term

Term is the most basic unit or operand within a programming language expression. It represents a single, static value or a straightforward way to access one.

• Key Property: It already is a value or a straightforward way to access one.

• Examples: Literals (numbers, strings), variables, or a parenthesized sub-expression.

Examples

Category	Description	C++ example	Lisp example	Prolog example
Literals	Fixed, constant values.	100, "hello", 3.14	100, "hello", 3.14	100, hello (atom)
Variables	Named storage locations.	x, user_count	x, user-count	X, Y (variables)
Function Calls	If the call returns a value directly.	get_time()	(get-time)	Arithmetic only: sin(90)

Why is it useful

1. Establishes Parsing Rules

The language grammar needs to distinguish between atomic values and composite operations. Without a clear term definition, the parser wouldn’t know where expressions begin and end

2. Enables Operator Precedence

Terms are used for precedence hierarchies. By defining what is an indivisible unit, the language can build up layers of operators with different precedence. In C++, without understanding terms, even x+++y becomes ambiguous (is it x++ + y or x + ++y?).

3. Type Checking Boundaries

Type systems need to know what units to check. Terms are where types originate—a literal has a type, a variable has a type. Expressions then propagate and validate these types through operations.

How does it correspond with AST?

• The term/expression hierarchy directly shapes the abstract syntax tree (AST).
  • Term nodes are the leaves of AST.
  • expression nodes are the internal operations.
  • This ensures the internal representation accurately reflects the intended computation order. This can remove ambiguity of programs

Relation to expression

• $\text{term} + \text{ operator } + \text{term} = \text{ expression}$
• every Term is a trivial expression, as it evaluates to itself.
• expression necessarily involves an operation (e.g., addition, comparison, function application), term doesn’t