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The first thing we'll need to do to begin the process of evaluating expressions is write a function to plug in a value for a specific variable.

In Haskell, these types have the following definitions:

There's a way to define 'id' and some ways to make it useful.

Later, the students discover the truth; their values are really types, and their types are really kinds.

It's complex and it's going to get worse.

One might have a great soundtrack and the other might have some actor or another.

It already means different things in different syntactic contexts, like function application or type (family) application.

And if you wanted to put the pieces together, you could build another function on top of it like this:

Suppose you have some tricky recursion, possibly involving "tying the knot" and want to show that it terminates, or to figure out under which conditiā€¦

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