A library for algebraic data types.
by Robert Smith
CL-ALGEBRAIC-DATA-TYPE, or ADT, is a library for defining algebraic data types in a similar spirit to Haskell or Standard ML, as well as for operating on them.
We can define ADTs using
(adt:defdata maybe (just t) nothing)
which will define a new type
maybe, with a unary constructor
and a nullary constructor
t represents the data type
of that field.
> (just 5) #.(JUST 5) > nothing #.NOTHING
Note that the
#. are printed so that they can be read back. This
allows them to be used literally in quoted lists, for example.
> '(#.(just 1) #.nothing) (#.(JUST 1) #.NOTHING) > (typep (first *) 'maybe) T
If this is annoying to you, you can set the variable
We can define our own version of a list via
(adt:defdata liszt (kons t liszt) knil)
which defines the binary constructor
kons and the nullary constructor
> (kons 1 (kons 2 knil)) #.(KONS 1 #.(KONS 2 #.KNIL))
At the end we will define
For efficiency, we might specify the types more exactly. For a
type that supports rectangular and polar coordinates, which is also
mutable, we might have:
(adt:defdata (point :mutable t) (rectangular float float) (polar float float))
:mutable option signifies that the data is mutable.
When we have constructed a value, we can extract data out of it using
> (let ((pt (rectangular 1.0 2.0))) (adt:match point pt ((rectangular x y) (+ x y)) ((polar _ _) nil))) 3.0
If we did not include the
polar case, we would get a warning.
> (let ((pt (rectangular 1.0 2.0))) (adt:match point pt ((rectangular x y) (+ x y)))) ; caught WARNING: ; Non-exhaustive match. Missing cases: (POLAR) 3.0
We can also specify a fall-through:
> (let ((pt (rectangular 1.0 2.0))) (adt:match point pt ((rectangular x y) (+ x y)) (_ nil))) 3.0
point is mutable, we can efficiently modify its fields using
> (defun mirror-point! (pt) (adt:with-data (rectangular x y) pt (adt:set-data pt (rectangular y x)))) > (let ((pt (rectangular 1.0 2.0))) (mirror-point! pt) (adt:match point pt ((rectangular x y) (format t "point is (~A, ~A)" x y)) (_ nil))
point is (2.0, 1.0).
See examples.txt for examples.
Frequently Asked Questions
Q. How do we define
(defun kar (l) (adt:match liszt l ((kons a _) a) (knil knil))) (defun kdr (l) (adt:match liszt l ((kons _ b) b) (knil knil)))
Q. Can I get the constructors dynamically for a particular ADT?
A. Yes. You can get the constructors and associated arity by
get-constructors function, which will return a list of
(<constructor> <arity>) pairs. For example, given the
example above, we have
> (adt:get-constructors 'liszt) ((KONS 2) (KNIL 0)) T
The second value
t represents the fact that the ADT is known and
Q. I have an ADT defined, and I'd like to extend it with another ADT. How can I do that?
A. You can define a new ADT which includes another one. For example, consider the following Boolean ADT.
(adt:defdata bool true false)
Suppose you wanted to extend this to have a "fuzzy" option, a
probability between true and false, specifically a
1 exclusive. We can create a
fuzzy-bool which includes the
bool type, as well as a unary
fuzzy constructor. This is done by
:include option to
(adt:defdata (fuzzy-bool :include bool) (fuzzy (real (0) (1))))
false are constructors for both
fuzzy-bool, as we can see with
> (adt:get-constructors 'bool) ((TRUE 0) (FALSE 0)) T > (adt:get-constructors 'fuzzy-bool) ((TRUE 0) (FALSE 0) (FUZZY 1)) T
Q. Can we do parametric ADTs like I can in Haskell?
A. There is no support for it because Lisp doesn't have any useful notion of definable parametric types that aren't aliases of another existing parametric type.
Q. Why doesn't deeper pattern matching work?
A. It's not implemented, but it could be implemented for fields which are themselves algebraic data types. Patches welcome!