science

Lexical grammar

Lexical grammar is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Lexical grammar rather than just read about it. In short: In computer science, a lexical grammar or lexical structure is a formal grammar defining the syntax of tokens. The program is written using characters that are defined by the lexical structure of the language used.

Key takeaways

Lexical grammar belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Lexical grammar to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Lexical grammar from memory before moving on to harder problems.

Reference excerpt

In computer science, a lexical grammar or lexical structure is a formal grammar defining the syntax of tokens. The program is written using characters that are defined by the lexical structure of the language used. The character set is equivalent to the alphabet used by any written language. The lexical grammar lays down the rules governing how a character sequence is divided up into subsequences of characters, each part of which represents an individual token. This is frequently defined in terms of regular expressions. For instance, the lexical grammar for many programming languages specifies that a string literal starts with a " character and continues until a matching " is found (escaping makes this more complicated), that an identifier is an alphanumeric sequence (letters and digits, usually also allowing underscores, and disallowing initial digits), and that an integer literal is a sequence of digits. So in the following character sequence "abc" xyz1 23 the tokens are string, identifier and number (plus whitespace tokens) because the space character terminates the sequence of characters forming the identifier. Further, certain sequences are categorized as keywords – these generally have the same form as identifiers (usually alphabetical words), but are categorized separately; formally they have a different token type.

Examples Regular expressions for common lexical rules follow (for example, C). Unescaped string literal (quote, followed by non-quotes, ending in a quote):

"[^"]*"

Escaped string literal (quote, followed by escaped characters or non-quotes, ending in a quote):

"(\.|[^\"])*"

Integer literal:

[0-9]+

Decimal integer literal (no leading zero):

[1-9][0-9]*|0

Hexadecimal integer literal:

0[Xx][0-9A-Fa-f]+

Octal integer literal:

0[0-7]+

Identifier:

[A-Za-z_$][A-Za-z0-9_$]*

Worked examples

Example 1 — a first encounter with Lexical grammar

Start with the simplest possible case. Write down what Lexical grammar claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Lexical grammar before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Lexical grammar ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Lexical grammar

In research: Lexical grammar appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Lexical grammar in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Lexical grammar is common in secondary-school and first-year university syllabi. It links to neighbouring topics Formal languages, Parsing, so understanding it makes those chapters shorter.
In everyday life: Look for Lexical grammar outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Lexical grammar in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Lexical grammar means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Lexical grammar out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Lexical grammar in simple terms?

Why does Lexical grammar matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Lexical grammar?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Lexical grammar.