HASKELL MODULES DATA HIDING

REVISED: Monday, February 12, 2024

Haskell Data Hiding.

I. HASKELL DATA MODULES

You are reading "Haskell Modules Data Hiding", the second half of the "Haskell Data Modules" tutorial.

The first half is "Haskell Modules No Data Hiding".

The two parts of this tutorial are a very brief outline of "Haskell Programming Tutorial 6 - Modules" by Sankha Mukherjee. 

A. SKELETON

STEP 1: We start off with the following file containing the vector functions:

module MyVectorsF where

(·) :: (Float, Float, Float) -> (Float, Float, Float) -> Float
(·) (x1, x2, x3)(y1, y2, y3) =  x1*y1+x2*y2+x3*y3

(×) :: (Float, Float, Float) -> (Float, Float, Float) -> (Float, Float, Float)
(×) (x1, x2, x3)(y1, y2, y3) =  (x2*y3-x3*y2, x3*y1-x1*y3, x1*y2-x2*y1)

1. Create a new data type.

data Vec = V3DCart Float Float Float
        deriving (Show)

We use the data keyword to define a new data type. The part before the = denotes the data type, which is Vec. The parts after the = are value constructors. They specify the different values that this data type can have. V3DCart is a value constructor that has three fields, parameters, which take floats. Value constructors are actually functions that return a value of a data type. The value constructor V3DCart returns a value of data type Vec. Adding deriving (Show) at the end makes our Vec data type part of the Show type class so Haskell knows how to get the string representation of our value and then Haskell prints that out to the terminal. Value constructors are just functions that take the fields as parameters and return a value of some data type as a result. Not exporting the value constructors of a data type makes them more abstract in such a way that we hide their implementation. Also, whoever uses our module can not pattern match against the value constructors.

2. Create accessor function.

make3DCV :: Float -> Float -> Float -> Vec
make3DCV a b c = V3DCart a b c

Type constructors can take types as parameters to produce new types. The a b c shown above are type parameters. Because there are type parameters involved, we call make3DCV a type constructor. Type parameters are useful because we can make different types with them depending on what kind of types we want contained in our data type. If our data type acts as some kind of box container, as does Vec, it is good to use type parameters. The parts after the = are value constructors. Value constructors specify the different values that make3DCV can have. V3DCart is a value constructor that has three fields, a b c type parameters.  Value constructors are actually functions that return a value of a data type. The value constructor V3DCart returns a value of data type Vec. 

3. Create a new type class.

class VectorC a where
        (·) :: a -> a -> Float
        (×) :: a -> a -> a

We use the classs keyword to define a new type class, which is VectorC. Type classes are like interfaces. We do not make data from type classes. The a after VectorC is the data type variable and it means that a will play the role of the data type that we will soon be making when we make an instance of VectorC. It does not have to be called a, it does not even have to be one letter, it just has to be a lowercase word. Then, we define several functions; e.g., (·) and (×). It is not mandatory to implement the function bodies themselves, we just have to specify the type declarations for the functions. 

4. Create instances of the new type class.

instance VectorC  Vec where
        (·) (V3DCart x1 x2 x3) (V3DCart y1 y2 y3) = x1*y1+x2*y2+x3*y3
        (×) (V3DCart x1 x2 x3) (V3DCart y1 y2 y3) = (V3DCart (x2*y3-x3*y2) (x3*y1-x1*y3) (x1*y2-x2*y1))

We make an instance of VectorC by using the instance keyword. So class is for defining new type classes and instance is for making our data types instances of type classes. When we were defining VectorC,  we wrote class VectorC a where and we said that a plays the role of whichever data type will be made an instance later on. We can see that clearly here, because when we are making an instance, we write instance VectorC  Vec where. We replace the a with the actual data type Vec.

In summary, first, we  create a new data type Vec. Second, we create accessor functions make3DCV. Third, we think about what the Vec data type can act like and create type classes VectorC, that can behave in that way. Fourth, the functions of our new data type Vec,  are made instances of that type class VectorC. Notice, the behavior of type classes is achieved by defining functions or just type declarations that we then implement. When we say that a data type is an instance of a type class, we mean that we can use the functions (·) and (×), that the type class defines with that data type.

STEP 2: We start off with the following file containing the main function:

import MyVectorsF

main = do
    print $ (2,4,5) · (0,1,0)
    print $ (2,4,5) × (0,1,0)

1. Call imported accessor functions.

    let a = make3DCV 2 4 5

    let b = make3DCV 0 2 0

2. Print new output.

    print $ a · b

    print $ a × b

B. FLESH ON BONES

1. SAVE

Save has two steps. "Save Step 1" saves the vector functions. "Save Step 2" saves the main function.

SAVE STEP 1

Use your editor to save  MyVectorsF.hs which is the final draft of vector dot product, and cross product, function signatures and definitions:

module MyVectorsF (make3DCV, VectorC(..)) where   -- Export accessor functions and everything in the class.

class VectorC a where   -- Creates a new "type class" VectorC, which takes any generic data type a.
    (·) :: a -> a -> Float    -- Generic function signatures which take any data type a.
    (×) :: a -> a -> a

data Vec = V3DCart Float Float Float   -- Creates a new "data type" Vec.
    deriving (Show)

make3DCV :: Float -> Float -> Float -> Vec   -- Accessor function returns data type Vec.
make3DCV a b c = V3DCart a b c

instance VectorC Vec where   -- Instances of the "type class" must agree with function signatures.
    (·) (V3DCart x1 x2 x3) (V3DCart y1 y2 y3) = x1*y1+x2*y2+x3*y3
    (×) (V3DCart x1 x2 x3) (V3DCart y1 y2 y3) = (V3DCart (x2*y3-x3*y2) (x3*y1-x1*y3) (x1*y2-x2*y1))

SAVE STEP 2

Use your editor to save MyVetorsM.hs which is the final draft of the main function:

import MyVectorsF

main = do
    let a = make3DCV 2 4 5   -- Calls imported accessor function.
    let b = make3DCV 0 2 0

    print $ a · b
    print $ a × b

2. LOAD

Load has two steps. "Load Step 1" loads the vector functions. "Load Step 2" loads the main function.

LOAD STEP 1

As shown below, load the above MyVectorsF.hs file into GHCi:

Prelude>  :load MyVectorsF

[1 of 1] Compiling MyVectorsF      ( MyVectorsF.hs, interpreted )

Ok, modules loaded: MyVectorsF.

Prelude>  

LOAD STEP 2

As shown below, load the above MyVectorsM.hs file into GHCi:

Prelude>  :load MyVectorsM

[1 of 2] Compiling MyVectorsF       ( MyVectorsF.hs, interpreted )

[2 of 2] Compiling Main             ( MyVectorsM.hs, interpreted )

Ok, modules loaded: Main, MyVectorsF.

Prelude>  

Now that we have loaded Main, we can run functions in GHCi that were defined in Main.

3. RUN

As shown below, run the function main, in GHCi:

Prelude>  main

8.0
V3DCart (-10.0) 0.0 4.0

Prelude>  

If we want to see the type of the accessor function make3DCV we can do the following:

Prelude>  :load MyVectorsF

Ok, modules loaded: MyVectorsF.

Prelude>

Prelude>  :type make3DCV

make3DCV :: Float -> Float -> Float -> MyVectorsF.Vec

Prelude>

It says, if you want a vector, give me three Floats. However, if you want to see the type of MyVectorsF.Vec watch what happens. It says I am not going to tell you what a vector is.

Prelude>  :type MyVectorsF2.Vec
<interactive>:1:1: Not in scope: data constructor `MyVectorsF2.Vec'
Prelude> 

The representation of MyVectorsF.Vec is hidden from you, the user. 

4. COMPILE 

As shown below, compile MyVectorsM.hs in GHC:

Prelude>  :! ghc --make "*MyVectorsM"
[1 of 2] Compiling MyVectorsF       ( MyVectorsF.hs, MyVectorsF.o )
[2 of 2] Compiling Main                  ( MyVectorsM.hs, MyVectorsM.o )
Linking MyVectorsM.exe ...
Prelude>  

The compile is shown so you know it compiles without error.

C. COMMENTS

Use the program shown above as an example. Rewrite the example and make it your own program.

Repeat 1. thru 3. above until your new program works the way you want it to work. Each time you make changes in your editor to your program, make sure you save the file and load it in GHCi.

II. CONCLUSION

In this tutorial, you have been introduced to the advantages of using "Haskell Modules Data Hiding."

III. REFERENCE

Haskell Programming by Sankha Mukherjee

Haskell Tutorial 6 - Modules

HASKELL MODULES NO DATA HIDING

REVISED: Monday, February 12, 2024

Haskell Modules No Data Hiding.

I. HASKELL DATA MODULES

You are reading "Haskell Modules No Data Hiding",  the first half of the "Haskell Data Modules" tutorial.

"Haskell Modules Data Hiding"  is the second half.

The two parts of this tutorial are a very brief outline of "Haskell Programming Tutorial 6 - Modules" by Sankha Mukherjee.

A. SKELETON

We start off with the following file containing both the main function and the vector functions:

main = do

       print $ (2,4,5) · (0,1,0)

       print $ (2,4,5) × (0,1,0)

(·) :: (Float, Float, Float) -> (Float, Float, Float) -> Float
(·) (x1, x2, x3)(y1, y2, y3) =  x1*y1+x2*y2+x3*y3

(×) :: (Float, Float, Float) -> (Float, Float, Float) -> (Float, Float, Float)
(×) (x1, x2, x3)(y1, y2, y3) =  (x2*y3-x3*y2, x3*y1-x1*y3, x1*y2-x2*y1)

What happens if we need these vector functions in hundreds of other programs? One solution would be to copy past them into each of the other programs. 

However, what happens if we want to change a function; for example, changing from a three element tuple to a two element tuple? Changes might have to be made to hundreds of files that were copy pasted.

A good programming maintenance technique is to use modules.

One module for each group of related functions.

One module containing the main function.

B. FLESH ON BONES

1. SAVE

Save has two steps. "Save Step1" saves the module containing the vector functions. "Save Step 2" saves the main function.

SAVE STEP 1

Use your editor to save  MyVectorsF.hs the vector dot product, and vector cross product, function signatures and definitions. Notice both of these functions are tied to a particular data type; i.e., Float. Also notice each vector function assumes a "three element tuple". What do you do when you need the dot product or cross product of a vector which has less tuple elements or more tuple elements? That question will be answered in "Haskell Data Hiding".

module MyVectorsF where

(·) :: (Float, Float, Float) -> (Float, Float, Float) -> Float
(·) (x1, x2, x3)(y1, y2, y3) =  x1*y1+x2*y2+x3*y3

(×) :: (Float, Float, Float) -> (Float, Float, Float) -> (Float, Float, Float)
(×) (x1, x2, x3)(y1, y2, y3) =  (x2*y3-x3*y2, x3*y1-x1*y3, x1*y2-x2*y1)

SAVE STEP 2

Use your editor to save MyVetorsM.hs the main function. Notice by importing MyVectorsF you do not have to copy paste the vector functions into the main function.

import MyVectorsF

main = do

    print $ (2,4,5) · (0,1,0)

    print $ (2,4,5) × (0,1,0)

2. LOAD

Load has two steps. "Load Step 1" loads the vector functions. "Load Step 2" loads the main function.

LOAD STEP 1

As shown below, load the above MyVectorsF.hs file into GHCi:

Prelude>  :load MyVectorsF

[1 of 1] Compiling MyVectorsF      ( MyVectorsF.hs, interpreted )

Ok, modules loaded: MyVectorsF.

Prelude>  

LOAD STEP 2

As shown below, load the above MyVectorsM.hs file into GHCi:

Prelude>  :load MyVectorsM

[1 of 2] Compiling MyVectorsF       ( MyVectorsF.hs, interpreted )

[2 of 2] Compiling Main             ( MyVectorsM.hs, interpreted )

Ok, modules loaded: Main, MyVectorsF.

Prelude>  

Now that we have loaded Main, we can run functions in GHCi that were defined in Main.

3. RUN

As shown below, run the main function, in GHCi:

Prelude>  main

4.0
(-5.0,0.0,2.0)

Prelude>  

4. COMPILE 

As shown below, compile MyVectorsM.hs in GHC:

Prelude>  :! ghc --make "*MyVectorsM"
[1 of 2] Compiling MyVectorsF       ( MyVectorsF.hs, MyVectorsF.o )
[2 of 2] Compiling Main             ( MyVectorsM.hs, MyVectorsM.o )
Linking MyVectorsM.exe ...
Prelude>  

The compile is shown so you know it compiles without error.

C. COMMENTS

Use the program shown above as an example. Rewrite the example and make it your own program.

Repeat 1. thru 3. above until your new program works the way you want it to work. Each time you make changes in your editor to your program, make sure you save the file and load it in GHCi.

II. CONCLUSION

You have just received an introduced to "Haskell Modules No Data Hiding", the first half of the "Haskell Data Modules" tutorial.   "Haskell Modules Data Hiding" is the second half of "Haskell Data Modules".

III. REFERENCE

Haskell Programming by Sankha Mukherjee

Haskell Tutorial 6 - Modules

HASKELL TOWERS OF HANOI

REVISED: Wednesday, January 24, 2024

Haskell Towers of Hanoi.

I. HASKELL TOWERS OF HANOI

The Towers of Hanoi is a game or puzzle. It consists of three vertical anchored rods of equal length and diameter, spaced an equal distance apart on a playing board. The puzzle includes a number of disks of different diameters and equal thickness with a hole in their center slightly larger than the diameter of the rods. The disks can slide onto any of the three rods. The puzzle starts with all the disks in a neat conical stack, the smallest disk at the top, in ascending order of size on one rod, the rod to the far left facing the player. The far right vertical rod can be used as a temporary resting place for the disks as they are moved back and forth between the three rods. The objective of the puzzle is to eventually move the entire stack of disks from the rod on the far left, to the rod in the middle, obeying the following rules:

A. Only one disk may be moved at a time.

B. Each move consists of taking the upper disk from one of the rods and sliding it onto another rod, on top of the other disks that may already be present on that rod.

C. No disk may be placed on top of a smaller disk.

A. SKELETON

main :: IO ()

main = do  

B. FLESH ON BONES

1. SAVE

Use your editor to save the following TowersOfHanoi.hs file:

main :: IO ()
main = do
        putStrLn "Given three stationary rods: r1, r2, and r3; enter number of disks you want to move: "
        a <- readLn
        let d = hanoi a "r1" "r2" "r3"
        putStrLn "Towers of Hanoi Disk Movement Solution: "
        putStr d

-- Towers of Hanoi
hanoi :: Integer -> String -> String -> String -> String
hanoi 1 r1 r2 r3 = "From " ++ r1 ++ " to " ++ r2 ++ "\n"
hanoi n r1 r2 r3 =(hanoi (n-1) r1 r3 r2) ++ (hanoi 1 r1 r2 r3) ++ (hanoi (n-1) r3 r2 r1)

2. LOAD

As shown below, load the above TowersOfHanoi.hs file into GHCi:

Prelude>  :load TowersOfHanoi
[1 of 1] Compiling Main             ( TowersOfHanoi.hs, interpreted )
Ok, modules loaded: Main.
Prelude>

Now that we have loaded Main, we can run functions in GHCi that were defined in Main.

3. RUN

As shown below, run the function main, in GHCi:

Prelude>  main
Given three stationary rods: r1, r2, and r3; enter number of disks you want to move: 
3
Towers of Hanoi Disk Movement Solution: 
From r1 to r2
From r1 to r3
From r2 to r3
From r1 to r2
From r3 to r1
From r3 to r2
From r1 to r2
Prelude>  

4. COMPILE 

As shown below, compile TowersOfHanoi.hs in GHC:

Prelude>  :! ghc --make "*TowersOfHanoi"
[1 of 1] Compiling Main             ( TowersOfHanoi.hs, TowersOfHanoi.o )
Linking TowersOfHanoi.exe ...
Prelude>

The compile is shown so you know it compiles without error.

C. COMMENTS

Use the program shown above as an example. Rewrite the example and make it your own program.

Repeat 1. thru 3. above until your new program works the way you want it to work. Each time you make changes in your editor to your program, make sure you save the file and load it in GHCi.

II. REFERENCE

Haskell Programming by Sankha Mukherjee

Haskell Tutorial 3 - Recursion

In this tutorial, you have been introduced to a Haskell recursive solution for the Towers of Hanoi.