Building Your Own Programming Language From Scratch: Part V - Arraysby@alexandermakeev

# Building Your Own Programming Language From Scratch: Part V - Arrays

July 15th, 2022

In this part of creating your programming language, we will implement arrays. We will be able to read array expressions, access and append/update values, and in the end, we'll test arrays by implementing the recursive binary search algorithm.

### Company Mentioned

In this part of creating your programming language, we will implement arrays. Please see the previous parts:

The full source code is available over on GitHub.

### Our language will provide the following abilities for the arrays:

• Define an array
array = { 1, 2, 3 }
• Define an empty array
empty_array = { }
• Contain arbitrary types of values: plain types, structure instantiations, function invocations, nested operators with other arrays, and any other composite expressions inheriting the Expression interface
arbitrary_array = { 1, "two", false, new Structure[4], get_value[5], { 6, 7 * 8 } }
• Append a value to the defined array with << operator
array = { 1, 2 }
array << 3 # will contain { 1, 2, 3 }
• Access array’s value by index position
first_value = array{0}
• Update array’s value by index position
array{0} = 1
array{1} = array{array{0} + 1} + 1

## 1 Lexical analysis

We will begin with lexical analysis. Basically, it’s a process to divide the source code into tokens, such as keyword, identifier/variable, operator, etc.

First, to define the array, we add curly brackets { } as the GroupDivider lexeme. We can’t use the square brackets [ ] or round brackets ( ) as they are already taken by the functions/structures definitions and by expression operators accordingly.

package org.example.toylanguage.token;

...
public enum TokenType {
...
GroupDivider("(\\[|\\]|\\,|\\{|})"),
...
}

Second, we need to introduce a new << Operator lexeme to define the "append a value to array" operation. We’ll extend the current less than operator < by adding an {1,2} quantifier after it, which will be able to catch either one or two < symbols:

...
public enum TokenType {
...
Operator("([+]|[-]|[*]|[/]|[%]|>=|>|<=|[<]{1,2}|[=]{1,2}|!=|[!]|[:]{2}|[(]|[)]|(new|and|or)(?=\\s|\$))"),
...
}

With all this being set, we will catch all the needed lexemes properly with defined TokenType values.

## 2 Syntax analysis

In this section, within the syntax analysis, we will convert tokens obtained from the lexical analysis into final statements following our language’s array rules. Arrays are just like any other part of the expression without any additional statements. Therefore, we just need to extend the existing functionality for the ExpressionStatement.

## 2.1 ArrayExpression

First, to declare any values in our array, we define the ArrayExpression class and add the List of values, which will accept the Expression values to allow us to place non-final values such as variables, structure invocations, function invocations, operators, and any other Expression implementations. Next, we implement the Expression interface, which requires us to override the evaluate() method. It’s a deferred interface to transform array Expression expressions into final Value values, which will be invoked only during direct code execution:

package org.example.toylanguage.expression;

@RequiredArgsConstructor
@Getter
public class ArrayExpression implements Expression {
private final List<Expression> values;

@Override
public Value<?> evaluate() {
return new ArrayValue(this);
}
}

## 2.2 ArrayValue

The next class we implement is ArrayValue, which will accept the ArrayExpression as a constructor argument to gather all the details about the array state. To change the array values, we include the corresponding getValue(), setValue(), appendValue() methods:

package org.example.toylanguage.expression.value;

public class ArrayValue extends Value<List<Value<?>>> {
public ArrayValue(ArrayExpression expression) {
this(expression.getValues()
.stream()
.map(Expression::evaluate)
.collect(Collectors.toList()));
}

public Value<?> getValue(int index) {
if (getValue().size() > index)
return getValue().get(index);
return NULL_INSTANCE;
}

public void setValue(int index, Value<?> value) {
if (getValue().size() > index)
getValue().set(index, value);
}

public void appendValue(Value<?> value) {
}
}

We can also override the equals() method, as it will be used by the EqualsOperator and NotEqualsOperator to compare:

...
public class ArrayValue extends Value<List<Value<?>>> {
...

@Override
public boolean equals(Object o) {
if (this == o) return true;
if (o == null) return false;
if (getClass() != o.getClass()) return false;
//noinspection unchecked
List<Value<?>> oValue = (List<Value<?>>) o;
return new HashSet<>(getValue()).containsAll(oValue);
}
}

## 2.3 Operator

### 2.3.1 ArrayValueOperator

With the ArrayExpression implementation, we can already instantiate arrays and fill them with values. The next goal is to access the array’s value by index position. For this purpose, we'll create the BinaryOperatorExpression operator implementation, which contains two operands. The evaluate() method will use the first operand as the array itself and the second operand as an index. The assign() method is used to set the array’s value by index using the same operands:

package org.example.toylanguage.expression.operator;

public class ArrayValueOperator extends BinaryOperatorExpression implements AssignExpression {
public ArrayValueOperator(Expression left, Expression right) {
super(left, right);
}

@Override
public Value<?> evaluate() {
Value<?> left = getLeft().evaluate();
if (left instanceof ArrayValue) {
Value<?> right = getRight().evaluate();
return ((ArrayValue) left).getValue(((Double) right.getValue()).intValue());
}
return left;
}

@Override
public void assign(Value<?> value, VariableScope variableScope) {
Value<?> left = getLeft().evaluate();
if (left instanceof ArrayValue) {
Value<?> right = getRight().evaluate();
((ArrayValue) left).setValue(((Double) right.getValue()).intValue(), value);
}
}
}

The new AssignExpression interface can be used to set the variable's value only within the assignment = operator:

public interface AssignExpression {
void assign(Value<?> value, VariableScope variableScope);
}

public class AssignmentOperator extends BinaryOperatorExpression {
...

@Override
public Value<?> evaluate() {
if (getLeft() instanceof AssignExpression) {
Value<?> right = getRight().evaluate();
((AssignExpression) getLeft()).assign(right, variableScope);
}
...
}
}

### 2.3.2 ArrayAppendOperator

Next, to transform the "append a value to array" operator defined as << Operator lexeme, we create a new BinaryOperatorExpression implementation. The left operand is still the array itself, and the right operand is the value we want to append:

package org.example.toylanguage.expression.operator;

public class ArrayAppendOperator extends BinaryOperatorExpression {
public ArrayAppendOperator(Expression left, Expression right) {
super(left, right);
}

@Override
public Value<?> evaluate() {
Value<?> left = getLeft().evaluate();
if (left instanceof ArrayValue) {
Value<?> right = getRight().evaluate();
((ArrayValue) left).appendValue(right);
}
return getLeft().evaluate();
}
}

Don’t forget to include this << operator in the Operator enum. It will have the same precedence as the Assignment operator:

...
public enum Operator {
...

ArrayAppend("<<", ArrayAppendOperator.class, 0),
Assignment("=", AssignmentOperator.class, 0);

...
}

In this section, we will complete syntax analysis for the array integration by reading an actual array instantiation and the array’s value. To make it work, we need to extend the ExpressionReader implementation to support array expressions within Dijkstra's Two-Stack algorithm.

### 2.4.1 Array instantiation

First, we will read the array instantiation. We extend the readExpression() filter to support the curly brackets as the marker of array beginning:

package org.example.toylanguage;

public class StatementParser {

...

...

while (hasNextToken()) {
...
}
}

private boolean hasNextToken() {
if (tokens.peekSameLine(TokenType.Operator, TokenType.Variable, TokenType.Numeric, TokenType.Logical, TokenType.Null, TokenType.Text))
return true;
//beginning of an array
if (tokens.peekSameLine(TokenType.GroupDivider, "{"))
return true;
return false;
}
}
}

Next, we implement the corresponding case for the GroupDivider { lexeme:

while (hasNextToken()) {
Token token = tokens.next();
switch (token.getType()) {
case Operator:
...
default:
String value = token.getValue();
Expression operand;
switch (token.getType()) {
case Numeric:
...
case Logical:
...
case Text:
...
case Null:
...
case GroupDivider:
if (Objects.equals(token.getValue(), "{")) {
break;
}
case Variable:
default:
...
}
operands.push(operand);
}
}
...
}

The pattern for the array expression is the same as for the function invocation except for using the curly brackets instead of square brackets: we read the array's values as the Expression expressions divided by a comma within the curly brackets. In the end, we build the ArrayExpression with the obtained values:

// read array instantiation: { 1, 2, 3 }
List<Expression> values = new ArrayList<>();

while (!tokens.peekSameLine(TokenType.GroupDivider, "}")) {

if (tokens.peekSameLine(TokenType.GroupDivider, ","))
tokens.next();
}

tokens.next(TokenType.GroupDivider, "}"); //skip close curly bracket

return new ArrayExpression(values);
}

### 2.4.2 Access array’s value by index

Accessing the array’s value by index position is less straightforward than the array’s append operation because our Dijkstra’s Two-Stack algorithm inside the ExpressionReader cannot handle the array’s index defined within the curly brackets as an operator. To solve this limitation, we will read the operator with operands together as a composite operand the same way we did read the structure instantiation, except for the fact that we don’t have the "new" operator in front of the structure and the array’s index is defined inside curly brackets instead of square brackets:

VariableExpression array = new VariableExpression(token.getValue());
tokens.next(TokenType.GroupDivider, "{");
tokens.next(TokenType.GroupDivider, "}");

return new ArrayValueOperator(array, arrayIndex);
}

while (hasNextToken()) {
Token token = tokens.next();
switch (token.getType()) {
case Operator:
...
default:
String value = token.getValue();
Expression operand;
switch (token.getType()) {
case Numeric:
...
case Logical:
...
case Text:
...
case Null:
...
case GroupDivider:
...
case Variable:
default:
if (!operators.isEmpty() && operators.peek() == Operator.StructureInstance) {
...
} else if (tokens.peekSameLine(TokenType.GroupDivider, "[")) {
...
} else if (tokens.peekSameLine(TokenType.GroupDivider, "{")) {
} else {
...
}
}
operands.push(operand);
}
}
...
}

## 3 Tests

We have finished embedding arrays in both lexical and syntax analyzers. Now we should be able to read array expressions, access and update array values. Let’s implement a more realistic task - the recursive binary search algorithm:

fun binary_search [ arr, n, lo, hi, key ]
if hi >= lo then
mid = (hi + lo) // 2 # floor division
if arr{mid} < key then
return binary_search [ arr, n, mid + 1, hi, key ]
elif arr{mid} > key then
return binary_search [ arr, n, lo, mid - 1, key ]
else then
return mid
end
else then
return -1
end
return
end

arr = {10, 20, 30, 50, 60, 80, 110, 130}
arr << 140
arr << 170
n = 10

print binary_search [ arr, n, 0, n - 1, 10 ] # 0
print binary_search [ arr, n, 0, n - 1, 80 ] # 5
print binary_search [ arr, n, 0, n - 1, 170 ] # 9
print binary_search [ arr, n, 0, n - 1, 5 ] # -1
print binary_search [ arr, n, 0, n - 1, 85 ] # -1
print binary_search [ arr, n, 0, n - 1, 175 ] # -1

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