Sorted Dictionary Assignment

Background

ref

How to use ref

Motivation

In this and the follow up Sorted Dictionary studio, you will build three implementations of a dictionary. Each will be an immutable data structure.

Reference

SML structure Option

datatype 'a option = NONE | SOME of 'a

Code To Investigate

signature Dictionary

Note the include in the DICTIONARY signature.

signature DICTIONARY_FUNCTOR_PARAMETER = sig
    type (''k,'v) dictionary
    type ''k create_parameter_type
    val create : ''k create_parameter_type -> (''k,'v) dictionary
    val get : ((''k,'v) dictionary *''k) -> 'v option
    val put : ((''k,'v) dictionary *''k *'v) -> (''k,'v) dictionary * 'v option
    val remove : ((''k,'v) dictionary *''k) -> (''k,'v) dictionary * 'v option
    val entries : (''k,'v) dictionary -> (''k*'v) list
end

signature DICTIONARY = sig include DICTIONARY_FUNCTOR_PARAMETER
    val keys : (''k,'v) dictionary -> ''k list
    val values : (''k,'v) dictionary -> 'v list
end

create

Specific to each structure. Creates an empty immutable Dictionary.

get

Behaves much like java.util.Map<K,V>'s get(key) method except instead of returning null or the associated value, it returns an option.

put

Behaves much like java.util.Map<K,V>'s put(key,value) method except

1. instead of mutating the provided dictionary, it returns an immutable updated dictionary.
2. instead of returning null or the previously associated value, it returns an option of the previously associated value (along with the updated dictionary in a 2-tuple).

remove

Behaves much like java.util.Map<K,V>'s remove(key) method except instead of returning null or the previously associated value, it returns an option.

1. instead of mutating the provided dictionary, it returns an immutable updated dictionary.
2. instead of returning null or the previously associated value, it returns an option of the previously associated value (along with the updated dictionary in a 2-tuple).

entries

Behaves much like java.util.Map<K,V>'s entrySet() method.

keys

Behaves much like java.util.Map<K,V>'s keySet() method.

values

Behaves much like java.util.Map<K,V>'s values() method.

Code To Implement

functor DictionaryFn

Each implementation of dictionary can reuse the same functions which given a list of entries produce the keys and values. functor DictionaryFn accepts a signature parameter which defines all of the necessary functions besides keys and values. Critically, this includes the entries function which can be employed to support the keys and values functions.

keys

One of List's higher order functions can be useful here. Which one is it?

fun keys(dict : (''k,'v) dictionary) : ''k list = 
	raise Fail "NotYetImplemented"

values

One of List's higher-order functions can be useful here. Which one is it?

fun values(dict : (''k,'v) dictionary) : 'v list = 
	raise Fail "NotYetImplemented"

structure Chain

Both the SingleChainedDictionary and the HashedDictionary will leverage chaining to deal with collisions. A collision is where more than one (key, value) entry wants to be store in the same chain (a.k.a. list of (key, value) entries). For the SingleChainedDictionary, every unique key will "collide" with every other one since all of them will be stored in the single chain of the SingleChainedDictionary. For the HashedDictionary, there should be fewer collisions since there will be a multiple chains to spread the load, but handling collisions should be similar to the SingleChainedDictionary once the appropriate chain is determined.

We implement structure Chain so we can use the code in both SingleChainedDictionary and HashedDictionary.

signature CHAIN = sig
	val get : (''k*'v) list * ''k -> 'v option
	val put : (''k*'v) list * ''k * 'v -> ((''k*'v) list * 'v option)
	val remove : (''k*'v) list * ''k -> ((''k*'v) list * 'v option)
end

get

fun get(chain : (''k*'v) list, key:''k) : 'v option =
    raise Fail "NotYetImplemented"

put

fun put(chain : (''k*'v) list, key:''k, value:'v) : (''k*'v) list * 'v option =
    raise Fail "NotYetImplemented"

remove

fun remove(chain : (''k*'v) list, key : ''k) : (''k*'v) list * 'v option =
    raise Fail "NotYetImplemented"

structure SingleChainedDictionary

One can imagine the utility of having a simple Dictionary without the overhead of a HashTable. Perhaps, the number of anticipated entries is small. Perhaps, its performance is not critical. Maybe the client wants to use a mutable key which would create an invalid HashedDictionary. Whatever the reason, it seems like a reasonable and straightforward implementation of Dictionary to provide.

structure SingleChainedDictionary = DictionaryFn(struct
    
    (* TODO: replace unit with the type you decide upon *)
    type (''k,'v) dictionary = unit

    type ''k create_parameter_type = unit
    
    fun create() : (''k,'v) dictionary = 
        raise Fail "NotYetImplemented"

    fun get(dict : (''k,'v) dictionary, key : ''k) : 'v option = 
        raise Fail "NotYetImplemented"

    fun put(dict : (''k,'v) dictionary, key : ''k , value : 'v) : (''k,'v) dictionary * 'v option =
        raise Fail "NotYetImplemented"
	
    fun remove(dict : (''k,'v) dictionary, key : ''k) : (''k,'v) dictionary * 'v option =
        raise Fail "NotYetImplemented"

    fun entries(dict : (''k,'v) dictionary) : (''k*'v) list =
        raise Fail "NotYetImplemented"

end)

type dictionary

Change the definition of type (''k,'v) dictionary to support SingleChainedDictionary.

(* TODO: replace unit with the type you decide upon *)
type (''k,'v) dictionary = unit

type create_parameter_type

Leave create_parameter_type unchanged. SingleChainedDictionary's create method accepts no parameters, so unit is the correct type.

type ''k create_parameter_type = unit

create function

fun create() : (''k,'v) dictionary = 
	raise Fail "NotYetImplemented"

get

fun get(dict : (''k,'v) dictionary, key : ''k) : 'v option = 
	raise Fail "NotYetImplemented"

remember to use the Chain structure.

put

fun put(dict : (''k,'v) dictionary, key : ''k , value : 'v) : (''k,'v) dictionary * 'v option =
	raise Fail "NotYetImplemented"

remember to use the Chain structure.

remove

fun remove(dict : (''k,'v) dictionary, key : ''k) : (''k,'v) dictionary * 'v option =
	raise Fail "NotYetImplemented"

remember to use the Chain structure.

entries

Define the entries method so we can take advantage of the keys and values functions you implemented on functor DictionaryFn.

fun entries(dict : (''k,'v) dictionary) : (''k*'v) list =
	raise Fail "NotYetImplemented"

structure HashedDictionary

Reference

Abstract Data Type

HashTable on Wikipedia

Hash table

SML structure Vector

1. tabulate : int * (int -> 'a) -> 'a vector
2. length : 'a vector -> int
3. sub : a vector * int -> 'a
4. update : 'a vector * int * 'a -> 'a vector
5. foldl : ('a * 'b -> 'b) -> 'b -> 'a vector -> 'b

shell

structure HashedDictionary = DictionaryFn(struct
    type ''k hash_function = ''k -> int

    (* TODO: replace unit with the type you decide upon *)
    type (''k,'v) dictionary = unit

    type ''k create_parameter_type = (int * (''k hash_function))

    fun create(bucket_count_request : int, hash : ''k hash_function) : (''k,'v) dictionary = 
        raise Fail "NotYetImplemented"

    fun positive_remainder(v : int, n : int) : int = 
        let
            val result = v mod n 
        in 
            if result >= 0 then result else result+n
        end 

    fun getChainForKey(dict : (''k,'v) dictionary, key : ''k) : (''k*'v) list =
        raise Fail "NotYetImplemented"

    fun updateChainForKey(dict : (''k,'v) dictionary, key : ''k, updater_function) : (''k,'v) dictionary * 'v option =
        raise Fail "NotYetImplemented"

    fun get(dict : (''k,'v) dictionary, key : ''k) : 'v option = 
        raise Fail "NotYetImplemented"

    fun put(dict : (''k,'v) dictionary, key : ''k , value : 'v) : (''k,'v) dictionary * 'v option =
        raise Fail "NotYetImplemented"

    fun remove(dict : (''k,'v) dictionary, key : ''k) : (''k,'v) dictionary * 'v option =
	raise Fail "NotYetImplemented"

    fun entries(dict : (''k,'v) dictionary) : (''k*'v) list =
        raise Fail "NotYetImplemented"

end)

type dictionary

Change the definition of type (''k,'v) dictionary to support HashedDictionary.

(* TODO: replace unit with the type you decide upon *)
type (''k,'v) dictionary = unit

type create_parameter_type

Leave create_parameter_type unchanged. HashedDictionary's create method accepts two parameters: an int for the requested bucket count and a hash_function.

type ''k create_parameter_type = (int * (''k hash_function))

create

fun create() : (''k,'v) dictionary = 
	raise Fail "NotYetImplemented"

positive_remainder

Hash codes can be negative. Vector indices cannot. Use this function to ensure a valid index.

fun positive_remainder(v : int, n : int) : int = 
	let
		val result = v mod n 
	in 
		if result >= 0 then result else result+n
	end

get

fun get(dict : (''k,'v) dictionary, key : ''k) : 'v option = 
	raise Fail "NotYetImplemented"

remember to use the Chain structure.

put

fun put(dict : (''k,'v) dictionary, key : ''k , value : 'v) : (''k,'v) dictionary * 'v option =
	raise Fail "NotYetImplemented"

remember to use the Chain structure.

remove

fun remove(dict : (''k,'v) dictionary, key : ''k) : (''k,'v) dictionary * 'v option =
	raise Fail "NotYetImplemented"

remember to use the Chain structure.

entries

Define the entries method so we can take advantage of the keys and values functions you implemented on functor DictionaryFn.

fun entries(dict : (''k,'v) dictionary) : (''k*'v) list =
	raise Fail "NotYetImplemented"

Testing

source folder:	src/test/sml/dictionary/chained
how to run with CM.make verbosity off:	sml -Ccm.verbose=false run_chained_testing.sml
how to run with CM.make verbosity on:	sml run_chained_testing.sml

note: ensure that you have removed all printing to receive credit for any assignment.

SML Error Messages

Pledge, Acknowledgments, Citations

file:

exercise-chained-dictionary-pledge-acknowledgments-citations.txt

More info about the Honor Pledge

Code To Use

Binary Search Tree

You will undoubtedly want to use the tree you implemented in the Binary Search Tree assignment.

HasEntriesFn

functor HasEntriesFn

Code To Implement

structure SortedDictionary

SortedDictionary must:

• have O(lg N) expected performance for find, insert, and remove.
• produce entries and keys in sorted order based on the provided compare_function.
• produce values in the sorted order of each value's key based on the provided compare_function.

structure SortedDictionary :> SORTED_DICTIONARY

 <nowiki>signature SORTED_DICTIONARY = sig include DICTIONARY
    type ''k compare_function = (''k*''k) -> order
    val create : ''k compare_function -> (''k,'v) dictionary
end

structure TypeHolder

Change the definition of type (''k,'v) dictionary to support SortedDictionary.

structure TypeHolder = struct
	(* TODO: replace unit with the type you decide upon *)
	type (''k,'v) dictionary = unit
end

structure SortedHasEntries

structure SortedHasEntries = HasEntriesFn (struct
	type (''k,'v) dictionary = (''k,'v) TypeHolder.dictionary
	fun entries(dict : (''k,'v) dictionary) : (''k*'v) list =
		raise Fail "NotYetImplemented"
end)

entries

Define the entries method so we can take advantage of the keys and values functions you implemented on functor HasEntriesFn.

create function

fun create(cmp : ''k compare_function) : (''k,'v) dictionary = 
	raise Fail "NotYetImplemented"

type (''k,'v) dictionary

We recall that BinarySearchTree.tree has two generic types 'a and 'k.

type ('a,'k) tree

'a represents the type of the contents of each node. 'k represents the type of the key for each node.

To implement a (''k,'v) SortedDictionary.dictionary with a BinarySearchTree.tree, what is the type of the contents at each node?

What is the type of the key for your BinarySearchTree.tree?

The answers to these questions will be instrumental in defining your type in the SortedDictionary structure:

(* TODO: replace unit with the type you decide upon *)
type (''k,'v) dictionary = unit

NOTE: the sorted dictionary is mutable.

create

fun create(cmp : ''k compare_function) : (''k,'v) dictionary
    raise NotYetImplemented

Testing

file: sml run_unit_test_sorted_dictionary.sml

in folder: src/test/sml/dictionary/sorted

Pledge, Acknowledgments, Citations

file:

studio-sorted-dictionary-pledge-acknowledgments-citations.txt

More info about the Honor Pledge