The relation between an evaluator and an interpreter?

An interpreter is a program that simulates the execution of a programming language and implements a function that carries a program into a value.

An evaluator is a program that reduces a program into a value.

Essentially, the line is pretty blurry:

• Interpreter sometimes emphasizes the operational aspect: stepping through a program instruction by instruction, maintaining state, simulating a machine.

• Evaluator sometimes emphasizes the denotational or reduction aspect: recursively computing the value of expressions according to semantic rules.

• But in reality, most interpreters are evaluators.

Some subtle connotations that occasionally appear:

• "Evaluator" might suggest a simpler, more mathematical framing (common in PL theory, lambda calculus).

• "Interpreter" might suggest something more full-featured: handling I/O, errors, a REPL, etc.

• In partial evaluation literature, an "evaluator" is specifically the semantic function being specialized.