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Starting to expand out the documentation in preparation of merging this

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original commit: d6f527a96f05fe949ef032c471e2abca9bc89da9
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Stevie Strickland 2008-07-13 16:07:29 -04:00
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collects/typed-scheme/typed-scheme.scrbl
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@ -185,6 +185,10 @@ process of elimination we can determine that @scheme[t] must be a
@section{Polymorphism}
Typed Scheme offers abstraction over types as well as values.
@subsection{Polymorphic Data Structures}
Virtually every Scheme program uses lists and sexpressions. Fortunately, Typed
Scheme can handle these as well. A simple list processing program can be
written like this:
@ -246,6 +250,52 @@ produces @scheme[(make-Just v)] when the number is found in the list,
and @scheme[(make-Nothing)] otherwise. Therefore, it produces a
@scheme[(Maybe Number)], just as the annotation specified.
@subsection{Polymorphic Functions}
Sometimes functions over polymorphic data structures only concern
themselves with the form of the structure. For example, one might
write a function that takes the length of a list of numbers:
@schememod[typed-scheme
(: list-number-length ((Listof Number) -> Integer))
(define (list-number-length l)
(if (null? l)
0
(add1 (list-number-length (cdr l)))))]
and also a function that takes the length of a list of strings:
@schememod[typed-scheme
(: list-string-length ((Listof String) -> Integer))
(define (list-string-length l)
(if (null? l)
0
(add1 (list-string-length (cdr l)))))]
Notice that both of these functions have almost exactly the same
definition; the only difference is the name of the function. This
is because neither function uses the type of the elements in the
definition.
We can abstract over the type of the element as follows:
@schememod[typed-scheme
(: list-length (All (A) ((Listof A) -> Integer)))
(define (list-length l)
(if (null? l)
0
(add1 (list-length (cdr l)))))]
The new type constructor @scheme[All] takes a list of type
variables and a body type. The type variables are allowed to
appear free in the body of the @scheme[All] form.
@section{Variable-Arity Functions}
@subsection{Uniform Variable-Arity Functions}
@subsection{Non-Uniform Variable-Arity Functions}
@section[#:tag "type-ref"]{Type Reference}
@subsubsub*section{Base Types}