Expression as Tree

Represent operators and operands as tree nodes

This notional machine represents a source code expression in the form of a tree. This makes the structure of the expression explicit, and it allows visualizing the various steps of expression evaluation. It also allows annotating the various subexpressions with their types.

An expression tree is essentially an abstract syntax tree (AST), focused on just an expression.

Here is an example Java expression:

1 + 2 + "AAA" + 3 + 4

The corresponding expression tree shows not only the expression’s structure but also the types and values of all subexpressions:

77 Misconceptions Expressible in this Notional Machine

A notional machine focuses on a subset of the syntax and semantics of a programming language. The following misconceptions are related to the language features expressible in this notional machine.

ArithmeticPlusPrecedes

Addition has higher precedence than string concatenation

ArrayAccessWithParentheses

Parenthesis are used to access an element in an array

ArrayAllocationWithoutNew

Arrays are created without the new keyword

ArrayBracketCountIsLength

The number of brackets in an array type or an array initializer corresponds to the length of the array

ArrayElementTypeRepeats

The type of a multi-dimensional array is written as T[] T[] T[]

ArrayHasLengthMethod

To get the length of an array, one needs to call its length method

ArrayInitializerContentsInBrackets

Array initializers list the elements in square brackets

ArrayRankIsLength

Array rank and array length are the same thing

AssignCompares

= compares two values

AssignmentNotExpression

An assignment a=b is not an expression

CallOnPrimitive

One can invoke a method on primitive values

CallRequiresVariable

One needs a variable to invoke a method

CannotChainMemberAccesses

Member accesses cannot be chained together

CannotChainMemberToConstructor

Method calls or field accesses cannot be chained to a constructor invocation

ChainedMethodsNotCalledFromOutside

Chained methods are all called on the object at the beginning of the chain

CharNotNumeric

Char is not a numeric type

CompareBooleanToConstant

To test whether an expression evaluates to true or false, one must compare it to a constant

ComparisonWithBoolLiteral

To test whether an expression is True or False, one must compare it to True or to False

ComparisonWithBooleanLiteral

To test whether an expression is true or false, one must compare it to true or to false

CompositeExpressionsUntyped

Expressions that consist of multiple parts have no type

ConstructorWithoutNew

One can write the constructor name, without new, to instantiate a class

EvaluationResultsArePrinted

Evaluating an expression means outputting its result

ExpressionAssigns

An expression that reads a variable also updates its value after the evaluation

ExpressionsDynamicallyTyped

One has to evaluate an expression to determine its type

InlineCallInExpressionTree

The expression tree of an expression involving a call inlines the call's computation of the returned value

InlineVariableInExpressionTree

The expression tree of an expression involving a variable inlines the variable's definition

IntegerDivisionToRational

Dividing two integers can produce a rational number

LiteralNoExpression

A literal is not an expression

LiteralString

When passing a literal string as argument to a method, no quotes are needed

MapToBooleanWithConditionalOperator

To map a boolean expression to a boolean, a conditional operator is necessary

MapToBooleanWithTernaryOperator

To map a boolean expression to a bool, a ternary conditional operator is necessary

MultiReferenceVariable

A reference variable can point to multiple objects

MultiValueVariable

A variable can contain more than one value

MultidimensionalArray

A multi-dimensional array is one thing

NoAtomicExpression

Expressions must consist of more than one piece

NoCallOnStringLiteral

One cannot invoke methods on String literals

NoCastIfSameSize

If a variable is at least as big (bit-width) as a value, then no cast is needed to a assign the value to the variable

NoFieldInheritance

An object contains only the fields declared in its class

NoFloatLiterals

There are no float literals

NoImplicitWidening

Smaller types are never automatically converted into bigger ones without an explicit cast

NoJaggedArrays

Multi-dimensional arrays have a rectangular shape

NoLongLiterals

There are no long literals

NoMethodInheritance

Subclasses inherit fields but not methods

NoShortCircuit

&& and || always evaluate both operands

NoShortCircuit

and/or always evaluate both operands

NoSingleLogicAnd

& is only a bitwise AND

NoStringToString

One cannot invoke toString() on a String

NullPointerExceptionCompileTime

NullPointerExceptions are detected at compile time

NumericToBooleanCoercion

Numeric types can be coerced to boolean

ObjectsMustBeNamed

A variable is needed to instantiate an object

OnlyInnermostArrayElements

Only the elements of the innermost array of a multi-dimensional array are accessible

OutOfBoundsElementsAreNull

Out-of-bounds array elements are null

OutsideInFunctionNesting

Nested function calls are invoked outside in

OutsideInMethodNesting

Nested method calls are invoked outside in

ParenthesesOnlyIfArgument

() are optional for method calls without arguments

ParenthesesOnlyIfArgument

() are optional for function calls without arguments

PrimitiveVariablesDynamicallyTyped

The type of a primitive variable depends on its value

PrivateAccessibleInSubclass

Private members of a superclass are accessible from a subclass

RationalLiterals

Rational fractions are literals

ReferenceToBooleanCoercion

Every reference type can be coerced to boolean

ReferenceToIntegerConversion

One can cast between references and ints

RightToLeftChaining

Chained accesses are invoked from right to left

SelfNoExpression

The name self is not an expression

SingleQuoteString

String literals can be in single quotes

StringLengthField

One can know the length of a String object by accessing its length field

StringLiteralNoObject

One needs to call the String constructor to get a String object from a literal

StringPlusStringifiesExpression

String concatenation stringifies non-String operand expressions

StringRepetitionOperator

The multiplication operator can repeat a String a number of times

SuperAlwaysHasParentheses

To call a method on a superclass, parentheses are needed after the keyword super

TargetTyping

The type of a numerical expression depends on the type expected by the surrounding context

ThisAssignable

One can assign to this

ThisCanBeNull

this can be null

ThisChildInCallExpression

Instance method or constructor call nodes in expression trees have a child labeled "this"

ThisInConstructorIsNull

In a constructor, this is null

ThisNoExpression

The name this is not an expression

ToStringPrints

Invoking toString() prints something

VariablesHoldExpressions

= stores an expression in a variable