Created
May 1, 2011 18:25
-
-
Save MSeven/950714 to your computer and use it in GitHub Desktop.
Patent 5,893,120
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
{- | | |
The claims of United States Patent 5,893,120 may be reduced to a set | |
of mathematical formulae expressed in the Typed Lambda Calculus, also | |
known as System F. This file contains these formulae. The language | |
used is Haskell, which is a version of System F with extra "syntactic | |
sugar" to make it useful for practical purposes. | |
It happens that formulae expressed in Haskell can also be transated by | |
a Haskell compiler into executable computer programs. However that | |
does not make a Haskell function any less of a mathematical formula. | |
Otherwise the quadratic formula | |
> x = (b +/- sqrt (-b^2 - 4ac))/2a | |
would be rendered patentable subject material by the same argument. | |
-} | |
module Patent120 where | |
import Data.Char (ord) | |
-- The "ord" function defines a bijection between text characters and | |
-- numbers. | |
import Data.Map (Map) | |
import qualified Data.Map as M | |
-- The Data.Map module is a standard module defined entirely as a set | |
-- of Haskell formulae, in the same way as this module. The "import" | |
-- means that these formulae are incorporated with the formulae given | |
-- here. | |
{- | |
Claim 1. An information storage and retrieval system, the system | |
comprising: | |
a linked list to store and provide access to records stored in a | |
memory of the system, at least some of the records automatically | |
expiring, | |
a record search means utilizing a search key to access the linked | |
list, | |
the record search means including a means for identifying and removing | |
at least some of the expired ones of the records from the linked list | |
when the linked list is accessed, and | |
means, utilizing the record search means, for accessing the linked | |
list and, at the same time, removing at least some of the expired ones | |
of the records in the linked list. | |
-} | |
-- | A record with Birth value below some threshold is considered "expired". | |
type Birth = Integer | |
-- | Records in the list have their birth recorded, and also contain | |
-- a key and a value. | |
data Record k a = Record Birth k a | |
-- | True iff the record is older than the threshold argument. | |
expired t (Record b _ _) = b < t | |
-- | True iff the record matches the key. | |
matches k (Record _ k1 _) = k == k1 | |
-- | The value stored in a record. | |
value (Record _ _ v) = v | |
-- | Records are stored in a linked list in the system memory. | |
type Storage k a = [Record k a] | |
-- | The "search1" function includes a threshold age parameter. | |
-- It returns both the items that match the key and the linked list | |
-- with the expired items removed. | |
-- | |
-- The recitation of "means" cannot be used to disguise the formula | |
-- given here. Otherwise any mathematical formula could be patented | |
-- by reciting e.g. "addition means" and "multiplication means" that are | |
-- mechanically derived from the formula. | |
search1 :: (Eq k) => Birth -> k -> Storage k a -> (Storage k a, [a]) | |
search1 t k records = foldr nextItem ([], []) records | |
where | |
nextItem r@(Record b k2 v) (retained,found) = | |
(if b > t then r:retained else retained, | |
if k == k2 then v:found else found) | |
{- | |
Claim 2. The information storage and retrieval system according to | |
claim 1 further including means for dynamically determining maximum | |
number for the record search means to remove in the accessed linked | |
list of records. | |
-} | |
-- | Similar to "search1", but with an added parameter for the maximum | |
-- number of records to remove. | |
search2 :: (Eq k) => Int -> Birth -> k -> Storage k a -> (Storage k a, [a]) | |
search2 n t k = (\(_,x,y) -> (x,y)) . foldr nextItem (n,[],[]) | |
where | |
nextItem r@(Record b k2 v) (n2,retained,found) = | |
(n2-1, | |
if b > t || n2 == 0 then r:retained else retained, | |
if k == k2 then v:found else found) | |
{- | |
Claim 3. A method for storing and retrieving information records using | |
a linked list to store and provide access to the records, at least | |
some of the records automatically expiring, the method comprising the | |
steps of: | |
accessing the linked list of records, | |
identifying at least some of the automatically expired ones of the | |
records, and | |
removing at least some of the automatically expired records from the | |
linked list when the linked list is accessed. | |
Claim 4. The method according to claim 3 further including the step of | |
dynamically determining maximum number of expired ones of the records | |
to remove when the linked list is accessed. | |
-} | |
-- | Claim 3 can be reduced to the same formula as Claim 1. The use of | |
-- a sequence of steps cannot disguise the fact that this represents | |
-- a mathematical formula. Otherwise it would be possible to patent | |
-- any mathematical formula simply by reciting the steps in evaluating | |
-- it. e.g. "step 3: the addition of the results of step 1 and step 2" | |
search3 :: (Eq k) => Birth -> k -> Storage k a -> (Storage k a, [a]) | |
search3 = search1 | |
-- | Likewise Claim 4 can be reduced to the same formula as Claim 2. | |
search4 :: (Eq k) => Int -> Birth -> k -> Storage k a -> (Storage k a, [a]) | |
search4 = search2 | |
{- | |
Claim 5. An information storage and retrieval system, the system | |
comprising: | |
a hashing means to provide access to records stored in a memory of the | |
system and using an external chaining technique to store the records | |
with same hash address, at least some of the records automatically | |
expiring, | |
a record search means utilizing a search key to access a linked list | |
of records having the same hash address, | |
the record search means including means for identifying and removing | |
at least some expired ones of the records from the linked list of | |
records when the linked list is accessed, and | |
meals, utilizing the record search means, for inserting, retrieving, | |
and deleting records from the system and, at the same time, removing | |
at least some expired ones of the records in the accessed linked list | |
of records. | |
-} | |
-- | Every key has a hash code. Strings of characters may be used as | |
-- keys. | |
class (Eq k) => Hashable k where | |
hash :: k -> Int -- Every key has a hash code. | |
instance Hashable Char where hash = ord | |
instance (Hashable a) => Hashable [a] where | |
hash = foldr (\x h -> ((hash x + h) * 53 + 1) `mod` 1733) 0 | |
type HashedStore k a = Map Int [Record k a] | |
-- | Access a hashed store with a function that returns the modified list of records. | |
hashAccess5 :: (Hashable k) => | |
(Storage k a -> (Storage k a, [a])) -> Birth -> k -> HashedStore k a -> (HashedStore k a, [a]) | |
hashAccess5 f t k store = (M.insert h retained store, result) | |
where | |
h = hash k | |
(retained, result) = case M.lookup h store of | |
Just records -> f $ filter (expired t) records | |
Nothing -> ([], []) | |
-- | Search using hashAccess. | |
search5 :: (Hashable k) => Birth -> k -> HashedStore k a -> (HashedStore k a, [a]) | |
search5 t k = hashAccess5 srch t k | |
where srch store = (store, map value $ filter (matches k) store) | |
-- | Insert using hashAccess. | |
insert5 :: (Hashable k) => Birth | |
-- ^ Expiry threshold for old entries. | |
-> Birth | |
-- ^ Birth date for new entry. | |
-> k -> a -> HashedStore k a -> HashedStore k a | |
insert5 t b k v = fst . hashAccess5 (\store -> (Record b k v : store, [])) t k | |
-- | Delete using hashAccess | |
delete5 :: (Hashable k) => Birth -> k -> HashedStore k a -> HashedStore k a | |
delete5 t k = fst . hashAccess5 (\store -> (filter (not . deleted) store, [])) t k | |
where deleted (Record _ k1 _) = (k == k1) | |
{- | |
Claim 6. The information storage and retrieval system according to | |
claim 5 further including means for dynamically determining maximum | |
number for the record search means to remove in the accessed linked | |
list of records. | |
-} | |
-- | Access a hashed store with a function that returns the modified list of records. The "Int" | |
-- argument is the maxiumum number of expired records to remove. | |
hashAccess6 :: (Hashable k) => | |
Int -> (Storage k a -> (Storage k a, [a])) -> Birth -> k -> HashedStore k a -> (HashedStore k a, [a]) | |
hashAccess6 n f t k store = (M.insert h retained store, result) | |
where | |
h = hash k | |
(retained, result) = case M.lookup h store of | |
Just records -> f $ filterN n (expired t) records | |
Nothing -> ([], []) | |
filterN _ _ [] = [] | |
filterN n1 p (x:xs) = if n1 <= 0 || p x then x : filterN n1 p xs else filterN (n1-1) p xs | |
-- | Search using hashAccess. | |
search6 :: (Hashable k) => Int -> Birth -> k -> HashedStore k a -> (HashedStore k a, [a]) | |
search6 n t k = hashAccess6 n srch t k | |
where srch store = (store, map value $ filter (matches k) store) | |
-- | Insert using hashAccess. | |
insert6 :: (Hashable k) => Int | |
-> Birth | |
-- ^ Expiry threshold for old entries. | |
-> Birth | |
-- ^ Birth date for new entry. | |
-> k -> a -> HashedStore k a -> HashedStore k a | |
insert6 n t b k v = fst . hashAccess6 n (\store -> (Record b k v : store, [])) t k | |
-- | Delete using hashAccess | |
delete6 :: (Hashable k) => Int -> Birth -> k -> HashedStore k a -> HashedStore k a | |
delete6 n t k = fst . hashAccess6 n (\store -> (filter (not . deleted) store, [])) t k | |
where deleted (Record _ k1 _) = (k == k1) | |
{- | |
Claim 7. A method for storing and retrieving information records using | |
a hashing technique to provide access to the records and using an | |
external chaining technique to store the records with same hash | |
address, at least some of the records automatically expiring, the | |
method comprising the steps of: | |
accessing a linked list of records having same hash address, | |
identifying at least some of the automatically expired ones of the records, | |
removing at least some of the automatically expired records from the | |
linked list when the linked list is accessed, and | |
inserting, retrieving or deleting one of the records from the system | |
following the step of removing. | |
Claim 8. The method according to claim 7 further including the step of | |
dynamically determining maximum number of expired ones of the records | |
to remove when the linked list is accessed. | |
-} | |
-- | As with Claim 3 vs Claim 1, the formulae for Claim 7 are the same as for Claim 5 | |
hashAccess7 :: (Hashable k) => | |
(Storage k a -> (Storage k a, [a])) -> Birth -> k -> HashedStore k a -> (HashedStore k a, [a]) | |
hashAccess7 = hashAccess5 | |
search7 :: (Hashable k) => Birth -> k -> HashedStore k a -> (HashedStore k a, [a]) | |
search7 = search5 | |
insert7 :: (Hashable k) => Birth | |
-- ^ Expiry threshold for old entries. | |
-> Birth | |
-- ^ Birth date for new entry. | |
-> k -> a -> HashedStore k a -> HashedStore k a | |
insert7 = insert5 | |
delete7 :: (Hashable k) => Birth -> k -> HashedStore k a -> HashedStore k a | |
delete7 = delete5 | |
-- | And the formulae for Claim 8 are the same as for Claim 6 | |
hashAccess8 :: (Hashable k) => | |
Int -> (Storage k a -> (Storage k a, [a])) -> Birth -> k -> HashedStore k a -> (HashedStore k a, [a]) | |
hashAccess8 = hashAccess6 | |
search8 :: (Hashable k) => Int -> Birth -> k -> HashedStore k a -> (HashedStore k a, [a]) | |
search8 = search6 | |
insert8 :: (Hashable k) => Int | |
-> Birth | |
-- ^ Expiry threshold for old entries. | |
-> Birth | |
-- ^ Birth date for new entry. | |
-> k -> a -> HashedStore k a -> HashedStore k a | |
insert8 = insert6 | |
delete8 :: (Hashable k) => Int -> Birth -> k -> HashedStore k a -> HashedStore k a | |
delete8 = delete6 |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment