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3.1b Homework Translating Contexts To Numerical Expressions Definition

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Arithmetic Operators and Numerical Expressions - C Primer Plus (5th Edition)

Arithmetic Operators and Numerical Expressions Arithmetic Operators and Numerical Expressions

You have already seen numerous examples of how C# performs arithmetic calculations by evaluating arithmetic expressions, such as the following:

((distance1 + distance2) / 2)

These examples give you a general idea of how a correct expression is put together and how it is evaluated. However, you can only create expressions that efficiently solve the computational problems of your particular program, if you know the different underlying building blocks of a C# expression and how these are combined to form valid expressions. The following sections are aimed at providing you with this knowledge.

Arithmetic operators (such as addition (+ ), subtraction (- ), multiplication (* ), and division (/ )) combine with numbers called operands to form arithmetic expressions. Arithmetic expressions written in C# are fairly easy to interpret; they more or less follow the arithmetic rules we are used to from school.

Binary Operators

The four basic arithmetic operators mentioned in the preceding section all need one operand on their left sides and one operand on their right sides. An arithmetic operator combining two operands to form an expression, such as

is called a binary operator. An operand can, in this context, take many forms. It can be a simple literal, such as 345.23, a variable, a constant representing a numerical value, or a numerical expression as in the following:

An operand can even be a method call. In this case, the method being called must have a return value. The following call to the Average method illustrates

These two method calls are both resolved before the addition operator is applied, and can then be regarded as the numbers 15.0 and 30.0, both of type double. the type of Average 's return values as specified in its method header.

We can concisely express the five forms of an operand, by utilizing the syntax notation introduced in the previous chapter. This is done in Syntax Box 7.1.

Syntax Box 7.1 The Operand

An operand can be defined in five different ways:

Note: The method called with <Method_call> must have a return value.

Additionally, our perception of a numerical expression can be formalized as in Syntax Box 7.2.

Syntax Box 7.2 The Numerical Expression

The latter definition (< Numerical_expression > < Binary_operator > < Numerical_expression >) can be deduced by combining the first definition (< Operand > < Binary_operator > < Operand >) with the fourth definition of an operand Operand. = <Numerical_expression> found in Syntax Box 7.1. This is illustrated here by substituting < Operand > with < Numerical_expression >:

There are other definitions for numerical expressions involving other operators not yet presented. These will be mentioned in due time.

Because an operator surrounded by two operands forms a numerical expression, and an operand itself can be defined as a numerical expression, one way to define a numerical expression is as follows:

Consequently, any expression using more than two operands can always be divided into sub-expressions, each consisting of only two operands and one binary operator. After the result of each of these sub-expressions has been found, the results can be used to calculate the next level of sub-expressions. Consider the following expression:

At first, the expression seems to contain an overwhelming number of operators and operands (numbers), until we realize that it is composed of many sub-expressions. Figure 7.1 shows how we can apply our definition of a numerical expression to calculate the given expression.

Figure 7.1. An expression hierarchy.

In Figure 7.1, notice how multiplications are performed before additions, in accordance with the rules we learned in school. This fact is highlighted in Figure 7.2.

Figure 7.2. Multiplication has higher precedence than addition.

Consequently, when an operand (such as number 3 in Figure 7.2) can be processed by more than one operator (+ or *, in this case), C# uses precedence rules to decide which operator is applied first. These rules determine how expressions, such as the one shown in Figure 7.1, are divided into sub-expression.

For simplicity, I have used literals in the numerical expressions of Figures 7.1 and 7.2. Obviously, I could have used a combination of any of the operand definitions given in Syntax Box 7.1.

C# contains arithmetic operators other than the four binary operators previously mentioned. Each of them carries an exact precedence in relation to the others.

Table 7.1 gives an overview of the operators discussed in this chapter along with their precedence. A listing of the operators presented in this book can be found in Appendix B, "Operator Precedence."

Table 7.1 shows several operators not yet presented; they have been included at this stage as a handy reference and overview when you read through the rest of the section.

Please locate the four binary operators presented so far in Table 7.1. Observe that the multiplication (*) and division (/) operators both have a higher precedence than the addition (+) and subtraction (-) operators. This fits in nicely with our numerical expression examples and their results in Figures 7.1 and 7.2.

Table 7.1. Arithmetic Operators�Precedence and Associativity

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About regular expressions (regex)

In the context of Analytics, regular expressions are specific sequences of characters that broadly or narrowly match patterns in your Analytics data.

For example, if you wanted to create a view filter to exclude site data generated by your own employees, you could use a regular expression to exclude any data from the entire range of IP addresses that serve your employees. Let’s say those IP addresses range from 123.456.789.0000 - 123.456.789.9999. Rather than enter 10,000 different IP addresses, you could create a regular expression like 123\.456\.789\.\d+ that matches the entire range of addresses.

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Regex metacharacters

How Do You Translate Phrases into Numerical Expressions?

How Do You Translate Phrases into Numerical Expressions? How Do You Translate Phrases into Numerical Expressions?

An expression is just a mathematical phrase. In this tutorial, you'll learn about two popular types of expressions: numerical and algebraic expressions. A numerical expression contains numbers and operations. An algebraic expression is almost exactly the same except it also contains variables. Check out this tutorial to learn about these two popular kinds of expressions!

Translating Between Words and Math

Knowing the mathematical meaning of words allows you to decipher word problems and gives you the power to write your own word problems, too! Take a look at these words and learn their mathematical translations.

Turning a word problem into a math problem you can solve can be tricky. Luckily, there's some key words to look out for in a word problem that help tell you what math operation to use! This tutorial shows you some of these key words to look for in a word problem.

Further Exploration Translating Between Words and Math

Need some practice translating phrases into mathematical expressions? Then this tutorial is for you! You'll get practice translating statements involving addition, subtraction, multiplication, or division into mathematical expressions.

3.1b homework translating contexts to numerical expressions definition

9.1 Introduction

The Spring Expression Language (SpEL for short) is a powerful expression language that supports querying and manipulating an object graph at runtime. The language syntax is similar to Unified EL but offers additional features, most notably method invocation and basic string templating functionality.

While there are several other Java expression languages available, OGNL, MVEL, and JBoss EL, to name a few, the Spring Expression Language was created to provide the Spring community with a single well supported expression language that can be used across all the products in the Spring portfolio. Its language features are driven by the requirements of the projects in the Spring portfolio, including tooling requirements for code completion support within the eclipse based Spring Tool Suite. That said, SpEL is based on a technology agnostic API allowing other expression language implementations to be integrated should the need arise.

While SpEL serves as the foundation for expression evaluation within the Spring portfolio, it is not directly tied to Spring and can be used independently. In order to be self contained, many of the examples in this chapter use SpEL as if it were an independent expression language. This requires creating a few bootstrapping infrastructure classes such as the parser. Most Spring users will not need to deal with this infrastructure and will instead only author expression strings for evaluation. An example of this typical use is the integration of SpEL into creating XML or annotated based bean definitions as shown in the section Expression support for defining bean definitions.

This chapter covers the features of the expression language, its API, and its language syntax. In several places an Inventor and Inventor’s Society class are used as the target objects for expression evaluation. These class declarations and the data used to populate them are listed at the end of the chapter.

9.2 Feature Overview

The expression language supports the following functionality

  • Literal expressions
  • Boolean and relational operators
  • Regular expressions
  • Class expressions
  • Accessing properties, arrays, lists, maps
  • Method invocation
  • Relational operators
  • Assignment
  • Calling constructors
  • Bean references
  • Array construction
  • Inline lists
  • Inline maps
  • Ternary operator
  • Variables
  • User defined functions
  • Collection projection
  • Collection selection
  • Templated expressions
9.3 Expression Evaluation using Spring’s Expression Interface

This section introduces the simple use of SpEL interfaces and its expression language. The complete language reference can be found in the section Language Reference .

The following code introduces the SpEL API to evaluate the literal string expression 'Hello World'.

The value of the message variable is simply 'Hello World'.

The SpEL classes and interfaces you are most likely to use are located in the packages org.springframework.expression and its sub packages and .

The interface ExpressionParser is responsible for parsing an expression string. In this example the expression string is a string literal denoted by the surrounding single quotes. The interface Expression is responsible for evaluating the previously defined expression string. There are two exceptions that can be thrown, ParseException and EvaluationException when calling parser.parseExpression and exp.getValue respectively.

SpEL supports a wide range of features, such as calling methods, accessing properties, and calling constructors.

As an example of method invocation, we call the concat method on the string literal.

The value of message is now 'Hello World!'.

As an example of calling a JavaBean property, the String property Bytes can be called as shown below.

SpEL also supports nested properties using standard dot notation, i.e. prop1.prop2.prop3 and the setting of property values

Public fields may also be accessed.

The String’s constructor can be called instead of using a string literal.

Note the use of the generic method public <T> T getValue(Class<T> desiredResultType). Using this method removes the need to cast the value of the expression to the desired result type. An EvaluationException will be thrown if the value cannot be cast to the type T or converted using the registered type converter.

The more common usage of SpEL is to provide an expression string that is evaluated against a specific object instance (called the root object). There are two options here and which to choose depends on whether the object against which the expression is being evaluated will be changing with each call to evaluate the expression. In the following example we retrieve the name property from an instance of the Inventor class.

In the last line, the value of the string variable name will be set to "Nikola Tesla". The class StandardEvaluationContext is where you can specify which object the "name" property will be evaluated against. This is the mechanism to use if the root object is unlikely to change, it can simply be set once in the evaluation context. If the root object is likely to change repeatedly, it can be supplied on each call to getValue. as this next example shows:

In this case the inventor tesla has been supplied directly to getValue and the expression evaluation infrastructure creates and manages a default evaluation context internally - it did not require one to be supplied.

The StandardEvaluationContext is relatively expensive to construct and during repeated usage it builds up cached state that enables subsequent expression evaluations to be performed more quickly. For this reason it is better to cache and reuse them where possible, rather than construct a new one for each expression evaluation.

In some cases it can be desirable to use a configured evaluation context and yet still supply a different root object on each call to getValue. getValue allows both to be specified on the same call. In these situations the root object passed on the call is considered to override any (which maybe null) specified on the evaluation context.

In standalone usage of SpEL there is a need to create the parser, parse expressions and perhaps provide evaluation contexts and a root context object. However, more common usage is to provide only the SpEL expression string as part of a configuration file, for example for Spring bean or Spring Web Flow definitions. In this case, the parser, evaluation context, root object and any predefined variables are all set up implicitly, requiring the user to specify nothing other than the expressions.

As a final introductory example, the use of a boolean operator is shown using the Inventor object in the previous example.

9.3.1 The EvaluationContext interface

The interface EvaluationContext is used when evaluating an expression to resolve properties, methods, fields, and to help perform type conversion. The out-of-the-box implementation, StandardEvaluationContext. uses reflection to manipulate the object, caching java.lang.reflect.Method. java.lang.reflect.Field. and java.lang.reflect.Constructor instances for increased performance.

The StandardEvaluationContext is where you may specify the root object to evaluate against via the method setRootObject() or passing the root object into the constructor. You can also specify variables and functions that will be used in the expression using the methods setVariable() and registerFunction(). The use of variables and functions are described in the language reference sections Variables and Functions. The StandardEvaluationContext is also where you can register custom ConstructorResolvers, MethodResolvers, and PropertyAccessors to extend how SpEL evaluates expressions. Please refer to the JavaDoc of these classes for more details.

Type Conversion

By default SpEL uses the conversion service available in Spring core ( org.springframework.core.convert.ConversionService ). This conversion service comes with many converters built in for common conversions but is also fully extensible so custom conversions between types can be added. Additionally it has the key capability that it is generics aware. This means that when working with generic types in expressions, SpEL will attempt conversions to maintain type correctness for any objects it encounters.

What does this mean in practice? Suppose assignment, using setValue(). is being used to set a List property. The type of the property is actually List<Boolean>. SpEL will recognize that the elements of the list need to be converted to Boolean before being placed in it. A simple example:

9.3.2 Parser configuration

It is possible to configure the SpEL expression parser using a parser configuration object ( org.springframework.expression.spel.SpelParserConfiguration ). The configuration object controls the behavior of some of the expression components. For example, if indexing into an array or collection and the element at the specified index is null it is possible to automatically create the element. This is useful when using expressions made up of a chain of property references. If indexing into an array or list and specifying an index that is beyond the end of the current size of the array or list it is possible to automatically grow the array or list to accommodate that index.

It is also possible to configure the behaviour of the SpEL expression compiler.

9.3.3 SpEL compilation

Spring Framework 4.1 includes a basic expression compiler. Expressions are usually interpreted which provides a lot of dynamic flexibility during evaluation but does not provide the optimum performance. For occasional expression usage this is fine, but when used by other components like Spring Integration, performance can be very important and there is no real need for the dynamism.

The new SpEL compiler is intended to address this need. The compiler will generate a real Java class on the fly during evaluation that embodies the expression behavior and use that to achieve much faster expression evaluation. Due to the lack of typing around expressions the compiler uses information gathered during the interpreted evaluations of an expression when performing compilation. For example, it does not know the type of a property reference purely from the expression but during the first interpreted evaluation it will find out what it is. Of course, basing the compilation on this information could cause trouble later if the types of the various expression elements change over time. For this reason compilation is best suited to expressions whose type information is not going to change on repeated evaluations.

For a basic expression like this:

someArray[0].someProperty.someOtherProperty < 0.1

which involves array access, some property derefencing and numeric operations, the performance gain can be very noticeable. In an example micro benchmark run of 50000 iterations, it was taking 75ms to evaluate using only the interpreter and just 3ms using the compiled version of the expression.

Compiler configuration

The compiler is not turned on by default, but there are two ways to turn it on. It can be turned on using the parser configuration process discussed earlier or via a system property when SpEL usage is embedded inside another component. This section discusses both of these options.

Is is important to understand that there are a few modes the compiler can operate in, captured in an enum ( org.springframework.expression.spel.SpelCompilerMode ). The modes are as follows:

  • OFF - The compiler is switched off; this is the default.
  • IMMEDIATE - In immediate mode the expressions are compiled as soon as possible. This is typically after the first interpreted evaluation. If the compiled expression fails (typically due to a type changing, as described above) then the caller of the expression evaluation will receive an exception.
  • MIXED - In mixed mode the expressions silently switch between interpreted and compiled mode over time. After some number of interpreted runs they will switch to compiled form and if something goes wrong with the compiled form (like a type changing, as described above) then the expression will automatically switch back to interpreted form again. Sometime later it may generate another compiled form and switch to it. Basically the exception that the user gets in IMMEDIATE mode is instead handled internally.

IMMEDIATE mode exists because MIXED mode could cause issues for expressions that have side effects. If a compiled expression blows up after partially succeeding it may have already done something that has affected the state of the system. If this has happened the caller may not want it to silently re-run in interpreted mode since part of the expression may be running twice.

After selecting a mode, use the SpelParserConfiguration to configure the parser:

When specifying the compiler mode it is also possible to specify a classloader (passing null is allowed). Compiled expressions will be defined in a child classloader created under any that is supplied. It is important to ensure if a classloader is specified it can see all the types involved in the expression evaluation process. If none is specified then a default classloader will be used (typically the context classloader for the thread that is running during expression evaluation).

The second way to configure the compiler is for use when SpEL is embedded inside some other component and it may not be possible to configure via a configuration object. In these cases it is possible to use a system property. The property spring.expression.compiler.mode can be set to one of the SpelCompilerMode enum values ( off. immediate. or mixed ).

Compiler limitations

With Spring Framework 4.1 the basic compilation framework is in place. However, the framework does not yet support compiling every kind of expression. The initial focus has been on the common expressions that are likely to be used in performance critical contexts. These kinds of expression cannot be compiled at the moment:

  • expressions involving assignment
  • expressions relying on the conversion service
  • expressions using custom resolvers or accessors
  • expressions using selection or projection

More and more types of expression will be compilable in the future.

9.4 Expression support for defining bean definitions

SpEL expressions can be used with XML or annotation-based configuration metadata for defining BeanDefinitions. In both cases the syntax to define the expression is of the form #< <expression string> > .

9.4.1 XML based configuration

A property or constructor-arg value can be set using expressions as shown below.

The variable systemProperties is predefined, so you can use it in your expressions as shown below. Note that you do not have to prefix the predefined variable with the # symbol in this context.

You can also refer to other bean properties by name, for example.

9.4.2 Annotation-based configuration

The @Value annotation can be placed on fields, methods and method/constructor parameters to specify a default value.

Here is an example to set the default value of a field variable.

The equivalent but on a property setter method is shown below.

Autowired methods and constructors can also use the @Value annotation.

9.5 Language Reference 9.5.1 Literal expressions

The types of literal expressions supported are strings, numeric values (int, real, hex), boolean and null. Strings are delimited by single quotes. To put a single quote itself in a string, use two single quote characters.

The following listing shows simple usage of literals. Typically they would not be used in isolation like this but rather as part of a more complex expression, for example using a literal on one side of a logical comparison operator.

Numbers support the use of the negative sign, exponential notation, and decimal points. By default real numbers are parsed using Double.parseDouble().

9.5.2 Properties, Arrays, Lists, Maps, Indexers

Navigating with property references is easy: just use a period to indicate a nested property value. The instances of the Inventor class, pupin, and tesla, were populated with data listed in the section Classes used in the examples. To navigate "down" and get Tesla’s year of birth and Pupin’s city of birth the following expressions are used.

Case insensitivity is allowed for the first letter of property names. The contents of arrays and lists are obtained using square bracket notation.

The contents of maps are obtained by specifying the literal key value within the brackets. In this case, because keys for the Officers map are strings, we can specify string literals.

9.5.3 Inline lists

Lists can be expressed directly in an expression using <> notation.

<> by itself means an empty list. For performance reasons, if the list is itself entirely composed of fixed literals then a constant list is created to represent the expression, rather than building a new list on each evaluation.

9.5.4 Inline Maps

Maps can also be expressed directly in an expression using notation.

<:> by itself means an empty map. For performance reasons, if the map is itself composed of fixed literals or other nested constant structures (lists or maps) then a constant map is created to represent the expression, rather than building a new map on each evaluation. Quoting of the map keys is optional, the examples above are not using quoted keys.

9.5.5 Array construction

Arrays can be built using the familiar Java syntax, optionally supplying an initializer to have the array populated at construction time.

It is not currently allowed to supply an initializer when constructing a multi-dimensional array.

9.5.6 Methods

Methods are invoked using typical Java programming syntax. You may also invoke methods on literals. Varargs are also supported.

9.5.17 Collection Selection

Selection is a powerful expression language feature that allows you to transform some source collection into another by selecting from its entries.

Selection uses the syntax ?[selectionExpression]. This will filter the collection and return a new collection containing a subset of the original elements. For example, selection would allow us to easily get a list of Serbian inventors:

Selection is possible upon both lists and maps. In the former case the selection criteria is evaluated against each individual list element whilst against a map the selection criteria is evaluated against each map entry (objects of the Java type Map.Entry ). Map entries have their key and value accessible as properties for use in the selection.

This expression will return a new map consisting of those elements of the original map where the entry value is less than 27.

In addition to returning all the selected elements, it is possible to retrieve just the first or the last value. To obtain the first entry matching the selection the syntax is ^[…​] whilst to obtain the last matching selection the syntax is $[…​] .

9.5.18 Collection Projection

Projection allows a collection to drive the evaluation of a sub-expression and the result is a new collection. The syntax for projection is ![projectionExpression]. Most easily understood by example, suppose we have a list of inventors but want the list of cities where they were born. Effectively we want to evaluate '' for every entry in the inventor list. Using projection:

A map can also be used to drive projection and in this case the projection expression is evaluated against each entry in the map (represented as a Java Map.Entry ). The result of a projection across a map is a list consisting of the evaluation of the projection expression against each map entry.

9.5.19 Expression templating

Expression templates allow a mixing of literal text with one or more evaluation blocks. Each evaluation block is delimited with prefix and suffix characters that you can define, a common choice is to use #< > as the delimiters. For example,

The string is evaluated by concatenating the literal text 'random number is ' with the result of evaluating the expression inside the #< > delimiter, in this case the result of calling that random() method. The second argument to the method parseExpression() is of the type ParserContext. The ParserContext interface is used to influence how the expression is parsed in order to support the expression templating functionality. The definition of TemplateParserContext is shown below.

9.6 Classes used in the examples