types.
To grasp the problem, consider a structured-meaning theory of meaning,
-on which the meaning of natural language expressions are represented
+on which the meanings of natural language expressions are represented
by objects that can have internal structure.
1. The center of mass of the solar system is a point.
weeks, the type of a DP will be a *sum type*: the disjoint union of the
class of objects that a directly referential term can refer to, and
the class of objects that can serve as complex meaning structures
-corresponding to DPs as in (1) that are not directly referential.
+corresponding to DPs as in (1) that are not directly referential.
+Our more systematic type-theoretic treatment permits us to dispense with worries
+about whether the meaning of the DP in (1) might itself be the empty set.
## Motivating Maybe
hungry*.
Setting aside such objections, we will see over and over again the
-utility of the general strategy instantiated in Kaplan's strategy for representing the meaning of
+utility of the general strategy instantiated in Kaplan's proposal for representing the meaning of
directly-referential expressions:
> Kaplan's rule for directly-referential expressions: a directly referential expression E contributes either:
-> {} if there is no object that E refers to, or else
-> {P} if E refers to P
+> {} (or what we'll call `None` or `Nothing`) if there is no object that E refers to, or else
+> {P} (or what we'll call `Some P` or `Just P`) if E refers to P
-In later weeks, we will call the general form of this technique the "option" or "Maybe" type, and the general strategy for deploying this type "the Maybe monad." (In OCaml one has types like `int option`; in Haskell they are `Maybe Int`.)
+We will call the type used here an "option" or "Maybe" type (from OCaml and Haskell, respectively). And we'll call the general strategy for deploying this type "the Option/Maybe monad."
Kaplan, D. 1989. "Demonstratives. In J. Almog, J. Perry, & H. Wettstein