In a grammar written down as production rules, what distinguishes a terminal from a nonterminal?
answer
- one kind of symbol never changes
- placeholders versus the words users type
- check which side of the arrow
- never on a left-hand side means terminal
- one nonterminal is designated the start
basics
~10 sTerminals are the literal symbols that appear in the generated text; nonterminals are named placeholders that some rule rewrites. A derivation starts at one designated start symbol and rewrites nonterminals until only terminals remain.
solid answer
~40 sA production rule has one nonterminal on its left and a sequence of symbols on its right. **Terminals** are the atoms of the language — the words, operators and punctuation a user actually types; nothing ever rewrites them. **Nonterminals** are names for structure, such as `FILTER`, `TERM` or `VALUE`; each one must be replaced by the right-hand side of some rule before the text is finished. One nonterminal is the **start symbol**, and the language the grammar defines is exactly the set of terminal-only strings reachable from it. The mechanical test is positional: if a symbol never appears on the left-hand side of any rule, it is a terminal. So in `TERM -> FIELD is VALUE`, the word `is` is a terminal and the three uppercase names are nonterminals.
go deeper
Recall the positional test: a symbol that never appears on the left of an arrow is a terminal and ends up in the text; everything else is a placeholder that must be rewritten first.
Explain the four parts of a grammar and walk an unfamiliar rule set out loud: name the terminals, the nonterminals, the alternatives hidden behind a vertical bar, and the designated start symbol.
Show that you read a rule set as a specification of legal inputs, and name the two faults that make one wrong in production: a nonterminal with no production, and rules unreachable from the start symbol.
Argue when a team is better served by a written rule set than by a hand-written validator as the definition of its input language, and who owns keeping the two in step.
## A grammar is a generator, not a parser A grammar written down as production rules is not code and not a parser. It is a **rewriting system** that generates strings. Formally it has four parts: 1. a finite set of **terminals** — the alphabet of the language being defined; 2. a finite set of **nonterminals** — names for the structures in it, disjoint from the terminals; 3. a finite set of **productions**, each of the form `A -> alpha`, where `A` is a single nonterminal and `alpha` is a possibly empty sequence of terminals and nonterminals; 4. a designated **start symbol**, one of the nonterminals. A string belongs to the language exactly when you can begin at the start symbol, repeatedly replace some nonterminal by the right-hand side of one of its productions, and end up with that string of terminals. Nothing else counts as membership, and no parser is needed to define it. ## The two kinds of symbol Take a four-rule set for a dashboard's saved-filter expression language, written before anyone has built a parser for it: ``` FILTER -> TERM and FILTER | TERM TERM -> FIELD is VALUE FIELD -> status | owner VALUE -> open | me ``` Here the terminals are `and`, `is`, `status`, `owner`, `open` and `me` — six literal words that can appear in something a user types, such as `status is open and owner is me`. The nonterminals are `FILTER`, `TERM`, `FIELD` and `VALUE`; none of them ever appears in a finished filter, because each is a placeholder waiting to be rewritten. `FILTER` is the start symbol. | | Terminal | Nonterminal | |---|---|---| | Appears on a left-hand side | never | always, in at least one rule | | Survives into the generated string | yes | no | | Can be rewritten | no | yes, by any of its productions | | Typical role | a keyword, operator, literal or punctuation mark | a named structure such as an expression or a clause | | Written how | often quoted, or in lower case by convention | often in angle brackets, or in upper case by convention | The notation varies — some documents quote every terminal, some put nonterminals in angle brackets, some rely on case alone — but the structural distinction never varies, and neither does the positional test: a symbol that is never on the left of an arrow cannot be rewritten, so it is a terminal. ## What the start symbol buys you The start symbol is **designated, not inferred**. A grammar with the same rules but a different start symbol defines a different language: starting from `TERM` in the rule set above gives only single comparisons such as `owner is me`, never a chain joined by `and`. Listing a rule first is a common convention for marking the start symbol, but it is a convention, and a careful spec states it outright. ## Alternatives, and two ways a rule set goes wrong The vertical bar is shorthand for several productions sharing one left-hand side: `FIELD -> status | owner` is two productions, not one. Alternatives are choices offered to the generator, so a derivation picks exactly one of them each time it rewrites that nonterminal. Two structural faults show up when reading an unfamiliar rule set, and both are worth naming aloud: - **A nonterminal with no production.** Any derivation that introduces it can never finish, because nothing can rewrite it and it is not a terminal. Such a rule set generates fewer strings than its author intended, sometimes none at all. - **A nonterminal unreachable from the start symbol.** Its rules are dead text: no derivation can ever introduce it, so deleting them changes nothing about the language. Neither fault is detectable by eye in a large rule set, which is why grammar tooling reports both. ## Why an engineer is asked this The distinction is the entry fee for every later conversation about syntax. A team that writes its saved-filter language down as a rule set gets one artefact that says precisely which strings are legal, independent of whichever hand-written validator happens to be deployed. Reading that artefact means knowing which symbols are the surface the user types and which are the structure the team invented to describe it. If a candidate cannot separate the two, nothing built on top of a grammar — a derivation, a tree, a generated parser, a diagnostic message — can be discussed with them.
- How do you know which nonterminal is the start symbol?It is designated by the grammar, not derived from the rules. Many documents adopt the convention that the first rule listed defines it, but that is only a convention. Changing the start symbol while keeping every rule changes the language: starting from a comparison rule generates single comparisons only, never the chained form the author intended.
- What does the vertical bar in a production mean?It is shorthand for several productions that share one left-hand side, so `FIELD -> status | owner` is two productions written on one line. Each is an alternative the generator may choose when it rewrites that nonterminal, and exactly one of them is used at each rewriting step.
- What happens if a nonterminal appears on some right-hand side but has no production of its own?Every derivation that introduces it becomes stuck: the symbol is not a terminal so the string is not finished, and no rule can replace it. The rule set therefore generates fewer strings than intended, and in the worst case none. Grammar tooling reports this alongside the opposite fault, a nonterminal unreachable from the start symbol.
saying these in an interview costs you the question
- Calls every symbol in the rules a keyword of the language.
- Thinks nonterminals can appear in the finished string.
- Believes any nonterminal may serve as the start symbol.
- Treats quoted punctuation as decoration rather than a terminal.
- Says a rule set defines a parser rather than a set of strings.
- Reads a vertical bar as one production instead of several.