1 Expressives such as "damn" have side effects that don't affect the
2 at-issue value of the sentence in which they occur. What this claim
3 says is unpacked at some length here: <http://tinyurl.com/cbarker/salt/interaction/salt.pdf>.
5 In brief, "The man read the damn book" means the same thing as "The
6 man read the book" as far as what must be the case in the world for
7 the sentence to be true. However, the sentence with the "damn" in it
8 in addition conveys the claim that something about the described
9 situtation is not as it should be. (The person who is committed to
10 that claim is whoever utters the sentence.)
12 So we need a way of evaluating sentences that allows "damn" to launch
13 a side effect without affecting the truth conditions of the sentence
16 Furthermore, we don't want to change the meaning of "the", "man",
17 "read", or "book"---those elements are completely innocent, and
18 shouldn't be burdened with helping compute affective content.
22 What we did in Monday's seminar
23 ===============================
25 We start with a simulation of semantic composition:
27 (cons (cons 'the 'man)
32 That evaluates to nested structure of pairs, that Scheme displays as:
34 '((the . man) . (read . (the . book)))
36 If you try it yourself, you may see instead:
38 '((the . man) read the . book)
40 This is shorthand for the same thing. Just trust me on that.
45 `(cons M N)` is a request to build an ordered pair out of the values M and N.
46 Scheme displays that pair as `'(M . N)` You can't write `(M . N)` yourself and expect Scheme to understand that you're talking about this pair. If you tried, to, Scheme would think you're trying to apply the function M to some arguments, which you're not, and also
47 Scheme would be confused by what argument the `.` is supposed to be. So, you say:
51 and that evaluates to an ordered pair, and Scheme displays that ordered pair as
55 You *can* write `'(M . N)` (with the prefixed single quote), and Scheme will understand you then. However, we're going to be using that same single quote prefix to do something else in a moment, and I don't want now to explain how these uses are related. So we'll write out `(cons M N)` longhand, and we'll leave the `'(M . N)` notation to Scheme for displaying the pair we built.
57 There is an underlying reason why parentheses are used both when displaying the ordered pair, and also to mean "apply this function to these arguments." However, at this point, you may well see this as a confusing overloading of parentheses to fill different syntactic roles.
59 Now what about the elements of our ordered pairs. Why do we say `(cons 'the 'man)`. Why are those single quotes there? Well, if you just said `(cons the man)`, Scheme would understand `the` and `man` to be variables, and it would complain that you hadn't bound these variables to any values. We don't want to build an ordered pair out of the values possessed by variables `the` and `man`. Instead, we want to just make up some primitive value THE to stand for the meaning of an object-language determiner, and some primitive value MAN to stand for the meaning of an object-language noun phrase. The notation `'the` is Scheme's way of designating a primitive atomic value. Note there is no closing single quote, only a prefixed one. Scheme calls these primitive atomic values "symbols." That term is a bit misleading, because the symbol `'the` is not the same as the variable `the`. Neither is it the same as what's called the string `"the"`. The latter is a structured value, composed out of three character values. The symbol `'the`, on the other hand, is an atomic value. It has no parts. (The notation the programmer uses to designate this atomic value has four characters, but the value designated itself has no parts.) If you think this is all somewhat confusing, you're right. It gets easier with practice.
61 `'the` can also be written `(quote the)`. This is even more confusing, because here the `the` is not interpreted as a variable. (Try `(let* ((the 3)) (quote the))`.) If you come across `(quote the)`, just read it as a verbose (and perhaps misleading) way of writing `'the`, not as the application of any function to any value.
63 Okay, so what we've done is just create a bunch of new atomic values `'the`, `'man`, and so on. Scheme doesn't know how to do much with these. It knows for instance that `'the` is the same value as `'the` and a different value than `'man`. But it doesn't know much more than that. That's all we need or want here.
65 And we built a tree out of those values, representing the tree by a nested structure of pairs of leaf-labels.
67 The program we submitted to Scheme:
69 (cons (cons 'the 'man)
74 evaluates to the nested structure of pairs that Scheme displays as:
76 '((the . man) . (read . (the . book)))
78 ---or as an equivalent shorthand. And although there aren't `'`s prefixed to each of the elements of this nested structure, those elements are still the `'the`, `'man` and so on primitive atomic values that we specified. Not the values (if any) possessed by some variables `the`, `man`, and so on.
80 We can think of this nested structure of pairs as the tree:
91 meaning of meaning of meaning of \
92 "the" "man" "read" / \
99 Okay, let's get back to "damn."
101 We start by defining `damn` as a "thunk" that when applied to zero arguments returns a trivial adjectival meaning, which we'll designate with the primitive symbol `'id`.
106 Remember, in Scheme you can have functions that take one value, and also functions that take two values, and also functions that take zero values. The last ones are called "thunks." The thunk is not identical to the value it returns. For instance:
110 is a thunk that returns the integer 3. If we bind the variable `t` to that thunk, then `t` is a function (Scheme will display it as `#<procedure>`)
111 not an integer. Whereas `(t)` is an integer not a function.
113 There's no reason yet on hand for us to make `damn` be a thunk. For present purposes, we could also just define `damn` to be the symbol `'id`. But what we're going to go on to do does require us to make `damn` be a thunk. The reason for that is to postpone the evaluation of some expressions until the continuations we want to operate on are in place. So for uniformity we're going to make `damn` be a thunk right from the beginning.
115 As we said, `damn` starts as a thunk that returns a trivial adjectival meaning `'id`:
117 (define damn (lambda () 'id))
121 (cons (cons 'the 'man)
129 '((the . man) . (read . (the . (id . book))))
131 ---or an equivalent shorthand. (I'm now going to stop saying this.)
134 How to get some affective meaning into damn?
135 --------------------------------------------
140 (define damn (lambda () 'bad))
144 (cons (cons 'the 'man)
152 '((the . man) . (read . (the . (bad . book))))
154 Which is not quite what we're looking for. We don't want to contribute the normal adjectival meaning of "bad" to the proposition asserted. Instead we want badness to be a side-issue linguistic contribution. We might try:
156 (define damn (lambda () (cons 'side-effect 'bad)))
160 '((the . man) . (read . (the . ((side-effect . bad) . book))))
162 and we said at the outset that the context `(the . (<> . book))` shouldn't need to know how to interact with affective meanings. That's precisely the problem we're trying to solve.
165 Let's use continuations
166 -----------------------
168 A promising way to handle this is with **continuations**, which you will get much more familiar with as this seminar progresses. Don't worry about not understanding what's going on quite yet. This is just an advertisement that's supposed to provoke your imagination.
170 Chris and others have applied the apparatus of continuations to the analysis of expressives in the paper cited at the top. For a simple in-class demonstration, here's what we tried to do.
172 (call/cc (lambda (k) ...))
174 is Scheme's way of saying:
176 > bind the continuation of this complex expression to `k` and evaluate the `...`
179 So now we define `damn` like this:
181 (define damn (lambda () (call/cc (lambda (k) (print "bad") (k 'id)))))
183 In other words, `damn` is a thunk. When that thunk is applied---we evaluate `(damn)`---we capture the pending future of that application and bind that to `k`. Then we print "bad" and supply the argument `'id` to `k`. This last step means we go on evaluating the pending future as if `(damn)` had simply returned `'id`.
185 What happens then when we evaluate:
187 (cons (cons 'the 'man)
193 We get something like this:
196 <strong>"bad"</strong> '((the . man) . (read . (the . (id . book))))
199 Yay! The affective meaning has jumped out of the compositional evaluation of the main sentence, and the context `(the . (<> . book))` only has to deal with the trivial adjectival meaning `'id`.
205 As came out in discussion, the `print` we're using here already constitutes a kind of side-effect mechanism of its own. If you say:
207 (define three-thunk (lambda () (print "hi") 3))
209 and then ask for the evaluation of:
211 (+ (+ 2 (three-thunk)) 1)
213 you'll see something like:
216 <strong>"hi"</strong> 6
219 In other words, the printing of "hi" already happens on the side, outside of the main evaluation. Continuations don't need to be explicitly invoked.
221 So the demonstration we tried in class was pedagogically flawed. It didn't properly display how continuations are a minimally effective apparatus for representing affective meaning. In fact, continuations *were* still doing the work, but it wasn't the explicit continuations we were writing out for you. It was instead continuations implicit in the `print` operation.
223 So a better demonstration would do without any device like `print` that already incorporates continuations implicitly. Any continuation-manipulation should be fully explicit.
229 Instead of representing the side-issue affective contribution by printing "bad", let's instead try to build a pair of side-effect contributions and at-issue assertion. Then what we want would be something like:
231 '((side-effect . bad) . ((the . man) . (read . (the . (id . book)))))
233 Only we want to get this from the evaluation of:
235 (cons (cons 'the 'man)
241 where `(damn)` doesn't have widest scope. And we don't want to have to recruit all the other semantic material into accepting and passing along a possible affective argument.
245 It's not immediately clear how to do it with "undelimited" continuations, of the sort captured by `call/cc`. This is the natural first thing to try:
248 (define damn (lambda () (call/cc (lambda (k) (cons (cons 'side-effect 'bad) (k 'id))))))
251 The idea here is we capture the continuation that the thunk `(damn)` has when it gets evaluated. This continuation is bound to the variable `k`. We supply `'id` as an argument to that continuation. When the main, at-issue tree is all built, then we return a pair `((side-effect bad) AT-ISSUE-TREE)`.
253 However, this doesn't work. The reason is that an undelimited continuation represents the future of the evaluation of `(damn)` *until the end of the computation*. So when `'id` is supplied to `k`, we go back to building the at-issue tree until we're finished *and that's the end of the computation*. We never get to go back and evaluate the context `(cons (cons 'side-effect 'bad) <>)`.
256 With undelimited continuations
257 ------------------------------
259 The straightforward way to fix this is to use, not undelimited continuations, but instead a more powerful apparatus called "delimited continuations." These too will be explained in due course, don't expect to understand all this now.
261 A delimited continuation is captured not by using `call/cc`, but instead by using a variety of other operators. We'll use the operator `shift`. This substitutes for `call/cc`. The syntax in Scheme is slightly different. Whereas we wrote:
263 (call/cc (lambda (k) ...))
269 but the behavior is the same. It's just that now our continuation doesn't stretch until the end of the computation, but only up to some specified limit. The limit of the continuation is specified using the syntax:
273 This is a kind of continuation-scope-marker. There are some interesting default behaviors if you don't explicitly specify where the limits are. But we'll be fully explicit here.
275 If a block `...` never invokes a shift, then `(reset ...)` will evaluate just the same as `...`. So for uniformity, we can designate our continuation-scopes even on computations that don't capture and manipulate continuations.
277 Going back to the beginning, then. We start with:
279 (define damn (lambda () 'id))
283 (reset (cons (cons 'the 'man)
289 Remember, the reset isn't actually *doing* anything. It's not a function that's taking the other material as an argument. It's instead a scope-marker. Here it's not even needed (and in fact in the interactive interpreter, it wouldn't even be needed when we invoke continuations, because of the default position it takes). But we're inserting it to be explicit and uniform.
291 Evaluating that gives us:
293 '((the . man) . (read . (the . (id . book))))
296 Now to pair that with an affective side-issue content, we'd instead define `damn` as:
298 (require racket/control) ; this tells Scheme to let us use shift and reset
299 (define damn (lambda () (shift k (cons (cons 'side-effect 'bad) (k 'id)))))
303 (reset (cons (cons 'the 'man)
311 '((side-effect bad) ((the . man) . (read . (the . (id . book)))))
313 So that's the straightforward way of repairing the strategy we used in class, without using `print`. We also have to switch to using delimited continuations.
319 Ken Shan pointed out a lovely way to get to the same end-point still using only undelimited continuations (`call/cc`).
322 ; An ordered pair whose first component is the assertion
323 ; operator, a unary function, and whose second component
324 ; is the meaning of "damn", a thunk.
327 (lambda () (k (cons (lambda (p) (cons (cons 'side-effect 'bad) p))
328 (lambda () 'id)))))))))
329 (let ((assert (car pragma)) ; this binds assert to the first element of the pair pragma
330 (damn (cdr pragma))) ; this binds damn to the second element of the pair pragma
331 (assert (cons (cons 'the 'student) (cons 'read (cons 'the (cons (damn) 'book)))))))
333 We won't do much to explain this. We'll just leave it for you to chew on.
339 ;(define damn (lambda () 'id))
340 (define damn (lambda () (call/cc (lambda (k)
342 (print "Something's bad")
346 (list (list 'the (list (damn) 'man))
348 (list 'the (list (damn) 'book))))
355 (require racket/control)
357 (define damn0 (lambda ()
360 (define damn1 (lambda ()
361 (cons '("side effect" bad)
364 (define damn2 (lambda () (shift k
365 (cons '("side effect" bad)
368 (define damn3 (lambda () (shift k
370 '("side effect" bad)))))
373 ; Now if we use damn0, our compositional semantics will work OK but
374 ; we don't yet have any affective contribution:
376 (list "main content" 'i (list 'like (list 'the (damn0) 'boy)))
377 ; '("main content" i (like (the id boy)))
380 ; If we use damn1, we've added in the affective side effect:
382 (list "main content" 'i (list 'like (list 'the (damn1) 'boy)))
383 ; '("main content" i (like (the (("side effect" bad) . id) boy)))
385 ; However, the context (list 'the <> 'boy) is now being asked to operate
386 ; on an element (("side effect" bad) . id), and it may complain it doesn't
387 ; know what that is. It knows how to use 'id to get (list 'the 'id 'boy),
388 ; and how to use 'bad to get (list 'the 'bad 'boy), but we're supposed to
389 ; have something different here.
391 ; To get what we want we need to use (delimited) continuations:
392 (reset (list "main content" 'i (list 'like (list 'the (damn2) 'boy))))
393 ; '(("side effect" bad) ("main content" i (like (the id boy))))
395 ; or to get the side effect at the end:
397 (reset (list "main content" 'i (list 'like (list 'the (damn3) 'boy))))
398 ; '(("main content" i (like (the id boy))) ("side effect" bad))
400 ; If you're working in the interactive interpreter, the outermost "reset" here
401 ; is already in its default position, so it doesn't need to be explicitly
404 (list "main content" 'i (list 'like (list 'the (damn2) 'boy)))
405 ; '(("side effect" bad) ("main content" i (like (the id boy))))
407 ; However, if you're executing this as a file, you would need to include explicit resets.
411 ; Instead of using reset/shift you could use an element like "print" in
412 ; building the side effect, as we did in class. Here you wouldn't require an
413 ; explicit continuation, but as Chris said, that's because "print" already
414 ; represents an implicit continuation.
416 (define damn4 (lambda () (begin (print "bad") 'id)))
417 (list "main content" 'i (list 'like (list 'the (damn4) 'boy)))
418 ; "bad"'("main content" i (like (the id boy)))