Understanding the 'assumes' Keyword in Haskell Functions
The `assumes` keyword in Haskell is used to specify a precondition or assumption that must be true for the function to be applicable. In other words, it specifies a condition that must hold before the function can be called.
For example, consider the following function:
```
f :: Int -> Int
f x = x + 1
```
This function takes an integer `x` and returns its successor (i.e., `x + 1`). However, this function is not applicable if `x` is negative, because the result of `x + 1` would be negative too. To specify this assumption, we can use the `assumes` keyword:
```
f :: Int -> Int assumes (x >= 0)
f x = x + 1
```
Now, the function `f` can only be called with positive integers, and if a negative integer is passed as an argument, the compiler will raise an error.
Similarly, we can use the `assumes` keyword to specify other assumptions or preconditions that must be true for a function to be applicable. For example:
```
g :: Int -> Int assumes (even x)
g x = x + 1
```
This function takes an integer `x` and returns its successor, but only if `x` is even. If `x` is odd, the compiler will raise an error.
In summary, the `assumes` keyword in Haskell is used to specify assumptions or preconditions that must be true for a function to be applicable. It allows us to express constraints on the input values that a function can accept, and can help prevent errors and improve the reliability of our code.
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