assignment operator is left or right associative

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Operator precedence

Operator precedence determines how operators are parsed concerning each other. Operators with higher precedence become the operands of operators with lower precedence.

Precedence and associativity

Consider an expression describable by the representation below, where both OP1 and OP2 are fill-in-the-blanks for OPerators.

The combination above has two possible interpretations:

Which one the language decides to adopt depends on the identity of OP1 and OP2 .

If OP1 and OP2 have different precedence levels (see the table below), the operator with the higher precedence goes first and associativity does not matter. Observe how multiplication has higher precedence than addition and executed first, even though addition is written first in the code.

Within operators of the same precedence, the language groups them by associativity . Left-associativity (left-to-right) means that it is interpreted as (a OP1 b) OP2 c , while right-associativity (right-to-left) means it is interpreted as a OP1 (b OP2 c) . Assignment operators are right-associative, so you can write:

with the expected result that a and b get the value 5. This is because the assignment operator returns the value that is assigned. First, b is set to 5. Then the a is also set to 5 — the return value of b = 5 , a.k.a. right operand of the assignment.

As another example, the unique exponentiation operator has right-associativity, whereas other arithmetic operators have left-associativity.

Operators are first grouped by precedence, and then, for adjacent operators that have the same precedence, by associativity. So, when mixing division and exponentiation, the exponentiation always comes before the division. For example, 2 ** 3 / 3 ** 2 results in 0.8888888888888888 because it is the same as (2 ** 3) / (3 ** 2) .

For prefix unary operators, suppose we have the following pattern:

where OP1 is a prefix unary operator and OP2 is a binary operator. If OP1 has higher precedence than OP2 , then it would be grouped as (OP1 a) OP2 b ; otherwise, it would be OP1 (a OP2 b) .

If the unary operator is on the second operand:

Then the binary operator OP2 must have lower precedence than the unary operator OP1 for it to be grouped as a OP2 (OP1 b) . For example, the following is invalid:

Because + has higher precedence than yield , this would become (a + yield) 1 — but because yield is a reserved word in generator functions, this would be a syntax error. Luckily, most unary operators have higher precedence than binary operators and do not suffer from this pitfall.

If we have two prefix unary operators:

Then the unary operator closer to the operand, OP2 , must have higher precedence than OP1 for it to be grouped as OP1 (OP2 a) . It's possible to get it the other way and end up with (OP1 OP2) a :

Because await has higher precedence than yield , this would become (await yield) 1 , which is awaiting an identifier called yield , and a syntax error. Similarly, if you have new !A; , because ! has lower precedence than new , this would become (new !) A , which is obviously invalid. (This code looks nonsensical to write anyway, since !A always produces a boolean, not a constructor function.)

For postfix unary operators (namely, ++ and -- ), the same rules apply. Luckily, both operators have higher precedence than any binary operator, so the grouping is always what you would expect. Moreover, because ++ evaluates to a value , not a reference , you can't chain multiple increments together either, as you may do in C.

Operator precedence will be handled recursively . For example, consider this expression:

First, we group operators with different precedence by decreasing levels of precedence.

• The ** operator has the highest precedence, so it's grouped first.
• Looking around the ** expression, it has * on the right and + on the left. * has higher precedence, so it's grouped first. * and / have the same precedence, so we group them together for now.
• Looking around the * / / expression grouped in 2, because + has higher precedence than >> , the former is grouped.

Within the * / / group, because they are both left-associative, the left operand would be grouped.

Note that operator precedence and associativity only affect the order of evaluation of operators (the implicit grouping), but not the order of evaluation of operands . The operands are always evaluated from left-to-right. The higher-precedence expressions are always evaluated first, and their results are then composed according to the order of operator precedence.

If you are familiar with binary trees, think about it as a post-order traversal .

After all operators have been properly grouped, the binary operators would form a binary tree. Evaluation starts from the outermost group — which is the operator with the lowest precedence ( / in this case). The left operand of this operator is first evaluated, which may be composed of higher-precedence operators (such as a call expression echo("left", 4) ). After the left operand has been evaluated, the right operand is evaluated in the same fashion. Therefore, all leaf nodes — the echo() calls — would be visited left-to-right, regardless of the precedence of operators joining them.

Short-circuiting

In the previous section, we said "the higher-precedence expressions are always evaluated first" — this is generally true, but it has to be amended with the acknowledgement of short-circuiting , in which case an operand may not be evaluated at all.

Short-circuiting is jargon for conditional evaluation. For example, in the expression a && (b + c) , if a is falsy , then the sub-expression (b + c) will not even get evaluated, even if it is grouped and therefore has higher precedence than && . We could say that the logical AND operator ( && ) is "short-circuited". Along with logical AND, other short-circuited operators include logical OR ( || ), nullish coalescing ( ?? ), and optional chaining ( ?. ).

When evaluating a short-circuited operator, the left operand is always evaluated. The right operand will only be evaluated if the left operand cannot determine the result of the operation.

Note: The behavior of short-circuiting is baked in these operators. Other operators would always evaluate both operands, regardless if that's actually useful — for example, NaN * foo() will always call foo , even when the result would never be something other than NaN .

The previous model of a post-order traversal still stands. However, after the left subtree of a short-circuiting operator has been visited, the language will decide if the right operand needs to be evaluated. If not (for example, because the left operand of || is already truthy), the result is directly returned without visiting the right subtree.

Consider this case:

Only C() is evaluated, despite && having higher precedence. This does not mean that || has higher precedence in this case — it's exactly because (B() && A()) has higher precedence that causes it to be neglected as a whole. If it's re-arranged as:

Then the short-circuiting effect of && would only prevent C() from being evaluated, but because A() && C() as a whole is false , B() would still be evaluated.

However, note that short-circuiting does not change the final evaluation outcome. It only affects the evaluation of operands , not how operators are grouped — if evaluation of operands doesn't have side effects (for example, logging to the console, assigning to variables, throwing an error), short-circuiting would not be observable at all.

The assignment counterparts of these operators ( &&= , ||= , ??= ) are short-circuited as well. They are short-circuited in a way that the assignment does not happen at all.

The following table lists operators in order from highest precedence (18) to lowest precedence (1).

Several general notes about the table:

• Not all syntax included here are "operators" in the strict sense. For example, spread ... and arrow => are typically not regarded as operators. However, we still included them to show how tightly they bind compared to other operators/expressions.
• Some operators have certain operands that require expressions narrower than those produced by higher-precedence operators. For example, the right-hand side of member access . (precedence 17) must be an identifier instead of a grouped expression. The left-hand side of arrow => (precedence 2) must be an arguments list or a single identifier instead of some random expression.
• Some operators have certain operands that accept expressions wider than those produced by higher-precedence operators. For example, the bracket-enclosed expression of bracket notation [ … ] (precedence 17) can be any expression, even comma (precedence 1) joined ones. These operators act as if that operand is "automatically grouped". In this case we will omit the associativity.
• The operand can be any expression.
• The "right-hand side" must be an identifier.
• The "right-hand side" can be any expression.
• The "right-hand side" is a comma-separated list of any expression with precedence > 1 (i.e. not comma expressions).
• The operand must be a valid assignment target (identifier or property access). Its precedence means new Foo++ is (new Foo)++ (a syntax error) and not new (Foo++) (a TypeError: (Foo++) is not a constructor).
• The operand must be a valid assignment target (identifier or property access).
• The operand cannot be an identifier or a private property access.
• The left-hand side cannot have precedence 14.
• The operands cannot be a logical OR || or logical AND && operator without grouping.
• The "left-hand side" must be a valid assignment target (identifier or property access).
• The associativity means the two expressions after ? are implicitly grouped.
• The "left-hand side" is a single identifier or a parenthesized parameter list.
• Only valid inside object literals, array literals, or argument lists.

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Assignment operators (C# reference)

• 11 contributors

The assignment operator = assigns the value of its right-hand operand to a variable, a property , or an indexer element given by its left-hand operand. The result of an assignment expression is the value assigned to the left-hand operand. The type of the right-hand operand must be the same as the type of the left-hand operand or implicitly convertible to it.

The assignment operator = is right-associative, that is, an expression of the form

is evaluated as

The following example demonstrates the usage of the assignment operator with a local variable, a property, and an indexer element as its left-hand operand:

The left-hand operand of an assignment receives the value of the right-hand operand. When the operands are of value types , assignment copies the contents of the right-hand operand. When the operands are of reference types , assignment copies the reference to the object.

This is called value assignment : the value is assigned.

ref assignment

Ref assignment = ref makes its left-hand operand an alias to the right-hand operand, as the following example demonstrates:

In the preceding example, the local reference variable arrayElement is initialized as an alias to the first array element. Then, it's ref reassigned to refer to the last array element. As it's an alias, when you update its value with an ordinary assignment operator = , the corresponding array element is also updated.

The left-hand operand of ref assignment can be a local reference variable , a ref field , and a ref , out , or in method parameter. Both operands must be of the same type.

Compound assignment

For a binary operator op , a compound assignment expression of the form

is equivalent to

except that x is only evaluated once.

Compound assignment is supported by arithmetic , Boolean logical , and bitwise logical and shift operators.

Null-coalescing assignment

You can use the null-coalescing assignment operator ??= to assign the value of its right-hand operand to its left-hand operand only if the left-hand operand evaluates to null . For more information, see the ?? and ??= operators article.

Operator overloadability

A user-defined type can't overload the assignment operator. However, a user-defined type can define an implicit conversion to another type. That way, the value of a user-defined type can be assigned to a variable, a property, or an indexer element of another type. For more information, see User-defined conversion operators .

A user-defined type can't explicitly overload a compound assignment operator. However, if a user-defined type overloads a binary operator op , the op= operator, if it exists, is also implicitly overloaded.

C# language specification

For more information, see the Assignment operators section of the C# language specification .

• C# operators and expressions
• ref keyword
• Use compound assignment (style rules IDE0054 and IDE0074)

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Additional resources

• A named space for holding data/information
• The name is often referred to as the identifier
• A representation of a datum
• A symbol indicating that an operation is to be performed (on one or more operands)
• A combination of variables, operators, and literals that represent a single value
• The smallest syntactically valid construct that conveys a complete command
• Placing a value into the memory identified by a variable/constant
• The assignment operator is a binary operator; the left-side operand is a variable/constant and the right-side operand is a literal or an expression (i.e., something that evaluates to a value)
• initial = 'H'
• initial = 'H';
• ok = false;
• A variable can only contain one value at a time
• int i; i = 5; // i contains the value 5 i = 27; // i now contains the value 27
• Confusing the assignment operator with the notion of "equality"
• Attempting to use expressions like 21 = age (which has an inappropriate left-side operand)
• The assignment operation evaluates to the value of the right-side operand (so, is an expression)
• int i, j; i = j = 5;
• It can cause confusion in more complicated statements, especially those involving arithmetic operators and relational operators
• In the previous example, which assignment is performed first?
• Associativity - determines whether (in the absence of other determinants) an expression is evaluated from left to right or right to left
• The assignment operator has right to left associativity, so i = j = 5 is equivalent to i = (j = 5)
• Ensuring that the type of the right-side operand is the same as the type of the left-side operand
• Java does not allow implicit losses of precision
• Java does allow widenings (though you should refrain from using them)
• double weight; int age; age = 21.0; // Not allowed (will generate a compile-time error) weight = 155; // Allowed but not recommended (use 155. instead)
• ( type ) expression
• Examples: double real; int small; long large; // ... small = (int)large; // ... small = (int)real;
• Loss of precision
• Possible loss of magnitude
• Possible change of sign
• Indicate that a value can only be assigned to a variable once
• final type variable [, variable ]... ;
• final boolean CORRECT;
• final double BUDGET;
• final int CAPACITY;
• Same as for other variables
• Must be all uppercase
• Underscores between "words" improve readability
• An error will be generated if an identifier that is declared to be final is the left-side operand of more than one assignment operator
• Include the assignment in the declaration
• The value of the right-side operand is assigned to the left-side operand
• The address of the right-side operand is assigned to the left-side operand

6.1 — Operator precedence and associativity

Chapter introduction

This chapter builds on top of the concepts from lesson 1.9 -- Introduction to literals and operators . A quick review follows:

An operation is a mathematical process involving zero or more input values (called operands ) that produces a new value (called an output value). The specific operation to be performed is denoted by a construct (typically a symbol or pair of symbols) called an operator .

For example, as children we all learn that 2 + 3 equals 5 . In this case, the literals 2 and 3 are the operands, and the symbol + is the operator that tells us to apply mathematical addition on the operands to produce the new value 5 . Because there is only one operator being used here, this is straightforward.

In this chapter, we’ll discuss topics related to operators, and explore many of the common operators that C++ supports.

Evaluation of compound expressions

Now, let’s consider a compound expression, such as 4 + 2 * 3 . Should this be grouped as (4 + 2) * 3 which evaluates to 18 , or 4 + (2 * 3) which evaluates to 10 ? Using normal mathematical precedence rules (which state that multiplication is resolved before addition), we know that the above expression should be grouped as 4 + (2 * 3) to produce the value 10 . But how does the compiler know?

In order to evaluate an expression, the compiler must do two things:

• At compile time, the compiler must parse the expression and determine how operands are grouped with operators. This is done via the precedence and associativity rules, which we’ll discuss momentarily.
• At compile time or runtime, the operands are evaluated and operations executed to produce a result.

Operator precedence

To assist with parsing a compound expression, all operators are assigned a level of precedence. Operators with a higher precedence level are grouped with operands first.

You can see in the table below that multiplication and division (precedence level 5) have a higher precedence level than addition and subtraction (precedence level 6). Thus, multiplication and division will be grouped with operands before addition and subtraction. In other words, 4 + 2 * 3 will be grouped as 4 + (2 * 3) .

Operator associativity

Consider a compound expression like 7 - 4 - 1 . Should this be grouped as (7 - 4) - 1 which evaluates to 2 , or 7 - (4 - 1) , which evaluates to 4 ? Since both subtraction operators have the same precedence level, the compiler can not use precedence alone to determine how this should be grouped.

If two operators with the same precedence level are adjacent to each other in an expression, the operator’s associativity tells the compiler whether to evaluate the operators from left to right or from right to left. Subtraction has precedence level 6, and the operators in precedence level 6 have an associativity of left to right. So this expression is grouped from left to right: (7 - 4) - 1 .

Table of operator precedence and associativity

The below table is primarily meant to be a reference chart that you can refer back to in the future to resolve any precedence or associativity questions you have.

• Precedence level 1 is the highest precedence level, and level 17 is the lowest. Operators with a higher precedence level have their operands grouped first.
• L->R means left to right associativity.
• R->L means right to left associativity.

You should already recognize a few of these operators, such as + , - , * , / , () , and sizeof . However, unless you have experience with another programming language, the majority of the operators in this table will probably be incomprehensible to you right now. That’s expected at this point. We’ll cover many of them in this chapter, and the rest will be introduced as there is a need for them.

Q: Where is the exponent operator?

C++ doesn’t include an operator to do exponentiation ( operator^ has a different function in C++). We discuss exponentiation more in lesson 6.3 -- Remainder and Exponentiation .

Note that operator<< handles both bitwise left shift and insertion, and operator>> handles both bitwise right shift and extraction. The compiler can determine which operation to perform based on the types of the operands.

Parenthesization

Due to the precedence rules, 4 + 2 * 3 will be grouped as 4 + (2 * 3) . But what if we actually meant (4 + 2) * 3 ? Just like in normal mathematics, in C++ we can explicitly use parentheses to set the grouping of operands as we desire. This works because parentheses have one of the highest precedence levels, so parentheses generally evaluate before whatever is inside them.

Use parenthesis to make compound expressions easier to understand

Now consider an expression like x && y || z . Does this evaluate as (x && y) || z or x && (y || z) ? You could look up in the table and see that && takes precedence over || . But there are so many operators and precedence levels that it’s hard to remember them all. And you don’t want to have to look up operators all the time to understand how a compound expression evaluates.

In order to reduce mistakes and make your code easier to understand without referencing a precedence table, it’s a good idea to parenthesize any non-trivial compound expression, so it’s clear what your intent is.

Best practice

Use parentheses to make it clear how a non-trivial compound expression should evaluate (even if they are technically unnecessary).

A good rule of thumb is: Parenthesize everything, except addition, subtraction, multiplication, and division.

There is one additional exception to the above best practice: Expressions that have a single assignment operator (and no comma operator) do not need to have the right operand of the assignment wrapped in parenthesis.

For example:

The assignment operators have the second lowest precedence (only the comma operator is lower, and it’s rarely used). Therefore, so long as there is only one assignment (and no commas), we know the right operand will fully evaluate before the assignment.

Expressions with a single assignment operator do not need to have the right operand of the assignment wrapped in parenthesis.

Value computation (of operations)

The C++ standard uses the term value computation to mean the execution of operators in an expression to produce a value. The precedence and association rules determine the order in which value computation happens.

For example, given the expression 4 + 2 * 3 , due to the precedence rules this groups as 4 + (2 * 3) . 2 * 3 must be evaluated first, so that the resulting value of 6 can be used as the right operand of operator+ .

Key insight

The precedence and associativity rules generally determine the order of value computation (of operators).

Order of evaluation (of operands)

The C++ standard (mostly) uses the term evaluation to refer to the evaluation of operands (not the evaluation of operators or expressions!). For example, given expression a + b , a will be evaluated to produce some value, and b will be evaluated to produce some value. These values can be then used as operands to operator+ to compute a value.

Nomenclature

Informally, we typically use the term “evaluates” to mean the evaluation of an entire expression (value computation), not just the operands of an expression.

The order of evaluation of operands and function arguments is mostly unspecified

In most cases, the order of evaluation for operands and function arguments is unspecified, meaning they may be evaluated in any order.

Consider the following expression:

We know from the precedence and associativity rules above that this expression will be grouped as if we had typed:

If a is 1 , b is 2 , c is 3 , and d is 4 , this expression will always compute the value 14 .

However, the precedence and associativity rules only tell us how operators and operands are grouped and the order in which value computation will occur. They do not tell us the order in which the operands or subexpressions are evaluated. The compiler is free to evaluate operands a , b , c , or d in any order. The compiler is also free to calculate a * b or c * d first.

For most expressions, this is irrelevant. In our sample expression above, it doesn’t matter whether in which order variables a , b , c , or d are evaluated for their values: the value calculated will always be 14 . There is no ambiguity here.

But it is possible to write expressions where the order of evaluation does matter. Consider this program, which contains a mistake often made by new C++ programmers:

If you run this program and enter the inputs 1 , 2 , and 3 , you might assume that this program would calculate 1 + (2 * 3) and print 7 . But that is making the assumption that the arguments to printCalculation() will evaluate in left-to-right order (so parameter x gets value 1 , y gets value 2 , and z gets value 3 ). If instead, the arguments evaluate in right-to-left order (so parameter z gets value 1 , y gets value 2 , and x gets value 3 ), then the program will print 5 instead.

The Clang compiler evaluates arguments in left-to-right order. The GCC compiler evaluates arguments in right-to-left order. You can run the above program on each of these compilers (e.g. on Wandbox ) and see for yourself.

The above program can be made unambiguous by making each function call to getValue() a separate statement:

In this version, a will always have value 1 , b will have value 2 , and c will have value 3 . When the arguments to printCalculation() are evaluated, it doesn’t matter which order the argument evaluation happens in -- parameter x will always get value 1 , y will get value 2 , and z will get value 3 . This version will deterministically print 7 .

Operands, function arguments, and subexpressions may be evaluated in any order.

Ensure that the expressions (or function calls) you write are not dependent on operand (or argument) evaluation order.

Related content

Operators with side effects can also cause unexpected evaluation results. We cover this in lesson 6.4 -- Increment/decrement operators, and side effects .

Question #1

You know from everyday mathematics that expressions inside of parentheses get evaluated first. For example, in the expression (2 + 3) * 4 , the (2 + 3) part is evaluated first.

For this exercise, you are given a set of expressions that have no parentheses. Using the operator precedence and associativity rules in the table above, add parentheses to each expression to make it clear how the compiler will evaluate the expression.

a) x = 3 + 4 + 5;

Show Solution

Binary operator + has higher precedence than = :

x = (3 + 4 + 5);

Binary operator + has left to right association:

Final answer: x = ((3 + 4) + 5);

b) x = y = z;

Binary operator = has right to left association:

Final answer: x = (y = z);

c) z *= ++y + 5;

Unary operator ++ has the highest precedence:

z *= (++y) + 5;

Binary operator + has the next highest precedence:

Final answer: z *= ((++y) + 5);

d) a || b && c || d;

Binary operator && has higher precedence than || :

a || (b && c) || d;

Binary operator || has left to right association:

Final answer: (a || (b && c)) || d;

Documentation

Operator precedence: we can do better.

Feb 26, 2019 • Jeff Walker

The longer I’ve thought about how to handle operator precedence and associatively in a programming language, the more convinced I’ve become that languages have fallen short. Because it was simple, easy and efficient, language designers have generally provided a total order for operator precedence and made all operators associative. This is typically expressed as a set of operator precedence levels and associativity for each operator. However, this often leads to unexpected or even confusing precedence between operators. Languages allowing programmers to define new operators from combinations of symbols are particularly hurt by forcing all operators to be placed in one of a few precedence levels. In reaction, some designers eschew operator precedence entirely. While simple, that violates deep-seated programmer intuitions opening the way for mistakes and surprise. I believe future languages should adopt intransitive operator precedence instead.

Note: I am focused here only on language with infix operators. Languages using prefix notation , such as Lisp variants, and languages using postfix notation , such as Forth, can be unambiguous without operator precedence.

Existing Practise

Most programming languages with infix operators fall into one of four categories:

• Total Order Precedence and Total Associativity: Every operator has a precedence relative to every other operator. Every operator is either left- or right-associative. Example Languages: C, C++, C♯, Java, Go, Lua, Kotlin
• Total Order Precedence with Partial Associativity: Every operator has a precedence relative to every other operator. Some operators are neither left- nor right-associative. In some languages, there are non-associative operators. For example, in Rust x <= y == z is illegal and would need to have parentheses added. In other languages, chained operators are interpreted differently. For example, in Python x < y < z is equivalent to x < y and y < z . Example Languages: Python, Rust, Prolog, Haskell, Perl
• Single Precedence and Associativity: Every infix operator has the same precedence and associativity. Unary operators may or may not have higher precedence than binary operators. Example Languages: Smalltalk, APL, Mary
• Single Precedence and Non-associative: Every infix operator has the same precedence and is non-associative. Thus all expressions must be fully disambiguated with parentheses. Unary operators may or may not have higher precedence than binary operators. Example Languages: occam , Pony , RELAX NG

Unfortunately, each these options has shortcomings. A set of test expressions best illustrates this.

• x + y * z is almost universally read as x + (y * z) because this is the convention everyone is taught from elementary school onward. Breaking this convention will only lead to confusion and frustration. Requiring explicit parentheses, in this case, isn’t as bad, but is still annoying.
• x < y < z is probably either a bug or meant to mean x < y and y < z . Treating relational operators as left-associative has led to hard to spot bugs in C code.
• By mathematical convention, logical-and has higher precedence than logical-or, so a or b and c should be parsed as a or (b and c) . However, there is no convention for the relative precedence of logical-xor. Any precedence assigned to it will be arbitrary. Yet, all logical connective should have lower precedence than equality. Thus we need an operator that has no precedence relative to some operators, but precedence relative to others so that a xor x == y parses as a xor (x == y) , but a xor b or c is an error.

Let’s consider how each of the approaches fairs on our test cases. Of course, we don’t want to evaluate a single language, but an idealized version of each approach. Single precedence and associativity requires that all operators be either left- or right-associative; which should we pick? Regardless of which is chosen, it will be easy to construct examples where it is incorrect for the operators involved. To simplify the test, I’ve always assumed the worst case for the given test.

Partial Order

Of the existing options, total order precedence with partial associativity scores the best. However, it fails to treat a xor b or c as an error. How can we fix this? Well, we could make operator precedence a partial order instead of a total order. We could then include in our precedence or ≺ and , xor ≺ == , or ≺ == , and and ≺ == . That would correctly handle both a xor x == y and a xor b or c .

However, using a partial order for operator precedence can still lead to problems. Consider the expression x and y + z . Since this mixes logical and arithmetic operators, there isn’t an obvious precedence. We want to force the developer to add parentheses. One might think this is not a problem for a partial order. Yet, logical operators are lower precedence than equality ( and ≺ == ) and equality is lower precedence than arithmetic ( == ≺ + ) . Since partial order relations are transitive, those imply that and ≺ + . That isn’t what we want, so we need a precedence relation that is intransitive .

Intransitive Precedence

Let’s define the kind of precedence we want. I’ll call this an intransitive operator precedence . We’ll define both an equivalence relation “≐” for operators at the same precedence and a compatible order relation “⋖” for operators with different precedence. However, our precedence relation will be intransitive. Additionally, we’ll require that the precedence form a DAG . We can then use them to define the precedence relationships between our operators. Associativity will be specified separately.

For the mathematically inclined, the relations have the following properties:

• a ≐ a ( reflexivity )
• if a ≐ b then b ≐ a ( symmetry )
• if a ≐ b and b ≐ c then a ≐ c ( transitivity )
• It is never the case that a ⋖ a ( irreflexivity )
• If a ⋖ b , then it is not the case that b ⋖ a ( asymmetry )
• If a ⋖ b and b ⋖ c , it does not follow that a ⋖ c (but it could be the case) ( intransitivity )
• There does not exist a 0 , … , a n such that a 0 ⋖ a 1 , … , a n -1 ⋖ a n and a n ⋖ a 0 ( acyclic )
• If a ≐ b and a ⋖ c , then b ⋖ c . Likewise if a ≐ b and d ⋖ a , then d ⋖ b .

This allows us to declare our desired precedence reasonably easily. First, we declare which operators have equal precedence, for example * ≐ / . Then we declare the relative precedence of operators, for example or ⋖ and . Operators of equal precedence share in the precedence we define. However, because precedence is intransitive, there can still be a lot of relations to specify. To simplify, we adopt two notational conveniences. First, that a precedence chain relates every operator to every other operator before and after it so that or ⋖ and ⋖ not states that or ⋖ not as well and second, that groups of operators can be related by using sets. For example, { and , or , not } ⋖ == relates all the boolean operators to the equality operator.

It’s easy to get lost in the math and notation. Let’s look at a concrete example to see how this might play out in a real language. Below I’ve defined a simple expression language over integers and booleans. To be clear, I’m not arguing for this particular set of operator precedences. Other language designers may prefer slightly different ones. I am arguing that languages should use this kind of flexible precedence to avoid undesirable precedence relationships.

I’ve used a form of EBNF augmented with additional notation to represent associativity and intransitive operator precedence. Without these additional annotations, the grammar would be an ambiguous expression grammar . The intent is that a hypothetical parser generator could directly use this grammar. The grammar notation section below gives a detailed explanation of the additional notation used.

This grammar tries to follow mathematical conventions without relating operators that have no conventional relationship. Powers are right associative and higher precedence than negation. The division slash is non-associative to avoid confusion. It does follow the C convention and make equality lower precedence than relations. The test cases below demonstrate the grammar has the desired properties.

Added Grammar Notation

In the grammar above (E) = indicates that E is a “parenthesized” nonterminal. Normally, the declaration of E would be ambiguous, but a parenthesized nonterminal defaults to disallowing alternatives containing recursive uses of the nonterminal from being immediate children of the production. Thus (P) = P "~" P | P "$" P | ID; is effectively transformed to P = P' "~" P' | P' "$" P'; P' = ID; . This has the effect of making the operators non-associative. The intuition here is that parenthesized nonterminals will have to be fully parenthesized unless additional associativity and precedence rules are declared.

Associativity is indicated by enclosing a recursive use of the nonterminal in parentheses. A recursive use enclosed in parentheses allows the same alternative to occur as a direct child of that nonterminal. Thus (E) = (E) "+" E is left-associative and (E) = E "^" (E) is right-associative. The rule (P) = (P) "~" (P) is ambiguous. Again, non-associative is the default for parenthesized nonterminals, i.e. (E) = E "<" E . Intuitively, the parentheses indicate which side expressions should be grouped on. One wrinkle this creates is that to allow nesting of parentheses in parentheses, the nonterminal must be enclosed in parentheses as (E) = "(" (E) ")" or else ((x)) is illegal.

Labels are applied to each alternative by placing them after the alternative. Labels are prefixed with a pound sign. The ANTLR parser generator uses the same notation. Labels provide a way to refer to alternatives later. They can also be used by a parser generator to name the AST node for that alternative.

Operator precedence is declared after the production rules using the precedence relation applied to the alternative labels. Using the labels makes it easy to give binary and unary versions of the same operator different precedences. Two operators are given the same precedence using the =.= operator. Relative precedence is established using the <. operator. As described in the previous section, chains and sets can be used to simplify the declaration of precedence. A precedence declaration affects recursive uses of the nonterminal in the alternatives it relates. Alternatives with higher precedence may be direct children at any use of the nonterminal. Alternatives with equal precedence may only be direct children where the nonterminal is enclosed in parentheses.

In some instances, more complex operators have different precedence for different subexpressions. An array indexing operator (P) = P "[" P "]" #Index; would be such a situation. Here, the bracketed P could be of any precedence while the left P must be higher precedence. In such situations, we can refer to the precedence of the subexpressions using a bracket notation listing the indexes of nonterminals in the alternative. For example, #Index[1] refers to the first subexpression, #Index[2] refers to the second, and #Index[1,2] refers to both. For convenience, four shorthands are provided. The names left and right refer to the leftmost and rightmost nonterminal not bracketed by a terminal. In the example, #Index[left] is the same as #Index[1] while #Index[right] is an error because the rightmost P has the terminal "]" to its right. The name outer refers to both the left and right so #X[outer] would be equal to #X[left, right] . The name inner refers to every subexpression that is not an outer subexpression. Thus #Index[inner] would be equal to #Index[2] . In the example grammar above, this is used to allow a negative sign in the exponent while giving exponentiation higher precedence and to allow logical but not arithmetic expressions in the condition of a conditional expression.

Don’t Mix Associativity

To consider the issues involved in mixing operators with different associativity at the same precedence level, imagine adding the following to the above grammar.

By the rules stated before, what would the effect of this be? Let’s look at each case.

Given that this is almost certainly not what one wants, it is best to simply make it illegal to have operators with the same precedence but different associativity.

Assignment Example

In C style languages the assignment operator is right-associative and evaluates to the value of the left-hand variable after it is assigned. Assignment has lower precedence than addition, so the expression a+b=c+d parses to (a+b)=(c+d) which is illegal. One might prefer that it parse as a+(b=(c+d)) . Setting aside whether that is a good idea, it can be achieved with this scheme. The example expression grammar could be extended with assignment by adding the rule and precedences below. By splitting the precedence of the left and right, we can make assignment bind very tightly on the left, but very loosely on the right.

I’m not the first one to propose something like intransitive operator precedence. The Fortress language has an elaborate operator precedence scheme that is similar. Check out The Fortress Language Specification v1.0 , chapter 16 for more information. However, it was difficult to find much else. The precedence level approach seems to have completely dominated. Hopefully, I’ve convinced you of the value of intransitive operator precedence or at least given you something to think about. I’d love to see future programming languages adopt this approach. Unfortunately, algorithms for parsing such precedence schemes are lacking. If you want to implement such a scheme or are interested in learning more, check out these sources:

• Parsing Fortress Syntax by Sukyoung Ryu.
• Parsing Mixfix Operators by Nils Anders Danielsson and Ulf Norell which proposes a similar scheme for the Agda language.
• SDF and SDF3 which provide both position based priority and intransitive priority for parsing.

Java Tutorial

Control statements, java object class, java inheritance, java polymorphism, java abstraction, java encapsulation, java oops misc.

Java Operator Associativity

Operators with the same precedence follow the operator group's operator associativity. Operators in Java can be left-associative, right-associative, or have no associativity at all. Left-associative operators are assessed from left to right, right-associative operators are reviewed from right to left, and operators with no associativity are evaluated in any order.

Operator Precedence Vs. Operator Associativity

The operator's precedence refers to the order in which operators are evaluated within an expression whereas associativity refers to the order in which the consecutive operators within the same group are carried out.

Precedence rules specify the priority (which operators will be evaluated first) of operators.

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The combination of values, variables , operators , and function calls is termed as an expression. The Python interpreter can evaluate a valid expression.

For example:

Here 5 - 7 is an expression. There can be more than one operator in an expression.

To evaluate these types of expressions there is a rule of precedence in Python. It guides the order in which these operations are carried out.

For example, multiplication has higher precedence than subtraction.

But we can change this order using parentheses () as it has higher precedence than multiplication.

The operator precedence in Python is listed in the following table. It is in descending order (upper group has higher precedence than the lower ones).

Let's look at some examples:

Suppose we're constructing an if...else block which runs if when lunch is either fruit or sandwich and only if money is more than or equal to 2 .

This program runs if block even when money is 0 . It does not give us the desired output since the precedence of and is higher than or .

We can get the desired output by using parenthesis () in the following way:

• Associativity of Python Operators

We can see in the above table that more than one operator exists in the same group. These operators have the same precedence.

When two operators have the same precedence, associativity helps to determine the order of operations.

Associativity is the order in which an expression is evaluated that has multiple operators of the same precedence. Almost all the operators have left-to-right associativity.

For example, multiplication and floor division have the same precedence. Hence, if both of them are present in an expression, the left one is evaluated first.

Note : Exponent operator ** has right-to-left associativity in Python.

We can see that 2 ** 3 ** 2 is equivalent to 2 ** (3 ** 2) .

• Non associative operators

Some operators like assignment operators and comparison operators do not have associativity in Python. There are separate rules for sequences of this kind of operator and cannot be expressed as associativity.

For example, x < y < z neither means (x < y) < z nor x < (y < z) . x < y < z is equivalent to x < y and y < z , and is evaluated from left-to-right.

Furthermore, while chaining of assignments like x = y = z = 1 is perfectly valid, x = y = z+= 2 will result in error.

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Python Operators

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In Python programming, Operators in general are used to perform operations on values and variables. These are standard symbols used for logical and arithmetic operations. In this article, we will look into different types of Python operators. 

• OPERATORS: These are the special symbols. Eg- + , * , /, etc.
• OPERAND: It is the value on which the operator is applied.

Types of Operators in Python

• Arithmetic Operators
• Comparison Operators
• Logical Operators
• Bitwise Operators
• Assignment Operators
• Identity Operators and Membership Operators

Arithmetic Operators in Python

Python Arithmetic operators are used to perform basic mathematical operations like addition, subtraction, multiplication , and division .

In Python 3.x the result of division is a floating-point while in Python 2.x division of 2 integers was an integer. To obtain an integer result in Python 3.x floored (// integer) is used.

Example of Arithmetic Operators in Python

Division operators.

In Python programming language Division Operators allow you to divide two numbers and return a quotient, i.e., the first number or number at the left is divided by the second number or number at the right and returns the quotient. 

There are two types of division operators: 

Float division

• Floor division

The quotient returned by this operator is always a float number, no matter if two numbers are integers. For example:

Example: The code performs division operations and prints the results. It demonstrates that both integer and floating-point divisions return accurate results. For example, ’10/2′ results in ‘5.0’ , and ‘-10/2’ results in ‘-5.0’ .

Integer division( Floor division)

The quotient returned by this operator is dependent on the argument being passed. If any of the numbers is float, it returns output in float. It is also known as Floor division because, if any number is negative, then the output will be floored. For example:

Example: The code demonstrates integer (floor) division operations using the // in Python operators . It provides results as follows: ’10//3′ equals ‘3’ , ‘-5//2’ equals ‘-3’ , ‘ 5.0//2′ equals ‘2.0’ , and ‘-5.0//2’ equals ‘-3.0’ . Integer division returns the largest integer less than or equal to the division result.

Precedence of Arithmetic Operators in Python

The precedence of Arithmetic Operators in Python is as follows:

• P – Parentheses
• E – Exponentiation
• M – Multiplication (Multiplication and division have the same precedence)
• D – Division
• A – Addition (Addition and subtraction have the same precedence)
• S – Subtraction

The modulus of Python operators helps us extract the last digit/s of a number. For example:

• x % 10 -> yields the last digit
• x % 100 -> yield last two digits

Arithmetic Operators With Addition, Subtraction, Multiplication, Modulo and Power

Here is an example showing how different Arithmetic Operators in Python work:

Example: The code performs basic arithmetic operations with the values of ‘a’ and ‘b’ . It adds (‘+’) , subtracts (‘-‘) , multiplies (‘*’) , computes the remainder (‘%’) , and raises a to the power of ‘b (**)’ . The results of these operations are printed.

Note: Refer to Differences between / and // for some interesting facts about these two Python operators.

Comparison of Python Operators

In Python Comparison of Relational operators compares the values. It either returns True or False according to the condition.

= is an assignment operator and == comparison operator.

Precedence of Comparison Operators in Python

In Python, the comparison operators have lower precedence than the arithmetic operators. All the operators within comparison operators have the same precedence order.

Example of Comparison Operators in Python

Let’s see an example of Comparison Operators in Python.

Example: The code compares the values of ‘a’ and ‘b’ using various comparison Python operators and prints the results. It checks if ‘a’ is greater than, less than, equal to, not equal to, greater than, or equal to, and less than or equal to ‘b’ .

Logical Operators in Python

Python Logical operators perform Logical AND , Logical OR , and Logical NOT operations. It is used to combine conditional statements.

Precedence of Logical Operators in Python

The precedence of Logical Operators in Python is as follows:

• Logical not
• logical and

Example of Logical Operators in Python

The following code shows how to implement Logical Operators in Python:

Example: The code performs logical operations with Boolean values. It checks if both ‘a’ and ‘b’ are true ( ‘and’ ), if at least one of them is true ( ‘or’ ), and negates the value of ‘a’ using ‘not’ . The results are printed accordingly.

Bitwise Operators in Python

Python Bitwise operators act on bits and perform bit-by-bit operations. These are used to operate on binary numbers.

Precedence of Bitwise Operators in Python

The precedence of Bitwise Operators in Python is as follows:

• Bitwise NOT
• Bitwise Shift
• Bitwise AND
• Bitwise XOR

Here is an example showing how Bitwise Operators in Python work:

Example: The code demonstrates various bitwise operations with the values of ‘a’ and ‘b’ . It performs bitwise AND (&) , OR (|) , NOT (~) , XOR (^) , right shift (>>) , and left shift (<<) operations and prints the results. These operations manipulate the binary representations of the numbers.

Python Assignment operators are used to assign values to the variables.

Let’s see an example of Assignment Operators in Python.

Example: The code starts with ‘a’ and ‘b’ both having the value 10. It then performs a series of operations: addition, subtraction, multiplication, and a left shift operation on ‘b’ . The results of each operation are printed, showing the impact of these operations on the value of ‘b’ .

Identity Operators in Python

In Python, is and is not are the identity operators both are used to check if two values are located on the same part of the memory. Two variables that are equal do not imply that they are identical. 

Example Identity Operators in Python

Let’s see an example of Identity Operators in Python.

Example: The code uses identity operators to compare variables in Python. It checks if ‘a’ is not the same object as ‘b’ (which is true because they have different values) and if ‘a’ is the same object as ‘c’ (which is true because ‘c’ was assigned the value of ‘a’ ).

Membership Operators in Python

In Python, in and not in are the membership operators that are used to test whether a value or variable is in a sequence.

Examples of Membership Operators in Python

The following code shows how to implement Membership Operators in Python:

Example: The code checks for the presence of values ‘x’ and ‘y’ in the list. It prints whether or not each value is present in the list. ‘x’ is not in the list, and ‘y’ is present, as indicated by the printed messages. The code uses the ‘in’ and ‘not in’ Python operators to perform these checks.

in Python, Ternary operators also known as conditional expressions are operators that evaluate something based on a condition being true or false. It was added to Python in version 2.5. 

It simply allows testing a condition in a single line replacing the multiline if-else making the code compact.

Syntax :   [on_true] if [expression] else [on_false] 

Examples of Ternary Operator in Python

The code assigns values to variables ‘a’ and ‘b’ (10 and 20, respectively). It then uses a conditional assignment to determine the smaller of the two values and assigns it to the variable ‘min’ . Finally, it prints the value of ‘min’ , which is 10 in this case.

In Python, Operator precedence and associativity determine the priorities of the operator.

Operator Precedence in Python

This is used in an expression with more than one operator with different precedence to determine which operation to perform first.

Let’s see an example of how Operator Precedence in Python works:

Example: The code first calculates and prints the value of the expression 10 + 20 * 30 , which is 610. Then, it checks a condition based on the values of the ‘name’ and ‘age’ variables. Since the name is “ Alex” and the condition is satisfied using the or operator, it prints “Hello! Welcome.”

Operator Associativity in Python

If an expression contains two or more operators with the same precedence then Operator Associativity is used to determine. It can either be Left to Right or from Right to Left.

The following code shows how Operator Associativity in Python works:

Example: The code showcases various mathematical operations. It calculates and prints the results of division and multiplication, addition and subtraction, subtraction within parentheses, and exponentiation. The code illustrates different mathematical calculations and their outcomes.

To try your knowledge of Python Operators, you can take out the quiz on Operators in Python . 

Python Operator Exercise Questions

Below are two Exercise Questions on Python Operators. We have covered arithmetic operators and comparison operators in these exercise questions. For more exercises on Python Operators visit the page mentioned below.

Q1. Code to implement basic arithmetic operations on integers

Q2. Code to implement Comparison operations on integers

Explore more Exercises: Practice Exercise on Operators in Python

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