Test.LeanCheck.Function.Show

This module is part of LeanCheck, a simple enumerative property-based testing library.

This module exports an orphan Show instance for functions. It shows functions as up to 8 case distinctions, one per line.

Warning: this is only intended to be used in testing modules. Avoid importing this on modules that are used as libraries.

This is intended to Show functions generated by the Listable instance for functions defined in Test.LeanCheck.Function.Listable: functions that have finite exceptions to a constant function. It does work on other types of functions, albeit using "...".

> print (&&)
\x y -> case (x,y) of
        (True,True) -> True
        _ -> False

> print (==>)
\x y -> case (x,y) of
        (True,False) -> False
        _ -> True

> print (==2)
\x -> case x of
      2 -> True
      _ -> False

> print (\x -> abs x < 2)
\x -> case x of
      0 -> True
      1 -> True
      -1 -> True
      _ -> False

When the function cannot be defined by finite exceptions to a constant function using 8 case-patterns, the rest of the function is represented by "...".

> print (+)
\x y -> case (x,y) of
        (0,0) -> 0
        (0,1) -> 1
        (1,0) -> 1
        (0,-1) -> -1
        (1,1) -> 2
        (-1,0) -> -1
        (0,2) -> 2
        (1,-1) -> 0
        ...

The exported orphan Show -> instance is actually defined in Test.LeanCheck.Function.Show.EightLines. An alternative is provided in Test.LeanCheck.Function.Show.FourCases.

The exported Show instance only works for functions whose ultimate return types are instances of ShowFunction. For user-defined algebraic datatypes that are instances of Show, their ShowFunction instance can be defined by using bindtiersShow:

import Test.LeanCheck.Function.ShowFunction

instance ShowFunction Ty where
  bindtiers = bindtiersShow