has a series of excellent talks regarding testing of state based and non-deterministic systems using QuviQ's proprietary QuickCheck implementation, which has been using these techniques to great effect for many years.

Hedgehog's current implementation in R is still quite young, and not nearly as feature rich, but does still allow for interesting properties in stateful systems to be investigated. See the state machine testing article for more information.