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).
15 * One student session will be held every Wednesday from 3-4. The other will
16 be arranged to fit the schedule of those who'd like to attend but can't
17 make the Wednesday time. (We first proposed Tuesdays from 11-12, but this
18 time turns out not to be so helpful.) If you're one of the students who
19 wants to meet for Q&A at some other time in the week, let us know.
21 You should see the student sessions as opportunities to clear up lingering
22 issues from material we've discussed, and help get a better footing for what
23 we'll be doing the next week. It would be smart to make a serious start on that
24 week's homework, for instance, before the session.
26 * There is now a [[lambda evaluator]] you can use in your browser (no need to
27 install any software). It can help you check whether your answer to some of the
28 homework questions works correctly.
30 There is also now a [library](/lambda_library) of lambda-calculus
31 arithmetical and list operations, some relatively advanced.
33 An evaluator with the definitions used for homework 3
34 preloaded is available at [[assignment 3 evaluator]].
36 * Henceforth, unless we say otherwise, every homework will be "due" by
37 Sunday morning after the Monday seminar in which we refer to it.
38 (Usually we'll post the assignment shortly before the seminar, but don't
39 rely on this.) However, for every assignment there will be a "grace
40 period" of one further week for you to continue working on it if you
41 have trouble and aren't able to complete the assignment to your
42 satisfaction by the due date. You shouldn't hesitate to talk to us---or
43 each other!---about the assignments when you do have trouble. We don't
44 mind so much if you come across answers to the assignment when browsing
45 the web, or the Little Schemer book, or anywhere. So long as you can
46 reason yourself through the solutions and experience for yourself the
49 We reserve the privilege to ruthlessly require you to
50 explain your solutions in conversations at any point, in section or in
53 You should always *aim* to complete the assignments by the "due" date,
54 as this will fit best with the progress of the seminar. Let's take
55 assignment 3 to be "due" on Sunday Oct 3 (the date of this
56 announcement), but as we announced last week in seminar, you can take up
57 until this coming Sunday to complete it. If you need to. Try to complete
58 it, and get assistance completing it if you need it, sooner.
60 * We'll shortly be posting another assignment, assignment 4, which will be
61 "due" on the Sunday before our next seminar. That is, on Sunday Oct 17.
62 (There's no seminar on Monday Oct 11.)
64 The assignments will tend to be quite challenging. Again, you should by
65 all means talk amongst yourselves, and to us, about strategies and
66 questions that come up when working through them.
68 We will not always be able to predict accurately which problems are
69 easy and which are hard. If we misjudge, and choose a problem that is
70 too hard for you to complete to your own satisfaction, it is still
71 very much worthwhile (and very much appreciated) if you would explain
72 what is difficult, what you tried, why what you tried didn't work, and
73 what you think you need in order to solve the problem.
78 To play around with a **typed lambda calculus**, which we'll look at later
79 in the course, have a look at the [Penn Lambda Calculator](http://www.ling.upenn.edu/lambda/).
80 This requires installing Java, but provides a number of tools for evaluating
81 lambda expressions and other linguistic forms. (Mac users will most likely
82 already have Java installed.)
86 ## Lecture Notes and Assignments ##
88 (13 Sept) Lecture notes for [[Week1]]; [[Assignment1]].
90 > Topics: [[Applications]], including [[Damn]]; Basics of Lambda Calculus; Comparing Different Languages
92 (20 Sept) Lecture notes for [[Week2]]; [[Assignment2]].
94 > Topics: Reduction and Convertibility; Combinators; Evaluation Strategies and Normalization; Decidability; [[Lists and Numbers]]
96 (27 Sept) Lecture notes for [[Week3]]; [[Assignment3]];
97 an evaluator with the definitions used for homework 3
98 preloaded is available at [[assignment 3 evaluator]].
100 > Topics: [[Evaluation Order]]; Recursion with Fixed Point Combinators
102 (4 Oct) Lecture notes for [[Week4]]; Assignment4
104 > Topics: More on Fixed Points; Sets; Aborting List Traversals; [[Implementing Trees]]
107 (18 Oct) Lecture notes for Week 5
109 > Topics: Types, Polymorphism
113 [Advanced Lambda Calculus Topics](/advanced lambda)
116 ##[[Offsite Reading]]##
118 There's lots of links here already to tutorials and encyclopedia entries about many of the notions we'll be dealing with.
122 ## Course Overview ##
124 The goal of this seminar is to introduce concepts and techniques from
125 theoretical computer science and show how they can provide insight
126 into established philosophical and linguistic problems.
128 This is not a seminar about any particular technology or software.
129 Rather, it's about a variety of conceptual/logical ideas that have been
130 developed in computer science and that linguists and philosophers ought to
131 know, or may already be unknowingly trying to reinvent.
133 Philosphers and linguists tend to reuse the same familiar tools in
134 ever more (sometime spectacularly) creative ways. But when your only
135 hammer is classical logic, every problem looks like modus ponens. In
136 contrast, computer scientists have invested considerable ingenuity in
137 studying tool design, and have made remarkable progress.
139 "Why shouldn't I reinvent some idea X for myself? It's intellectually
140 rewarding!" Yes it is, but it also takes time you might have better
141 spent elsewhere. After all, you can get anywhere you want to go by walking, but you can
142 accomplish more with a combination of walking and strategic subway
145 More importantly, the idiosyncrasies of your particular
146 implementation may obscure what's fundamental to the idea you're
147 working with. Your implementation may be buggy in corner cases you
148 didn't think of; it may be incomplete and not trivial to generalize; its
149 connection to existing literature and neighboring issues may go
150 unnoticed. For all these reasons you're better off understanding the
153 The theoretical tools we'll be introducing aren't very familiar to
154 everyday programmers, but they are prominent in academic computer science,
155 especially in the fields of functional programming and type theory.
157 Of necessity, this course will lay a lot of logical groundwork. But throughout
158 we'll be aiming to mix that groundwork with real cases
159 in our home subjects where these tools play central roles. Our aim for the
160 course is to enable you to make these tools your own; to have enough
161 understanding of them to recognize them in use, use them yourself at least
162 in simple ways, and to be able to read more about them when appropriate.
164 Once we get up and running, the central focii of the course will be
165 **continuations**, **types**, and **monads**. One of the on-going themes will
166 concern evaluation order and issues about how computations (inferences,
167 derivations) unfold in (for instance) time. The key analytic technique is to
168 form a static, order-independent model of a dynamic process. We'll be
169 discussing this in much more detail as the course proceeds.
171 The logical systems we'll be looking at include:
173 * the pure/untyped lambda calculus
174 * combinatorial logic
175 * the simply-typed lambda calculus
176 * polymorphic types with System F
177 * some discussion of dependent types
178 * if time permits, "indeterministic" or "preemptively parallel" computation and linear logic
183 recursion using the Y-combinator
184 evaluation-order stratgies
185 normalizing properties
186 the Curry-Howard isomorphism(s)
187 monads in category theory and computation
190 ## Who Can Participate? ##
192 The course will not presume previous experience with programming. We
193 will, however, discuss concepts embodied in specific programming
194 languages, and we will encourage experimentation with running,
195 modifying, and writing computer programs.
197 The course will not presume lots of mathematical or logical background, either.
198 However, it will demand a certain amount of comfort working with such material; as a result,
199 it will not be especially well-suited to be a first graduate-level course
200 in formal semantics or philosophy of language. If you have concerns about your
201 background, come discuss them with us.
203 This class will count as satisfying the logic requirement for Philosophy
204 PhD students; however if this would be your first or only serious
205 engagement with graduate-level formal work you should consider
206 carefully, and must discuss with us, (1) whether you'll be adequately
207 prepared for this course, and (2) whether you'd be better served by
208 taking a logic course (at a neighboring department, or at NYU next year)
209 with a more canonical syllabus.
212 Faculty and students from outside of NYU Linguistics and Philosophy are welcome
213 to audit, to the extent that this coheres well with the needs of our local
217 ## Recommended Software ##
219 During the course, we'll be encouraging you to try out various things in Scheme
220 and Caml, which are prominent *functional programming languages*. We'll explain
221 what that means during the course.
223 * **Scheme** is one of two major dialects of *Lisp*, which is a large family
224 of programming languages. Scheme
225 is the more clean and minimalistic dialect, and is what's mostly used in
227 Scheme itself has umpteen different "implementations", which share most of
228 their fundamentals, but have slightly different extensions and interact with
229 the operating system differently. One major implementation used to be called
230 PLT Scheme, and has just in the past few weeks changed their name to Racket.
231 This is what we recommend you use. (If you're already using or comfortable with
232 another Scheme implementation, though, there's no compelling reason to switch.)
234 Racket stands to Scheme in something like the relation Firefox stands to HTML.
236 * **Caml** is one of two major dialects of *ML*, which is another large
237 family of programming languages. Caml has only one active implementation,
238 OCaml, developed by the INRIA academic group in France.
240 * Those of you with some programming background may have encountered a third
241 prominent functional programming language, **Haskell**. This is also used a
242 lot in the academic contexts we'll be working through. Its surface syntax
243 differs from Caml, and there are various important things one can do in
244 each of Haskell and Caml that one can't (or can't as easily) do in the
245 other. But these languages also have a lot in common, and if you're
246 familiar with one of them, it's not difficult to move between it and the
249 [[How to get the programming languages running on your computer]]
251 [[Family tree of functional programming languages]]
254 ## Recommended Books ##
256 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.
258 * *An Introduction to Lambda Calculi for Computer Scientists*, by Chris
259 Hankin, currently $17 on
260 [Amazon](http://www.amazon.com/Introduction-Lambda-Calculi-Computer-Scientists/dp/0954300653).
262 * (Another good book covering the same ground as the Hankin book, but
263 more thoroughly, and in a more mathematical style, is *Lambda-Calculus and Combinators:
264 an Introduction*, by J. Roger Hindley and Jonathan P. Seldin. If you choose to read
265 both the Hankin book and this book, you'll notice the authors made some different
266 terminological/notational choices. At first, this makes comprehension slightly slower,
267 but in the long run it's helpful because it makes the arbitrariness of those choices more salient.)
270 * *The Little Schemer, Fourth Edition*, by Daniel P. Friedman and Matthias
271 Felleisen, currently $23 on [Amazon](http://www.amazon.com/exec/obidos/ASIN/0262560992).
272 This is a classic text introducing the gentle art of programming, using the
273 functional programming language Scheme. Many people love this book, but it has
274 an unusual dialog format that is not to everybody's taste. **Of particular
275 interest for this course** is the explanation of the Y combinator, available as
276 a free sample chapter [at the MIT Press web page for the
277 book](http://www.ccs.neu.edu/home/matthias/BTLS/).
279 * *The Seasoned Schemer*, also by Daniel P. Friedman and Matthias Felleisen, currently $28
280 on [Amazon](http://www.amazon.com/Seasoned-Schemer-Daniel-P-Friedman/dp/026256100X)
282 * *The Little MLer*, by Matthias Felleisen and Daniel P. Friedman, currently $27
283 on [Amazon](http://www.amazon.com/Little-MLer-Matthias-Felleisen/dp/026256114X).
284 This covers some of the same introductory ground as The Little Schemer, but
285 this time in ML. It uses another dialect of ML (called SML), instead of OCaml, but there are only
286 superficial syntactic differences between these languages. [Here's a translation
287 manual between them](http://www.mpi-sws.org/~rossberg/sml-vs-ocaml.html).
293 All wikis are supposed to have a [[SandBox]], so this one does too.
295 This wiki is powered by [[ikiwiki]].