What is the precise definition of the term "type expression" as used in Thompson's "Haskell - the craft of functional programming" book ? It seems that this term is not defined in the book.

It is for example not listed in the index. Also, I tried to search for a clear explicit definition in the book but found nothing.

Related question: is a `type variable`

a `type expression`

?

Let's consider for example the following type (expression?):

`a->b`

Now, if I replace `a`

with `c`

, then will `c->b`

be an instance of `a->b`

?

The terminology "type expression" is used for example on page 314 (third edition of the book):

As sets of types, we look for the intersection of the sets given by (a, [Char] ) and (Int, [b] ) . How can we work out a description of this intersection? Before we do this, we revise and introduce some terminology.

Recall that an instance of a type is given by replacing a type variable or variables by type expressions. A type expression is a common instance of two type expressions if it is an instance of each expression.

The most general common instance of two expressions is a common instance mgci with the property that every other common instance is an instance of mgci.

Now we can describe the intersection of the sets given by two type expressions. It is called the unification of the two, which is the most general common instance of the two type expressions.

Answer:

If you want to think of types as "things", then one can talk about the words we write to describe them, words like `Int`

and `Cont (r -> a) (Maybe q)`

as a language to describe those things. A similar distinction lies between the number 3 and the Haskell code fragment `3`

.

In the same way that `3`

is a (value) expression denoting the number 3, `Integer`

is a type expression denoting the type of integers.

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