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When this value is evaluated, the semantics of Haskell no longer yield a meaningful value. In other words, further operations on the value cannot be defined in Haskell.

Several ways exist to express bottoms in Haskell code. For instance, undefined is an easily called example of a bottom value. This function has type a but lacks any type constraints in its type signature.

Thus, undefined is able to stand in for any type in a function body, allowing type checking to succeed, even if the function is incomplete or lacking a definition entirely. The undefined function is extremely practical for debugging or to accommodate writing incomplete programs.

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Another example of a bottom value comes from the evaluation of the error function, which takes a String and returns something that can be of any type. This property is quite similar to undefined, which also can also stand in for any type. Calling error in a function causes the compiler to throw an exception, halt the program, and print the specified error message.

In the divByY function below, passing the function 0 as the divisor results in this function results in such an exception. These bottoms exist because the operations cannot be defined in native Haskell.

Such operations are baked into the compiler at a very low level. However, this module exists so that Haddock can generate documentation for these primitive operations, while the looping syntax serves as a placeholder for the actual implementation of the primops. Perhaps the most common introduction to bottoms is writing a partial function that does not have exhaustive pattern matching defined.

For example, the following code has non-exhaustive pattern matching because the case expression, lacks a definition of what to do with a B: The compiler inserts an exception to account for the non-exhaustive patterns: A similar situation can arise with records.

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Although constructing a record with missing fields is rarely useful, it is still possible. Bottoms are used extensively throughout the Preludealthough this fact may not be immediately apparent. The reasons for including bottoms are either practical or historical.

This function could not be well-typed without the bottom. Err import Prelude hiding head,!!

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The preferred method for handling exceptions is to combine the use of safe variants provided in Data.For nonnegative integers n and m, the value of n m is the number of functions from a set of m elements to a set of n elements (see cardinal exponentiation).Such functions can be represented as m-tuples from an n-element set (or as m-letter words from an n-letter alphabet).Some examples for particular values of m and n are given in the following table.

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