Baby monads
-----------
-Read the material on dividing by zero/towards monads from the end of lecture
-notes for week 6, then write a function `lift'` that generalized the
+Read the material on dividing by zero/towards monads from <strike>the end of lecture
+notes for week 6</strike> the start of lecture notes for week 7, then write a function `lift'` that generalized the
correspondence between + and `add'`: that is, `lift'` takes any two-place
operation on integers and returns a version that takes arguments of type `int
option` instead, returning a result of `int option`. In other words, `lift'`
-The intensionality monad
-------------------------
+Now we'll look at using monads to do intensional function application.
+This really is just another application of the reader monad, not a new monad.
+In Shan (2001) [Monads for natural
+language semantics](http://arxiv.org/abs/cs/0205026v1), Ken shows that
+making expressions sensitive to the world of evaluation is conceptually
+the same thing as making use of the reader monad.
+This technique was beautifully re-invented
+by Ben-Avi and Winter (2007) in their paper [A modular
+approach to
+>>>>>>> f879a647e289a67b992caaafd497910259a81040
+intensionality](http://parles.upf.es/glif/pub/sub11/individual/bena_wint.pdf),
+though without explicitly using monads.
+
+
+All of the code in the discussion below can be found here: [[intensionality-monad.ml]].
+To run it, download the file, start OCaml, and say
-In the meantime, we'll look at several linguistic applications for
-monads, based on what's called the *reader monad*, starting with
-intensional function application.
+ # #use "intensionality-monad.ml";;
+
+Note the extra `#` attached to the directive `use`.
First, the familiar linguistic problem:
both true, they denote the same object, and Ann's beliefs can't
distinguish between them.
-In Shan (2001) [Monads for natural language
-semantics](http://arxiv.org/abs/cs/0205026v1), Ken shows that making
-expressions sensitive to the world of evaluation is conceptually the
-same thing as making use of a *reader monad*. This technique was
-beautifully re-invented by Ben-Avi and Winter (2007) in their paper [A
-modular approach to
-intensionality](http://parles.upf.es/glif/pub/sub11/individual/bena_wint.pdf),
-though without explicitly using monads.
-
-All of the code in the discussion below can be found here: [[intensionality-monad.ml]].
-To run it, download the file, start OCaml, and say
-
- # #use "intensionality-monad.ml";;
-
-Note the extra `#` attached to the directive `use`.
-
The traditional solution to the problem sketched above is to allow
sentences to denote a function from worlds to truth values, what
Montague called an intension. So if `s` is the type of possible