How many distinct characters can be used to implement Boolean Algebra in your programming language [closed]

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I am interested in the following problem:

What is the minimum number of distinct characters used in any programming language that can implement Boolean Algebra?

In particular, what is the set that has the least number of distinct characters used in a programming language of your choosing that satisfies the following:

• The characters must be able to construct a valid program in the chosen language, following the latter restrictions. In other words, all errors (compile time and runtime) ARE NOT ALLOWED. The program is allowed to have unlimited length. Warnings are also allowed.
• Can assign values to the constant True and False. Equivalent formulations such as 0 and 1, true and false, or "true" and "false" is allowed as long as it satisfies the NAND formulation (see below)
• Can define functions with or without parameters
• Can implement the NAND binary operator. That is, the program must be able to define a function NAND(a, b) that takes two values a and b and return False if both are True, and True otherwise. Note that equivalent formulations are allowed, so you may use f(a, b) or similar strategies to reduce the character count. Also note that you can implement this function in any way possible.
• Lowercase and uppcase letters are count seperately. That means AaAa counts as 2 distinct characters, but aaaa as 1.
• I/O is not required.

For example, your program should be able to implement the following Python code:

a = True
b = False
def NAND(a: bool, b: bool) -> bool:
 # note that any equivalent way to implement this is OK, this is one example. Another method is `return False if (a == True and b == True) else True`
 return not(a, b)
print(NAND(a, b))

With that, what is the answer for your programming language?

Note: The reason I chose NAND is because NAND is able to construct all other operators (AND, NOT, OR, etc.) If you don't like the NAND, feel free to construct other logical operators instead, as long as the expressions can be combined to create a formula equivalent to a NAND b for some a and b

update: added an example pseudocode for clarity

update 2 (by doubleunary): The number of distinct characters is the output of the following Python code, replacing the placeholder with your code:

your_code = """
<your_code_here>
"""
print(len(set(your_code)))

For example, my example above has 28ドル$ distinct characters.

• Rhaixer: lambd,not01=: ?
• dnn25519: @Rhaixer what language is that, and how do you use it?
• xnor: When you say "define a function", does it need to be given a name, or are anonymous formulations fine? Similarly, for assigning values True/False? Or do you simply mean we can write an expression that has the right behavior or value?
• dnn25519: @xnor oh I forgot, but in essence, yes an expression equivalent to a NAND b with a and b as the true/false values should suffice.
• xnor: As it stands, the challenge seems very unclear to me, and I don't know which of the answers are valid.

Answer 1

Google Sheets / Excel, 6 distinct characters

=1-A1*B1

Characters: {=, 1, -, A, *, B}

In GS/Excel AND(a,b) is logically equivalent to a*b and NOT(x) is logically equivalent to 1-x.

So NOT(AND(a,b)) is logically equivalent to NOT(a*b) which is logically equivalent to 1-a*b. (This is assuming a, b are either booleans, 1s or 0s)

• Martin Modrák: I think you need to also include 0 to encode the false literal in an input cell, if I understand the challenge correctly.
• doubleunary: @MartinModrák 0 === 1-1. Further, in Google Sheets, a blank value is treated the same as zero in math contexts.

Answer 2

PowerShell, 13 distinct characters

$o={!$args[!!$a]-or!$args[!$a]}

Try it online!

a nand b is the same as !(a and b), which is the same as !a or !b; implementing it using or avoids the need for round brackets before applying the ! operator after and (PS has no native -nand), and it also has less distinct characters than and.
$o = {...} defines an (unnamed) function and saves it in the variable $o (o because that character is already required for the operator -or).
Any positional parameters passed to the function will end up in the default array $args.
!!$a will evaluate to 0: $a starts out as $null, negating it will turn it to $true, negating it again will turn it $false, and using it as array index will turn it to 0.
Accordingly, !$a will evaluate to 1.

Answer 3

JavaScript, 6 distinct characters

In JavaScript, only []()!+ are required because JSF*ck.

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console.log(a(0,0));
console.log(a(0,1));
console.log(a(1,0));
console.log(a(1,1));

Answer 4

APL+WIN, 12 distinct characters

NAND is a single character that takes a left and right argument which can be matching boolean arrays of any dimension. The following code prompts for a and b and outputs the NAND result. Try it online shows it for scalar, vector and 2d matrix inputs.

⎕⍲⎕

Try it online! Thanks to Dyalog Classic

Answer 5

Desmos, 8 distinct characters

Characters

a_(),=1-

False literal

Assigns a to 0

a=1-1

True literal

Assigns a_1 to 1

a_1=1

NAND function

Defines a_a as the NAND function

a_a(a,a_1)=1-aa_1

(Note: the function parameters a and a_1 are distinct from the variables defined as false and true earlier. Despite that, the program still works completely fine.)

Try It On Desmos!

---

Explanation:

a_(),=1-

a_: Need for naming (variables, functions, and function parameters)

(),: Needed for function definition

=: Assignment operator

1: Used as both the constant 1, and as a subscript for naming

-: Used to get 0 from 1, and in the NAND function definition

• corvus_192: you can use a1 and a11 as variable/function names, removing the need for _
• Aiden Chow: @corvus_192 That does not work since Desmos is scored by the code that is being pasted into the graphing calculator, not code that is typed into the calculator. If you try to paste in a1 and a11 verbatim into the graphing calculator, it will not subscript like you likely expect it to. So if you try to paste in code like a1=1-1 or a11=1, it will simply give an error. You can see the results of that here.
• corvus_192: I see, it's a peculiarity of the desmos scoring. thanks for the explanation.

Answer 6

Don't know if my answer is valid. Here we go: 2 distinct chars ! and |.

Tcl, 27 bytes

proc N {a b} {expr !$a|!$b}

Try it online!

Answer 7

Python 3, 11 distinct characters

Characters used (note the space character \u20 and the start of the code block):

 *,-1:abdlm

Solution:

lambda a,aa:1-a*aa

Usage in the terminal (two examples):

>>> for i in [True, False]:
... for j in [True, False]:
... print( (lambda a,aa:1-a*aa)(i, j) )
...
0
1
1
1
>>> for i in [True, False]:
... for j in [True, False]:
... print( bool( (lambda a,aa:1-a*aa)(i, j) ) )
...
False
True
True
True

The reason this works is because in Python,

True * True == 1
True * False == 0
False * True == 0
False * False == 0
1 == int(True)
0 == int(False)

Answer 8

R, 6 distinct characters

F=\()&

• F is the built-in false literal and reused in function/param names
• = is an assignment operator (which is also used to define named functions). Also let's us build NOT as ==F
• \ defines an anonymous function
• () function call
• & logical AND

the NAND definition is then:

FF=\(FF)\(FFF)((FF&FFF)==F)

We can the define the true literal as

FFF=FF(F)(F)

The full NAND truth table is then

FF(F)(F)
#TRUE
FF(F)(FFF)
#TRUE
FF(FFF)(F)
#TRUE
FF(FFF)(FFF)
#FALSE

If you want to define multiple functions or evaluate multiple expressions or define the function AND evaluate an expression you also need a single separator character (not counted above), either ; or newline will work.

Attempt it online