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  2. Why do most programming languages only have binary equality comparison operators?

Why do most programming languages only have binary equality comparison operators?

由 杀马特。学长 韩版系。学妹 提交于 2019-11-28 06:18:06

In Haskell, it is easy to define a function to do this:

matches x ps = foldl (||) False $  map (\ p -> p x) ps

This function takes a value list of predicates (of type a -> Bool) and returns True if any of the the predicates match the value.

This allows you to something like this:

isMammal m = m `matches` [(=="Dog"), (=="Cat"), (=="Human")]

The nice thing is that it doesn't have to just be equality, you can use anything with the correct type:

isAnimal a = a `matches` [isMammal, (=="Fish"), (=="Bird")]

I think that most people consider something like

isPrimaryColor = ["Red", "Blue", "Yellow"].contains(someColor)

to be sufficiently clear that they don't need extra syntax for this.

In python you can do something like this:

color = "green"

if color in ["red", "green", "blue"]:
    print 'Yay'

It is called in operator, which tests for set membership.

In perl 6 you could do this with junctions:

if $color eq 'Red'|'Blue'|'Green' {
    doit()
}

Alternately you could do it with the smart match operator (~~). The following is roughly equivalent to python's if value in list: syntax, except that ~~ does a lot more in other contexts.

if ($color ~~ qw/Red Blue Green/) {
    doit()
}

The parens also make it valid perl 5 (>=5.10); in perl 6 they're optional.

Ruby

Contained in list:

irb(main):023:0> %w{red green blue}.include? "red"
=> true
irb(main):024:0> %w{red green blue}.include? "black"
=> false

Numeric Range:

irb(main):008:0> def is_valid_num(x)
irb(main):009:1>   case x
irb(main):010:2>     when 1..100, 1000..2000 then true
irb(main):011:2>     else false
irb(main):012:2>   end
irb(main):013:1> end
=> nil
irb(main):014:0> is_valid_num(1)
=> true
irb(main):015:0> is_valid_num(100)
=> true
irb(main):016:0> is_valid_num(101)
=> false
irb(main):017:0> is_valid_num(1050)
=> true

So far, nobody has mentioned SQL. It has what you are suggesting:

SELECT
    employee_id
FROM 
    employee
WHERE
    hire_date BETWEEN '2009-01-01' AND '2010-01-01' -- range of values
    AND employment_type IN ('C', 'S', 'H', 'T')     -- list of values

COBOL uses 88 levels to implement named values, named groups of values and named ranges of values.

For example:

01 COLOUR         PIC X(10).
   88 IS-PRIMARY-COLOUR VALUE 'Red', 'Blue', 'Yellow'.
...
MOVE 'Blue' TO COLOUR
IF IS-PRIMARY-COLOUR
   DISPLAY 'This is a primary colour'
END-IF

Range tests are covered as follows:

01 SOME-NUMBER    PIC S9(4) BINARY.
   88 IS-LESS-THAN-ZERO    VALUE -9999 THRU -1.
   88 IS-ZERO              VALUE ZERO.
   88 IS-GREATER-THAN-ZERO VALUE 1 THRU 9999.
...
MOVE +358 TO SOME-NUMBER
EVALUATE TRUE
    WHEN IS-LESS-THAN-ZERO
         DISPLAY 'Negative Number'
    WHEN IS-ZERO
         DISPLAY 'Zero'
    WHEN IS-GREATER-THAN-ZERO
         DISPLAY 'Positive Number'
    WHEN OTHER
         DISPLAY 'How the heck did this happen!'
END-EVALUATE

I guess this all happened because COBOL was supposed to emulate English to some extent.

You'll love Perl 6 because it has:

And you can combine both with ranges:

$someNumber ~~ (1..100) | (1000..2000)

Python actually gives you the ability to do the last thing quite well:

>>> x=5
>>> (1<x<1000 or 2000<x<3000)
True

In Python you can say ...

isPrimaryColor = someColor in ('Red', 'Blue', 'Yellow')

... which I find more readable than your (== "Red" or == "Blue") syntax. There's a few reasons to add syntax support for a language feature:

  • Efficiency: Not a reason here, since there's no speed improvement.
  • Functionality: Also not a concern; there's nothing you can do in the new syntax that you can't do in the old.
  • Legibility: Most languages handle the case where you're checking the equality of multiple values just fine. In other cases (e.g., someNumber (> 1 and < 10)) it might be more useful, but even then it doesn't buy you much (and Python allows you to say 1 < someNumber < 10, which is even clearer).

So it's not clear the proposed change is particularly helpful.

My guess would be that languages are designed by force of habit. Early languages only would have had binary comparison operators because they are simpler to implement. Everyone got used to saying (x > 0 and x < y) until language designers didn't ever bother to support the common form in mathematics, (0 < x < y).

In most languages a comparison operator returns a boolean type. In the case of 0 < x < y, if this is interpreted as (0 < x) < y it would be meaningless, since < does not make sense for comparing booleans. Therefore, a new compiler could interpret 0 < x < y as tmp:=x, 0 < tmp && tmp < y without breaking backward compatibility. In the case of x == y == z, however, if the variables are already booleans, it is ambiguous whether this means x == y && y == z or (x == y) == z.

In C# I use the following extension method so that you can write someColor.IsOneOf("Red", "Blue", "Yellow"). It is less efficient than direct comparison (what with the array, loop, Equals() calls and boxing if T is a value type), but it sure is convenient.

public static bool IsOneOf<T>(this T value, params T[] set) 
{
    object value2 = value;
    for (int i = 0; i < set.Length; i++)
        if (set[i].Equals(value2))
            return true;
    return false;
}

Icon has the facility you describe.

if y < (x | 5) then write("y=", y)

I rather like that aspect of Icon.

In C#:

if ("A".IsIn("A", "B", "C"))
{
}

if (myColor.IsIn(colors))
{
}

Using these extensions:

public static class ObjectExtenstions
{
    public static bool IsIn(this object obj, params object [] list)
    {
        foreach (var item in list)
        {
            if (obj == item)
            {
                return true;
            }
        }

        return false;
    }

    public static bool IsIn<T>(this T obj, ICollection<T> list)
    {
        return list.Contains(obj);
    }

    public static bool IsIn<T>(this T obj, IEnumerable<T> list)
    {
        foreach (var item in list)
        {
            if (obj == item)
            {
                return true;
            }
        }

        return false;
    }
}

You'll have to go a bit down the abstraction layer to find out the reason why. x86's comparison/jump instructions are binary (since they can be easily computed in a few clock cycles), and that's the way things have been.

If you want, many languages offer an abstraction for that. In PHP, for example you could use:

$isPrimaryColor = in_array($someColor, array('Red', 'White', 'Blue'));

I don't see an Objective-C answer yet. Here is one:

BOOL isPRimaryColour = [[NSSet setWithObjects: @"red", @"green", @"blue", nil] containsObject: someColour];

The question is reasonable, and I wouldn't regard the change as syntactic sugar. If the value being compared is the result of computation, it would be nicer to say:

  if (someComplicatedExpression ?== 1 : 2 : 3 : 5)

than to say

  int temp;
  temp = someComplicatedExpression;
  if (temp == 1 || temp == 2 || temp == 3 || temp == 5)

particularly if there was no other need for the temp variable in question. A modern compiler could probably recognize the short useful lifetime of 'temp' and optimize it to a register, and could probably recognize the "see if variable is one of certain constants" pattern, but there'd be no harm in allowing a programmer to save the compiler the trouble. The indicated syntax wouldn't compile on any existing compiler, but I don't think it would be any more ambiguous than (a+b >> c+d) whose behavior is defined in the language spec.

As to why nobody's done that, I don't know.

I'm reminded of when I first started to learn programming, in Basic, and at one point I wrote

if X=3 OR 4

I intended this like you are describing, if X is either 3 or 4. The compiler interpreted it as:

if (X=3) OR (4)

That is, if X=3 is true, or if 4 is true. As it defined anything non-zero as true, 4 is true, anything OR TRUE is true, and so the expression was always true. I spent a long time figuring that one out.

I don't claim this adds anything to the discussion. I just thought it might be a mildly amusing anecdote.

As a mathematician, I would say that the colour is primary if and only if it is a member of the set {red, green, blue} of primary colours.

And this is exactly how you could say in Delphi:

isPrimary := Colour in [clRed, clGreen, clBlue]

In fact, I employ this technique very often. Last time was three days ago. Implementing my own scripting language's interpreter, I wrote

const
  LOOPS = [pntRepeat, pntDoWhile, pntFor];

and then, at a few lines,

if Nodes[x].Type in LOOPS then

The Philosophical Part of the Question

@supercat, etc. ("As to why nobody's done that, I don't know."):

Probably because the designers of programming languages are mathematicians (or, at least, mathematically inclined). If a mathematician needs to state the equality of two objects, she would say

X = Y,

naturally. But if X can be one of a number of things A, B, C, ..., then she would define a set S = {A, B, C, ...} of these things and write

X ∈ S.

Indeed, it is extremely common that you (mathematicians) write X ∈ S, where S is the set

S = {x ∈ D; P(x)}

of objects in some universe D that has the property P, instead of writing P(X). For instance, instead of saying "x is a positive real number", or "PositiveReal(x)", one would say x ∈ ℝ⁺.

It's because programming languages are influenced by mathematics, logic and set theory in particular. Boolean algebra defines ∧, ∨ operators in a way that they do not work like spoken natural language. Your example would be written as:

Let p(x) be unary relation which holds if and only if x is a primary color
p(x) ⇔ r(x) ∨ g(x) ∨ b(x)
or
p(x) ⇔ (x=red) ∨ (x=green) ∨ (x=blue)

As you see, it's pretty similar to notation that would be used in programming language. As mathematics provide strong theoretic foundations, programming languages are based on mathematics rather than natural language which always leaves a lot of space for interpretation.

EDIT: Above statement could be simplified by using set notation:

p(x) ⇔ x ∈ {red, green, blue}

and indeed, some programming languages, most notably Pascal, included set, so you could type:

type
    color = (red, green, blue, yellow, cyan, magenta, black, white);

function is_primary (x : color) : boolean;
begin
    is_primary := x in [red, green, blue]
end

But sets as a language feature didn't catch on.

PS. Sorry for my imperfect English.

The latter examples you give are effectively syntactic sugar, they'd have to evaluate to the same code as the longer form as at some point the executed code has to compare your value with each of the conditions in turn.

The array comparison syntax, given in several forms here, closer and I suspect there are other languages which get even closer.

The main problem with making syntax closer to natural language is that the latter is not just ambiguous, it's hideously ambiguous. Even keeping ambiguity to a minimum we still manage to introduce bugs into our apps, can you imagine what it would be like if you programmed in natural english?!

Just to add to language examples

Scheme

(define (isPrimaryColor color)
  (cond ((member color '(red blue yellow)) #t)
        (else #f)))

(define (someNumberTest x)
  (cond ((or (and (>= x 1) (<= x 100)) (and (>= x 10000 (<= x 2000))) #t)
        (else #f)))

Two possibilities

Java

boolean isPrimary = Arrays.asList("red", "blue", "yellow").contains(someColor);

Python

a = 1500
if  1 < a < 10 or  1000 < a < 2000:
     print "In range"

This can be replicated in Lua with some metatable magic :D

local function operator(func)
    return setmetatable({},
        {__sub = function(a, _)
            return setmetatable({a},
                {__sub = function(self, b)
                    return f(self[1], b)
                end}
            )
        end}
    )
end


local smartOr = operator(function(a, b)
    for i = 1, #b do
        if a == b[i] then
            return true
        end
    end
    return false
end)


local isPrimaryColor = someColor -smartOr- {"Red", "Blue", "Either"}

Note: You can change the name of -smartOr- to something like -isEither- to make it even MORE readable.

Languages on computers compare as binary because they are all for a machine that uses binary to represent information. They were designed using similar logic and with broadly similar goals. The English language wasn't designed logically, designed to describe algorithms, and human brains (the hardware it runs on) aren't based on binary. They're tools designed for different tasks.

标签
language-design
boolean-operations
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