Consider the following three function definitions in Haskell: first x y = x ident x = x omega x = omega x We could also define these in ML, although with a slightly different syntax: fun Ident x = x; etc. How would the evaluations of the following expression in Haskell and ML compare= first (ident 3) (omega 1) (First (Ident 3) (Omega 1). in ML}

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Chapter6: User-defined Functions
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### Function Definitions in Haskell and ML

**Consider the following three function definitions in Haskell:**

```haskell
first x y = x
ident x = x
omega x = omega x
```

- `first x y = x`: This function takes two arguments `x` and `y`, and returns `x`.
- `ident x = x`: This function takes a single argument `x` and returns `x`.
- `omega x = omega x`: This function is recursive and will cause an infinite loop when called, as it is defined in terms of itself with the same argument.

**The same functions can also be defined in ML, although with a slightly different syntax:**

```ml
fun Ident x = x;
```
- `fun Ident x = x;`: This is equivalent to `ident x = x` in Haskell, taking a single argument `x` and returning `x`.

**Comparison of Evaluations in Haskell and ML**

Consider the evaluation of the following expression in Haskell and ML:

```haskell
first (ident 3) (omega 1)
```
```ml
{First (Ident 3) (Omega 1). in ML}
```

- In Haskell:
  - `ident 3` evaluates to `3` since `ident x = x`.
  - `omega 1` does not terminate as it initiates an infinite loop (`omega 1 = omega 1`).
  - `first` takes two arguments but will return the first one without evaluating the second, so `first (ident 3) (omega 1)` will effectively return `3` without getting stuck in the infinite loop caused by `omega 1`.

- In ML:
  - `Ident 3` evaluates to `3`, analogous to Haskell's `ident 3`.
  - However, `Omega` would initiate an infinite loop in ML just as in Haskell with the `omega` function.
  - In ML, depending on the language's evaluation strategy, the overall result may differ from Haskell. In strict evaluation (which most ML variants follow), `Omega 1` would be evaluated before being passed into `First`, causing an infinite loop and preventing a result.

By comparing these evaluations, one can observe the differences in how Haskell and ML approach function evaluation, particularly in the handling of non-terminating functions and short-circuiting behavior.
Transcribed Image Text:### Function Definitions in Haskell and ML **Consider the following three function definitions in Haskell:** ```haskell first x y = x ident x = x omega x = omega x ``` - `first x y = x`: This function takes two arguments `x` and `y`, and returns `x`. - `ident x = x`: This function takes a single argument `x` and returns `x`. - `omega x = omega x`: This function is recursive and will cause an infinite loop when called, as it is defined in terms of itself with the same argument. **The same functions can also be defined in ML, although with a slightly different syntax:** ```ml fun Ident x = x; ``` - `fun Ident x = x;`: This is equivalent to `ident x = x` in Haskell, taking a single argument `x` and returning `x`. **Comparison of Evaluations in Haskell and ML** Consider the evaluation of the following expression in Haskell and ML: ```haskell first (ident 3) (omega 1) ``` ```ml {First (Ident 3) (Omega 1). in ML} ``` - In Haskell: - `ident 3` evaluates to `3` since `ident x = x`. - `omega 1` does not terminate as it initiates an infinite loop (`omega 1 = omega 1`). - `first` takes two arguments but will return the first one without evaluating the second, so `first (ident 3) (omega 1)` will effectively return `3` without getting stuck in the infinite loop caused by `omega 1`. - In ML: - `Ident 3` evaluates to `3`, analogous to Haskell's `ident 3`. - However, `Omega` would initiate an infinite loop in ML just as in Haskell with the `omega` function. - In ML, depending on the language's evaluation strategy, the overall result may differ from Haskell. In strict evaluation (which most ML variants follow), `Omega 1` would be evaluated before being passed into `First`, causing an infinite loop and preventing a result. By comparing these evaluations, one can observe the differences in how Haskell and ML approach function evaluation, particularly in the handling of non-terminating functions and short-circuiting behavior.
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