Jacobson as a monad

diff --git a/week8.mdwn b/week8.mdwn
index 4388e44..7f42092 100644 (file)
--- a/week8.mdwn
+++ b/week8.mdwn
@@ -11,7 +11,9 @@ positions.  The system does not make use of assignment functions or
 variables.  We'll see that from the point of view of our discussion of
 monads, Jacobson's system is essentially a reader monad in which the
 assignment function threaded through the computation is limited to at
 variables.  We'll see that from the point of view of our discussion of
 monads, Jacobson's system is essentially a reader monad in which the
 assignment function threaded through the computation is limited to at

-most one assignment.
+most one assignment.  More specifically, Jacobson's geach combinator
+*g* is exactly our `lift` operator, and her binding combinator *z* is
+exactly our `bind` with the arguments reversed!

 
 Jacobson's system contains two main combinators, *g* and *z*.  She
 calls *g* the Geach rule, and *z* effects binding.  (There is a third
 
 Jacobson's system contains two main combinators, *g* and *z*.  She
 calls *g* the Geach rule, and *z* effects binding.  (There is a third


@@ -156,3 +158,15 @@ Jacobson's variable-free semantics is essentially a reader monad.
 
 One of Jacobson's main points survives: restricting the reader monad
 to a single-value environment eliminates the need for variable names.
 
 One of Jacobson's main points survives: restricting the reader monad
 to a single-value environment eliminates the need for variable names.

+
+It requires some cleverness to use the link monad to bind more than
+one variable at a time.  Whereas in the standard reader monad a single
+environment can record any number of variable assignments, because
+Jacobson's monad only tracks a single dependency, binding more than
+one pronoun requires layering the monad, so that intermediate regions
+of the computation will be functors inside of a link monad box inside
+another link monad box, and so on.  
+
+[Give details of the readings of *Everyone said someone thinks that he
+likes her*.  Jacobson needs to add a variant of g; is it necessary to 
+write a link swap that reverses the nesting of the monad boxes?]