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 is 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."
6 The seminar meets on Mondays from 4-6, in
7 the Linguistics building at 10 Washington Place, in room 104 (back of the first floor).
8 One student session will be held every Wednesday from 3-4 on the
9 fourth floor at 10 Washington Place.
11 Here is $some^2 x^{e \pi} + 3y$ math, and $$here_{is} some + more$$ End of math.
12 Except I want to add this: $\frac{-b\pm\sqrt{b^2-4ac}}{2a\pi^i}$ Okay now I'm finished.
20 print "hello, world\n"
40 * This is the time of the semester when some people start slipping
41 behind with the homework. Don't.
44 * We've added a page on [[Translating between OCaml Scheme and Haskell]]
46 * We've added some [commentary](/hints/assignment_6_commentary) on some common issues in your solutions to [[Assignment6]].
48 * We've added a [[Monad Library]] for OCaml.
50 * We've posted a [[State Monad Tutorial]].
52 [[Older Announcements]]
54 ##[[Lambda Evaluator]]##
56 Usable in your browser. It can help you check whether your answer to some of
57 the homework questions works correctly.
59 There is also now a [library](/lambda_library) of lambda-calculus
60 arithmetical and list operations, some relatively advanced.
65 ## Lecture Notes and Assignments ##
67 (13 Sept) Lecture notes for [[Week1]]; [[Assignment1]].
69 > Topics: [[Applications]], including [[Damn]]; Basics of Lambda Calculus; Comparing Different Languages
71 (20 Sept) Lecture notes for [[Week2]]; [[Assignment2]].
73 > Topics: Reduction and Convertibility; Combinators; Evaluation Strategies and Normalization; Decidability; [[Lists and Numbers]]
75 (27 Sept) Lecture notes for [[Week3]]; [[Assignment3]];
76 an evaluator with the definitions used for homework 3
77 preloaded is available at [[assignment 3 evaluator]].
79 > Topics: [[Evaluation Order]]; Recursion with Fixed Point Combinators
81 (4 Oct) Lecture notes for [[Week4]]; [[Assignment4]].
83 > Topics: More on Fixed Points; Sets; Aborting List Traversals; [[Implementing Trees]]
86 (18 Oct, 25 Oct) Lecture notes for [[Week5]] and [[Week6]]; [[Assignment5]].
88 > Topics: Types, Polymorphism, Unit and Bottom
90 (1 Nov) Lecture notes for [[Week7]]; [[Assignment6]].
92 > Topics: Monads; [[Reader Monad for Variable Binding]]; [[Reader Monad for Intensionality]]
94 (8 Nov) Lecture notes for [[Week8]].
96 > Topics: Reader Monad for Jacobson's Variable-Free Semantics
98 (15 Nov) Lecture notes for [[Week9]]; [[Assignment7]]. Everyone auditing in the class is encouraged to do this assignment, or at least work through the substantial "hints".
100 > Topics: Mutable Variables; Passing by Reference; [[State Monad Tutorial]] (added recently)
102 (22 Nov) Lecture notes for [[Week10]]
104 > Topics: Calculator Improvements, including mutation
106 (30 Nov) Lecture notes for [[Week11]]; [[Assignment8]].
108 > Topics: [[Tree and List Zippers]]; [[Coroutines and Aborts]]; [[From List Zippers to Continuations]]
110 (6 Dec) Lecture notes for [[Week12]]; [[Assignment9]].
112 > Topics: [[List Monad as Continuation Monad]]; [[Manipulating Trees with Monads]] (updated); [[Monad Transformers]] (added recently)
114 (13 Dec) Lecture notes for Week13; [[Assignment10]].
116 > Topics: [[CPS and Continuation Operators]]; Curry-Howard
120 > Topics: Version 4 lists, Monads in Category Theory
124 See [below](#installing) for how to get the programming languages running on your computer.
126 * Links for help [[learning Scheme]]
128 * Links for help [[learning OCaml]]
130 * [[Translating between OCaml Scheme and Haskell]]
133 ##[[Offsite Reading]]##
135 There's lots of links here already to tutorials and encyclopedia entries about many of the notions we'll be dealing with.
139 ## Course Overview ##
141 The goal of this seminar is to introduce concepts and techniques from
142 theoretical computer science and show how they can provide insight
143 into established philosophical and linguistic problems.
145 This is not a seminar about any particular technology or software.
146 Rather, it's about a variety of conceptual/logical ideas that have been
147 developed in computer science and that linguists and philosophers ought to
148 know, or may already be unknowingly trying to reinvent.
150 Philosphers and linguists tend to reuse the same familiar tools in
151 ever more (sometime spectacularly) creative ways. But when your only
152 hammer is classical logic, every problem looks like modus ponens. In
153 contrast, computer scientists have invested considerable ingenuity in
154 studying tool design, and have made remarkable progress.
156 "Why shouldn't I reinvent some idea X for myself? It's intellectually
157 rewarding!" Yes it is, but it also takes time you might have better
158 spent elsewhere. After all, you can get anywhere you want to go by walking, but you can
159 accomplish more with a combination of walking and strategic subway
162 More importantly, the idiosyncrasies of your particular
163 implementation may obscure what's fundamental to the idea you're
164 working with. Your implementation may be buggy in corner cases you
165 didn't think of; it may be incomplete and not trivial to generalize; its
166 connection to existing literature and neighboring issues may go
167 unnoticed. For all these reasons you're better off understanding the
170 The theoretical tools we'll be introducing aren't very familiar to
171 everyday programmers, but they are prominent in academic computer science,
172 especially in the fields of functional programming and type theory.
174 Of necessity, this course will lay a lot of logical groundwork. But throughout
175 we'll be aiming to mix that groundwork with real cases
176 in our home subjects where these tools play central roles. Our aim for the
177 course is to enable you to make these tools your own; to have enough
178 understanding of them to recognize them in use, use them yourself at least
179 in simple ways, and to be able to read more about them when appropriate.
181 Once we get up and running, the central focii of the course will be
182 **continuations**, **types**, and **monads**. One of the on-going themes will
183 concern evaluation order and issues about how computations (inferences,
184 derivations) unfold in (for instance) time. The key analytic technique is to
185 form a static, order-independent model of a dynamic process. We'll be
186 discussing this in much more detail as the course proceeds.
188 The logical systems we'll be looking at include:
190 * the pure/untyped lambda calculus
191 * combinatorial logic
192 * the simply-typed lambda calculus
193 * polymorphic types with System F
194 * some discussion of dependent types
195 * if time permits, "indeterministic" or "preemptively parallel" computation and linear logic
200 recursion using the Y-combinator
201 evaluation-order stratgies
202 normalizing properties
203 the Curry-Howard isomorphism(s)
204 monads in category theory and computation
207 ## Who Can Participate? ##
209 The course will not presume previous experience with programming. We
210 will, however, discuss concepts embodied in specific programming
211 languages, and we will encourage experimentation with running,
212 modifying, and writing computer programs.
214 The course will not presume lots of mathematical or logical background, either.
215 However, it will demand a certain amount of comfort working with such material; as a result,
216 it will not be especially well-suited to be a first graduate-level course
217 in formal semantics or philosophy of language. If you have concerns about your
218 background, come discuss them with us.
220 This class will count as satisfying the logic requirement for Philosophy
221 PhD students; however if this would be your first or only serious
222 engagement with graduate-level formal work you should consider
223 carefully, and must discuss with us, (1) whether you'll be adequately
224 prepared for this course, and (2) whether you'd be better served by
225 taking a logic course (at a neighboring department, or at NYU next year)
226 with a more canonical syllabus.
229 Faculty and students from outside of NYU Linguistics and Philosophy are welcome
230 to audit, to the extent that this coheres well with the needs of our local
234 ## Recommended Software ##
236 During the course, we'll be encouraging you to try out various things in Scheme
237 and Caml, which are prominent *functional programming languages*. We'll explain
238 what that means during the course.
240 * **Scheme** is one of two major dialects of *Lisp*, which is a large family
241 of programming languages. Scheme
242 is the more clean and minimalistic dialect, and is what's mostly used in
244 Scheme itself has umpteen different "implementations", which share most of
245 their fundamentals, but have slightly different extensions and interact with
246 the operating system differently. One major implementation used to be called
247 PLT Scheme, and has just in the past few weeks changed their name to Racket.
248 This is what we recommend you use. (If you're already using or comfortable with
249 another Scheme implementation, though, there's no compelling reason to switch.)
251 Racket stands to Scheme in something like the relation Firefox stands to HTML.
253 * **Caml** is one of two major dialects of *ML*, which is another large
254 family of programming languages. Caml has only one active implementation,
255 OCaml, developed by the INRIA academic group in France.
257 * Those of you with some programming background may have encountered a third
258 prominent functional programming language, **Haskell**. This is also used a
259 lot in the academic contexts we'll be working through. Its surface syntax
260 differs from Caml, and there are various important things one can do in
261 each of Haskell and Caml that one can't (or can't as easily) do in the
262 other. But these languages also have a lot in common, and if you're
263 familiar with one of them, it's not difficult to move between it and the
266 <a name=installing></a>
267 [[How to get the programming languages running on your computer]]
269 [[Family tree of functional programming languages]]
271 [[Translating between OCaml Scheme and Haskell]]
273 ## What is Functional Programming? ##
275 Here's a [survey conducted at Microsoft](http://research.microsoft.com/apps/pubs/default.aspx?id=141506) asking programmers what they understand "functional programming" to be. Don't take their responses to be authoritative... this is a just a "man in the street" (seat?) poll.
277 Read more about the [uptake of Haskell](http://steve-yegge.blogspot.com/2010/12/haskell-researchers-announce-discovery.html) among programmers in the street.
280 ## Recommended Books ##
282 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.
284 * *An Introduction to Lambda Calculi for Computer Scientists*, by Chris
285 Hankin, currently $17 on
286 [Amazon](http://www.amazon.com/dp/0954300653).
288 * (Another good book covering the same ground as the Hankin book, but
289 more thoroughly, and in a more mathematical style, is *Lambda-Calculus and Combinators:
290 an Introduction*, by J. Roger Hindley and Jonathan P. Seldin, currently $52 on [Amazon](http://www.amazon.com/dp/0521898854). If you choose to read
291 both the Hankin book and this book, you'll notice the authors made some different
292 terminological/notational choices. At first, this makes comprehension slightly slower,
293 but in the long run it's helpful because it makes the arbitrariness of those choices more salient.)
295 * (Another good book, covering some of the same ground as the previous two, but also delving much deeper into typed lambda calculi, is *Types and Programming Languages*, by Benjamin Pierce, currently $61 on [Amazon](http://www.amazon.com/dp/0262162091). This book has many examples in OCaml.)
297 * *The Little Schemer, Fourth Edition*, by Daniel P. Friedman and Matthias
298 Felleisen, currently $23 on [Amazon](http://www.amazon.com/exec/obidos/ASIN/0262560992).
299 This is a classic text introducing the gentle art of programming, using the
300 functional programming language Scheme. Many people love this book, but it has
301 an unusual dialog format that is not to everybody's taste. **Of particular
302 interest for this course** is the explanation of the Y combinator, available as
303 a free sample chapter [at the MIT Press web page for the
304 book](http://www.ccs.neu.edu/home/matthias/BTLS/).
306 * *The Seasoned Schemer*, also by Daniel P. Friedman and Matthias Felleisen, currently $28
307 on [Amazon](http://www.amazon.com/Seasoned-Schemer-Daniel-P-Friedman/dp/026256100X)
309 * *The Little MLer*, by Matthias Felleisen and Daniel P. Friedman, currently $27
310 on [Amazon](http://www.amazon.com/Little-MLer-Matthias-Felleisen/dp/026256114X).
311 This covers some of the same introductory ground as The Little Schemer, but
312 this time in ML. It uses another dialect of ML (called SML), instead of OCaml, but there are only
313 superficial syntactic differences between these languages. [Here's a translation
314 manual between them](http://www.mpi-sws.org/~rossberg/sml-vs-ocaml.html).
320 All wikis are supposed to have a [[SandBox]], so this one does too.
322 This wiki is powered by [[ikiwiki]].