X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?a=blobdiff_plain;ds=sidebyside;f=week8.mdwn;h=4388e4407626df6f2452663fae7f82d4aeefe003;hb=2f32f675472a4cef4f4d6bf47c8531946a717760;hp=e99e223ab91f6bf1d4bbd350355f0f9ecaeed97c;hpb=adaf5a4a914b56ca7be6c3fce6da8269e1ed23ca;p=lambda.git diff --git a/week8.mdwn b/week8.mdwn index e99e223a..4388e440 100644 --- a/week8.mdwn +++ b/week8.mdwn @@ -15,20 +15,22 @@ most one assignment. Jacobson's system contains two main combinators, *g* and *z*. She calls *g* the Geach rule, and *z* effects binding. (There is a third -combinator, *l*, which we'll make use of to adjust function/argument -order to better match English word order; N.B., though, that -Jacobson's name for this combinator is "lift", but it is different -from the monadic lift discussed in some detail below.) Here is a -typical computation (based closely on email from Simon Charlow, with -beta reduction as performed by the on-line evaluator): +combinator which following Curry and Steedman, I'll call *T*, which +we'll make use of to adjust function/argument order to better match +English word order; N.B., though, that Jacobson's name for this +combinator is "lift", but it is different from the monadic lift +discussed in some detail below.) Here is a typical computation (based +closely on email from Simon Charlow, with beta reduction as performed +by the on-line evaluator):
 ; Analysis of "Everyone_i thinks he_i left"
 let g = \f g x. f (g x) in
 let z = \f g x. f (g x) x in
-let everyone = \P. FORALL x (P x) in
 let he = \x. x in
-everyone ((z thinks) (g left he))
+let everyone = \P. FORALL x (P x) in
+
+everyone (z thinks (g left he))
 
 ~~>  FORALL x (thinks (left x) x)
 
@@ -44,8 +46,8 @@ Second, *g* plays the role of transmitting a binding dependency for an embedded constituent to a containing constituent. If the sentence had been *Everyone_i thinks Bill said he_i left*, there would be an occurrence of *g* in the most deeply embedded clause (*he left*), and -another occurrence of (a variant of) *g* in the next most deeply -embedded clause (*Bill said he left*). +another occurrence of *g* in the next most deeply +embedded constituent (*said he left*), and so on (see below). Third, binding is accomplished by applying *z* not to the element that will (in some pre-theoretic sense) bind the pronoun, here, *everyone*, @@ -136,14 +138,14 @@ the parallel with the reader monad even more by writing a `shift` operator that used `unit` to produce a monadic result, if we wanted to. The monad version of *Everyone_i thinks he_i left*, then (remembering -that `he = fun x -> x`, and that `l a f = f a`) is +that `he = fun x -> x`, and letting `t a f = f a`) is
 everyone (z thinks (g left he))
 
 ~~> forall w (thinks (left w) w)
 
-everyone (z thinks (g (l bill) (g said (g left he))))
+everyone (z thinks (g (t bill) (g said (g left he))))
 
 ~~> forall w (thinks (said (left w) bill) w)