[Declarative Programming + Elm] Bài 4 – Math & Type Variable

Now we will start talking about the points to note about the common handling operations for data types introduced in the previous article. However, before starting with detailed examples, I still want to re-list the names of the data types here so that we can easily follow the logic circuit and the relationship between the types (if any) –

• Float , Int , number – arithmetic values. For example: 10.01 , 10 , …
• Bool – logical identifiers True and False
• Char – single characters. For example: 'A' , 'z' , …
• String – text strings. Example: "Elm Language"
• Record – describe records similar to C struct and JS Object
• Tuple – concise description of records without field names
• List – stores values ​​of the same type in the form of an enumeration list

Ok.. let’s get started. To save time, we will interact with Elm REPL like the previous article. However, you can create module files to save the example code if you want.

Arithmetic operations

Package: elm/core/Basics

Not much different from Imperative languages ​​like C or JavaScript that we already know. + , - , * , / basic operations.

However, the first note is that Elm does not support automatic conversion of the data type from Int to Float . The value returned by round is of type Int , and 1 : Int cannot be added directly to 2.0 : Float –

But 1 : number and 2.0 : Float are valid for such + calculation. As for the reason, we will save it for the last item.

There is division to get the integer part with the // symbol, I have never seen it.

The exponentiation uses the ^ notation, which is different from JS ‘s ** .

In addition, other operations will be handled by sub-program . For example, division with remainder 9 % 2 in JS –

Taking the inverse of a number in Elm will not use the - operator. The reason is, I would like to save it for the next Sub-Series . Here we just treat it as a special handling convention and use it like that.

Absolute value –

Square root of 2 –

Round the value to the nearest boundary –

Round up and down –

Decreasing to origin 0 –

Checks the NaN of a value obtained from an implementation that returns type Float –

Division by 0/0 and taking the square root of -1 cannot give an arithmetically significant result, so we get the value NaN . However, in the case below, the result is positive infinity. Infinite is still of type Float .

and to check if a return value from a Float type operation is Infinite –

NaN and Infinite are fundamentally different: NaN has no arithmetic meaning, and Infinite is an arithmetic value.

Logical calculations

The symbols && and || used by Elm with the same meaning as C and JS . However, negation, also known as the inverse of a Bool value, is handled by the not program, instead of the ! like C and JS .

Comparative statements, most still use the notations as we know == , > , < , >= , <= . The only symbol != in C and JS to check the identity of two values ​​is different, replaced by Elm by /= .

Type Variable

Purely Declarative languages ​​are mostly built with one spirit in mind – very strong typing and strict strong-typing . And here we have Elm as one of them.

Specifically the error message like the + calculation example between an Int value and a Float value that we saw at the beginning of the article. Although Elm ‘s compiler already has enough information about the received values ​​before performing the calculation, Elm simply does not support automatic implicit type conversion in this case. And we will need to do the data type conversion in our code –

Oh but why does the calculation 1 + 2.0 have no error message?

The value 1 returned by round is typed Int . The value 1 that we write directly into our code file is untyped, so Elm will treat it as a variable of type number .

The concept of variable type Type Variable , can be understood simply as any data type that the compiler does not find explicit type information in the code. And will try to find a most suitable success processing logic when getting the actual value at code runtime .

Precisely, a variable type a is understood as a Union type that includes all data types that the compiler collects in the definition code of the entire project program. However, Elm also generates a few Type Variable with more limited possibilities than a . That is –

• number – is an arithmetic value; So it can be Float or Int .
• comparable – is a value that can be compared by the compare program; Includes Int , Float , Char , String , and List/Tupple of those types.
• appendable – is a value that can perform content concatenation operations; So it could be a String or a List .
• compappend – is a value that is both comparable and appendable .

Thus, when the compiler reads the calculation 1 + 2.0 , the value 2.0 already has enough clear type information to be Float due to the decimal point . ; The value 1 does not have specific type information, so it will be number . The most suitable success logic is Float + Float and we have the compiled logic as 1.0 + 2.0 . The calculation is done and there is no error message.

comparable

By the way, after introducing the concept of Type Variable variable type, we have some predefined types as listed above. The number we just used to illustrate the example above, and among the remaining types, here we have enough knowledge to talk about comparable .

A value of type comparable can be used in a comparison operation using the compare program.

Here we need to pay a little attention to avoid confusion. The logical operations > , < , == , /= , etc.. that return Bool values ​​are used to test a comparison statement. In other words, to test an evaluation. And such a kiểm tra operation will have a slightly different meaning from the so sánh compare that we just talked about above.

A test a == b will give the answer to the question: ” a is equal to b . True or False? If đúng , choose True , and if sai , choose False . !”

And a compare ab comparison, on the other hand, will give the answer to the question: “What is a vs b ? Equal to EQ ? Or less than LT ? Or greater than GT ? Answer immediately and always !”

The result of a so sánh , then, of course can also be used to navigate the operating logic of the code we build. And Elm also has some basic, very useful programs that use these Order values.

About how the two strings "abc" and "xyz" are compare with logic, we will save it for the next article.

(unpublished) [Declarative Programming + Elm] Lesson 5 – String & List