Substitution is the process of replacing occurrences of a variable in an expression with another expression. The notation `{e1/x} e2` means "substitute `e1` for `x` in `e2`".

1. `{y z/x} (fn x : int ⇒ y x)`

In this case, we are substituting `y z` for `x` in the expression `(fn x : int ⇒ y x)`. However, `x` is bound by the function abstraction `fn x : int ⇒ y x`, so it is not replaced. The result is the same as the original expression:

`(fn x : int ⇒ y x)`

2. `{z x/x} (fn y : int ⇒ y x)`

Here, we are substituting `z x` for `x` in the expression `(fn y : int ⇒ y x)`. The `x` in `y x` is free, so it is replaced:

`(fn y : int ⇒ y (z x))`

3. `{z x/x} (fn z : int ⇒ (fn x : int ⇒ y x) x z)`

In this case, we are substituting `z x` for `x` in the expression `(fn z : int ⇒ (fn x : int ⇒ y x) x z)`. The `x` in `y x` and `x z` are bound by their nearest function abstractions, so they are not replaced. The `x` in `(fn x : int ⇒ y x) x z` is free, so it is replaced:

`(fn z : int ⇒ (fn x : int ⇒ y x) (z x) z)`

Question

Substitution is the process of replacing occurrences of a variable in an expression with another expression. The notation `{e1/x} e2` means "substitute `e1` for `x` in `e2`".

1. `{y z/x} (fn x : int ⇒ y x)`

In this case, we are substituting `y z` for `x` in the expression `(fn x : int ⇒ y x)`. However, `x` is bound by the function abstraction `fn x : int ⇒ y x`, so it is not replaced. The result is the same as the original expression:

`(fn x : int ⇒ y x)`

2. `{z x/x} (fn y : int ⇒ y x)`

Here, we are substituting `z x` for `x` in the expression `(fn y : int ⇒ y x)`. The `x` in `y x` is free, so it is replaced:

`(fn y : int ⇒ y (z x))`

3. `{z x/x} (fn z : int ⇒ (fn x : int ⇒ y x) x z)`

In this case, we are substituting `z x` for `x` in the expression `(fn z : int ⇒ (fn x : int ⇒ y x) x z)`. The `x` in `y x` and `x z` are bound by their nearest function abstractions, so they are not replaced. The `x` in `(fn x : int ⇒ y x) x z` is free, so it is replaced:

`(fn z : int ⇒ (fn x : int ⇒ y x) (z x) z)`

Knowee AI · Accepted Answer

Substitution is the process of replacing occurrences of a variable in an expression with another expression. The notation `{e1/x} e2` means "substitute `e1` for `x` in `e2`".

1. `{y z/x} (fn x : int ⇒ y x)`

In this case, we are substituting `y z` for `x` in the expression `(fn x : int ⇒ y x)`. However, `x` is bound by the function abstraction `fn x : int ⇒ y x`, so it is not replaced. The result is the same as the original expression:

`(fn x : int ⇒ y x)`

2. `{z x/x} (fn y : int ⇒ y x)`

Here, we are substituting `z x` for `x` in the expression `(fn y : int ⇒ y x)`. The `x` in `y x` is free, so it is replaced:

`(fn y : int ⇒ y (z x))`

3. `{z x/x} (fn z : int ⇒ (fn x : int ⇒ y x) x z)`

In this case, we are substituting `z x` for `x` in the expression `(fn z : int ⇒ (fn x : int ⇒ y x) x z)`. The `x` in `y x` and `x z` are bound by their nearest function abstractions, so they are not replaced. The `x` in `(fn x : int ⇒ y x) x z` is free, so it is replaced:

`(fn z : int ⇒ (fn x : int ⇒ y x) (z x) z)`

Question 6 Perform the following substitutions:1. {y z/x} (fn x : int ⇒ y x)2. {z x/x} (fn y : int ⇒ y x)3. {z x/x} (fn z : int ⇒ (fn x : int ⇒ y x) x z)

Question

Solution

Similar Questions

Upgrade your grade with Knowee