Pragmatic Side Effects

In the quest to give a formal compositional semantics to natural languages, semanticists have started turning their attention to phenomena that have been also considered as parts of pragmatics (e.g., discourse anaphora and presupposition projection). To account for these phenomena, the very kinds of meanings assigned to words and phrases are often revisited. To be more specific, in the prevalent paradigm of modeling natural language denotations using the simply-typed lambda calculus (higher-order logic) this means revisiting the types of denotations assigned to individual parts of speech. However, the lambda calculus also serves as a fundamental theory of computation, and in the study of computation, similar type shifts have been employed to give a meaning to side effects. Side effects in programming languages correspond to actions that go beyond the lexical scope of an expression (a thrown exception might propagate throughout a program, a variable modified at one point might later be read at an another) or even beyond the scope of the program itself (a program might interact with the outside world by e.g., printing documents, making sounds, operating robotic limbs...).