A functional enumeration of type t is a partition of t into finite numbered sets called Parts. Each parts contains values of a certain cost (typically the size of the value).

A class of functionally enumerable types

Version of enumerate that ensures that the enumeration is shared between all accesses. Should always be used when combining enumerations.

For nullary constructors such as True and [].

For any non-nullary constructor. Apply funcurry until the type of the result is unary (i.e. n-1 times where n is the number of fields of the constructor).

A free pair constructor. The cost of constructing a free pair is equal to the sum of the costs of its components.

Uncurry a function (typically a constructor) to a function on free pairs.

Produces the enumeration of a type given the enumerators for each of its constructors. The result of unary should typically not be used directly in an instance even if it only has one constructor. So you should apply consts even in that case.

Derive an instance of Enumberable with Template Haskell. To derive an instance for Enumerable A, just put this as a top level declaration in your module (with the TemplateHaskell extension enabled):

  deriveEnumerable ''A

An optimal version of enumerate. Used by all library functions that access enumerated values (but not by combining functions). Library functions should ensure that optimal is not reevaluated.

Mainly as a proof of concept we define a function to index into an enumeration. (If this is repeated multiple times it might be very inefficient, depending on whether the dictionary for the Enumerable is shared or not.)

A more fine grained version of index that takes a size and an index into the values of that size. select p i is only defined for i

All values of the enumeration by increasing cost (which is the number of constructors for most types). Also contains the cardinality of each list.

A version of values with a limited number of values in each inner list. If the list corresponds to a Part which is larger than the bound it evenly distributes the values across the enumeration of the Part.

Compatibility with QuickCheck. Distribution is uniform generator over values bounded by the given size. Typical use: sized uniform.

Check a property for all values up to a given size. featCheck p prop = ioAll p (inputRep prop)

A rather simple but general property testing driver. The property is an (funcurried) IO function that both tests and reports the error. The driver goes on forever or until the list is exhausted, reporting its progress and the number of tests before each new part.

Defined as ioAll p = ioFeat (take p values)

Defined as ioBounded n p = ioFeat (take p $ bounded n)

Functions that test a property and reports the result.

Reports counterexamples to the given predicate by printing them