1 # Seminar in Semantics / Philosophy of Language #
3 or: **What Philosophers and Linguists Can Learn From Theoretical Computer Science But Didn't Know To Ask**
5 This course will be co-taught by [Chris Barker](http://homepages.nyu.edu/~cb125/) and [Jim Pryor](http://www.jimpryor.net/). Linguistics calls it "G61.3340-002" and Philosophy calls it "G83.2296-001."
10 * The seminar meets on Mondays from 4-6, in
11 the Linguistics building at 10 Washington Place, in room 104 (back of the first floor).
14 * One student session will be held every Wednesday from 3-4. The other will
15 be arranged to fit the schedule of those who'd like to attend but can't
16 make the Wednesday time. (We first proposed Tuesdays from 11-12, but this
17 time turns out not to be so helpful.) If you're one of the students who
18 wants to meet for Q&A at some other time in the week, let us know.
20 You should see the student sessions as opportunities to clear up lingering
21 issues from material we've discussed, and help get a better footing for what
22 we'll be doing the next week. It would be smart to make a serious start on that
23 week's homework, for instance, before the session.
25 * There is now a [[lambda evaluator]] you can use in your browser (no need to
26 install any software). It can help you check whether your answer to some of the
27 homework questions works correctly.
29 There is also now a [library](/lambda_library) of lambda-calculus
30 arithmetical and list operations, some relatively advanced.
32 An evaluator with the definitions used for homework 3 preloaded is available at [[assignment 3 evaluator]].
34 * Henceforth, unless we say otherwise, every homework will be "due" by
35 Sunday morning after the Monday seminar in which we refer to it.
36 (Usually we'll post the assignment shortly before the seminar, but don't
37 rely on this.) However, for every assignment there will be a "grace
38 period" of one further week for you to continue working on it if you
39 have trouble and aren't able to complete the assignment to your
40 satisfaction by the due date. You shouldn't hesitate to talk to us---or
41 each other!---about the assignments when you do have trouble. We don't
42 mind so much if you come across answers to the assignment when browsing
43 the web, or the Little Schemer book, or anywhere. So long as you can
44 reason yourself through the solutions and experience for yourself the
47 We reserve the privilege to ruthlessly require you to
48 explain your solutions in conversations at any point, in section or in
51 You should always *aim* to complete the assignments by the "due" date,
52 as this will fit best with the progress of the seminar. Let's take
53 assignment 3 to be "due" on Sunday Oct 3 (the date of this
54 announcement), but as we announced last week in seminar, you can take up
55 until this coming Sunday to complete it. If you need to. Try to complete
56 it, and get assistance completing it if you need it, sooner.
58 * We'll shortly be posting another assignment, assignment 4, which will be
59 "due" on the Sunday before our next seminar. That is, on Sunday Oct 17.
60 (There's no seminar this coming Monday.)
62 The assignments will tend to be quite challenging. Again, you should by
63 all means talk amongst yourselves, and to us, about strategies and
64 questions that come up when working through them.
66 We will not always be able to predict accurately which problems are
67 easy and which are hard. If we misjudge, and choose a problem that is
68 too hard for you to complete to your own satisfaction, it is still
69 very much worthwhile (and very much appreciated) if you would explain
70 what is difficult, what you tried, why what you tried didn't work, and
71 what you think you need in order to solve the problem.
75 To play around with a **typed lambda calculus**, which we'll look at later
76 in the course, have a look at the [Penn Lambda Calculator](http://www.ling.upenn.edu/lambda/).
77 This requires installing Java, but provides a number of tools for evaluating
78 lambda expressions and other linguistic forms. (Mac users will most likely
79 already have Java installed.)
83 ## Lecture Notes and Assignments ##
85 (13 Sept) Lecture notes for [[Week1]]; [[Assignment1]].
87 Topics: Applications; Basics of Lambda Calculus; Comparing Different Languages
89 (20 Sept) Lecture notes for [[Week2]]; [[Assignment2]].
91 Topics: Reduction and Convertibility; Combinators; Evaluation Strategies and Normalization; Decidability; Lists and Numbers
93 (27 Sept) Lecture notes for [[Week3]]; [[Assignment3]].
95 Topics: Recursion with Fixed Point Combinators
97 (4 Oct) Lecture notes for Week 4
99 <!-- Introducing the notion of a "continuation", which technique we'll now already have used a few times
105 ##[[Offsite Reading]]##
107 There's lots of links here already to tutorials and encyclopedia entries about many of the notions we'll be dealing with.
111 ## Course Overview ##
113 The goal of this seminar is to introduce concepts and techniques from
114 theoretical computer science and show how they can provide insight
115 into established philosophical and linguistic problems.
117 This is not a seminar about any particular technology or software.
118 Rather, it's about a variety of conceptual/logical ideas that have been
119 developed in computer science and that linguists and philosophers ought to
120 know, or may already be unknowingly trying to reinvent.
122 Philosphers and linguists tend to reuse the same familiar tools in
123 ever more (sometime spectacularly) creative ways. But when your only
124 hammer is classical logic, every problem looks like modus ponens. In
125 contrast, computer scientists have invested considerable ingenuity in
126 studying tool design, and have made remarkable progress.
128 "Why shouldn't I reinvent some idea X for myself? It's intellectually
129 rewarding!" Yes it is, but it also takes time you might have better
130 spent elsewhere. After all, you can get anywhere you want to go by walking, but you can
131 accomplish more with a combination of walking and strategic subway
134 More importantly, the idiosyncrasies of your particular
135 implementation may obscure what's fundamental to the idea you're
136 working with. Your implementation may be buggy in corner cases you
137 didn't think of; it may be incomplete and not trivial to generalize; its
138 connection to existing literature and neighboring issues may go
139 unnoticed. For all these reasons you're better off understanding the
142 The theoretical tools we'll be introducing aren't very familiar to
143 everyday programmers, but they are prominent in academic computer science,
144 especially in the fields of functional programming and type theory.
146 Of necessity, this course will lay a lot of logical groundwork. But throughout
147 we'll be aiming to mix that groundwork with real cases
148 in our home subjects where these tools play central roles. Our aim for the
149 course is to enable you to make these tools your own; to have enough
150 understanding of them to recognize them in use, use them yourself at least
151 in simple ways, and to be able to read more about them when appropriate.
153 Once we get up and running, the central focii of the course will be
154 **continuations**, **types**, and **monads**. One of the on-going themes will
155 concern evaluation order and issues about how computations (inferences,
156 derivations) unfold in (for instance) time. The key analytic technique is to
157 form a static, order-independent model of a dynamic process. We'll be
158 discussing this in much more detail as the course proceeds.
160 The logical systems we'll be looking at include:
162 * the pure/untyped lambda calculus
163 * combinatorial logic
164 * the simply-typed lambda calculus
165 * polymorphic types with System F
166 * some discussion of dependent types
167 * if time permits, "indeterministic" or "preemptively parallel" computation and linear logic
172 recursion using the Y-combinator
173 evaluation-order stratgies
174 normalizing properties
175 the Curry-Howard isomorphism(s)
176 monads in category theory and computation
179 ## Who Can Participate? ##
181 The course will not presume previous experience with programming. We
182 will, however, discuss concepts embodied in specific programming
183 languages, and we will encourage experimentation with running,
184 modifying, and writing computer programs.
186 The course will not presume lots of mathematical or logical background, either.
187 However, it will demand a certain amount of comfort working with such material; as a result,
188 it will not be especially well-suited to be a first graduate-level course
189 in formal semantics or philosophy of language. If you have concerns about your
190 background, come discuss them with us.
192 This class will count as satisfying the logic requirement for Philosophy
193 PhD students; however if this would be your first or only serious
194 engagement with graduate-level formal work you should consider
195 carefully, and must discuss with us, (1) whether you'll be adequately
196 prepared for this course, and (2) whether you'd be better served by
197 taking a logic course (at a neighboring department, or at NYU next year)
198 with a more canonical syllabus.
201 Faculty and students from outside of NYU Linguistics and Philosophy are welcome
202 to audit, to the extent that this coheres well with the needs of our local
206 ## Recommended Software ##
208 During the course, we'll be encouraging you to try out various things in Scheme
209 and Caml, which are prominent *functional programming languages*. We'll explain
210 what that means during the course.
212 * **Scheme** is one of two major dialects of *Lisp*, which is a large family
213 of programming languages. Scheme
214 is the more clean and minimalistic dialect, and is what's mostly used in
216 Scheme itself has umpteen different "implementations", which share most of
217 their fundamentals, but have slightly different extensions and interact with
218 the operating system differently. One major implementation used to be called
219 PLT Scheme, and has just in the past few weeks changed their name to Racket.
220 This is what we recommend you use. (If you're already using or comfortable with
221 another Scheme implementation, though, there's no compelling reason to switch.)
223 Racket stands to Scheme in something like the relation Firefox stands to HTML.
225 * **Caml** is one of two major dialects of *ML*, which is another large
226 family of programming languages. Caml has only one active implementation,
227 OCaml, developed by the INRIA academic group in France.
229 * Those of you with some programming background may have encountered a third
230 prominent functional programming language, **Haskell**. This is also used a
231 lot in the academic contexts we'll be working through. Its surface syntax
232 differs from Caml, and there are various important things one can do in
233 each of Haskell and Caml that one can't (or can't as easily) do in the
234 other. But these languages also have a lot in common, and if you're
235 familiar with one of them, it's not difficult to move between it and the
238 [[How to get the programming languages running on your computer]]
240 [[Family tree of functional programming languages]]
243 ## Recommended Books ##
245 It's not necessary to purchase these for the class. But they are good ways to get a more thorough and solid understanding of some of the more basic conceptual tools we'll be using.
247 * *An Introduction to Lambda Calculi for Computer Scientists*, by Chris
248 Hankin, currently $17 on
249 [Amazon](http://www.amazon.com/Introduction-Lambda-Calculi-Computer-Scientists/dp/0954300653).
251 * (Another good book covering the same ground as the Hankin book, but
252 more thoroughly, and in a more mathematical style, is *Lambda-Calculus and Combinators:
253 an Introduction*, by J. Roger Hindley and Jonathan P. Seldin. If you choose to read
254 both the Hankin book and this book, you'll notice the authors made some different
255 terminological/notational choices. At first, this makes comprehension slightly slower,
256 but in the long run it's helpful because it makes the arbitrariness of those choices more salient.)
259 * *The Little Schemer, Fourth Edition*, by Daniel P. Friedman and Matthias
260 Felleisen, currently $23 on [Amazon](http://www.amazon.com/exec/obidos/ASIN/0262560992).
261 This is a classic text introducing the gentle art of programming, using the
262 functional programming language Scheme. Many people love this book, but it has
263 an unusual dialog format that is not to everybody's taste. **Of particular
264 interest for this course** is the explanation of the Y combinator, available as
265 a free sample chapter [at the MIT Press web page for the
266 book](http://www.ccs.neu.edu/home/matthias/BTLS/).
268 * *The Seasoned Schemer*, also by Daniel P. Friedman and Matthias Felleisen, currently $28
269 on [Amazon](http://www.amazon.com/Seasoned-Schemer-Daniel-P-Friedman/dp/026256100X)
271 * *The Little MLer*, by Matthias Felleisen and Daniel P. Friedman, currently $27
272 on [Amazon](http://www.amazon.com/Little-MLer-Matthias-Felleisen/dp/026256114X).
273 This covers some of the same introductory ground as The Little Schemer, but
274 this time in ML. It uses another dialect of ML (called SML), instead of OCaml, but there are only
275 superficial syntactic differences between these languages. [Here's a translation
276 manual between them](http://www.mpi-sws.org/~rossberg/sml-vs-ocaml.html).
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