Monday, May 3, 2021

Lightweight table

You don't need a data structure to make a lookup table. You can make a table just out of the lookup function. In this example, we start with a continuation passing style lookup function:

lookup (key if-found if-not-found)
    Invokes (funcall if-found value) if key is in the table,
    invokes (funcall if-not-found) otherwise.
An empty table just invokes the if-not-found continuation:
(defun table/empty ()
  (lambda (key if-found if-not-found)
    (declare (ignore key if-found))
    (funcall if-not-found)))
A table can be extended by wrapping it:
(defun table/extend (table key* value)
  (lambda (key if-found if-not-found)
    (if (eql key key*)
        (funcall if-found value)
        (funcall table key if-found if-not-found))))
So let's try it out:
(defvar *table-1* (table/extend 
                      'foo 42)
                    'bar 69))

* (funcall *table-1* 'foo #'identity (constantly 'not-found))

* (funcall *table-1* 'quux #'identity (constantly 'not-found))
You can also redact an entry from a table by wrapping the table:
(defun table/redact (table redacted)
  (lambda (key if-found if-not-found)
    (if (eql key redacted)
        (funcall if-not-found)
        (funcall table key if-found if-not-found))))

(defvar *table-2* (table/redact *table-1* 'foo))

* (funcall *table-2* 'foo #'identity (constantly 'not-found))

Are there any advantages to implementing a table in this curious manner? Building a table by nesting a series of lookup steps leads to a linear lookup in linear space, so this kind of table should be more or less comparable to an alist for individual entries. Unlike a traditional table made with a data structure, you cannot enumerate the keys and values in the table. On the other hand, you gain the ability to map keys to values without having to enumerate the keys:

(defun table/bind-predicate (table predicate value)
  (lambda (key if-found if-not-found)
    (if (funcall predicate key)
        (funcall if-found value)
        (funcall table key if-found if-not-found))))

;;; bind all even numbers to the symbol 'EVEN
(defvar *table-3* 
  (table/bind-predicate *table-2* (lambda (n) (and (numberp n) (evenp n))) 'even))

* (funcall *table-3* 6 #'identity (constantly 'not-found))
Or you can add a default value to an existing table:
(defun table/add-default (table default-value)
  (lambda (key if-found if-not-found)
    (declare (ignore if-not-found))
    (funcall table key
      (lambda () (funcall if-found default-value)))))

(defvar *table-4* (table/add-default *table-3* 'default))

* (funcall *table-4* 'bar #'identity (constantly 'not-found))
* (funcall *table-4* 'xyzzy #'identity (constantly 'not-found))

Perhaps the biggest disadvantage of this implementation is the difficulty in inspecting a table.

* *table-4*
We can use the object inspector to peek inside the closure and maybe sleuth out what this table is made out of, but it isn't just an alist where we can print out the entries.

So far, we've defined a table as being a procedure with the (key if-found if-not-found) signature, but we can flip this around and say that any procedure with a (key if-found if-not-found) signature can be thought of as a table. For example, a regular expression matcher could be considered to be a table of strings (if that were a more useful model).

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