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.
13 * This is the time of the semester when some people start slipping
14 behind with the homework. Don't.
16 [[Older Announcements]]
18 ##[[Lambda Evaluator]]##
20 Usable in your browser. It can help you check whether your answer to some of
21 the homework questions works correctly.
23 There is also now a [library](/lambda_library) of lambda-calculus
24 arithmetical and list operations, some relatively advanced.
27 ## Lecture Notes and Assignments ##
29 (13 Sept) Lecture notes for [[Week1]]; [[Assignment1]].
31 > Topics: [[Applications]], including [[Damn]]; Basics of Lambda Calculus; Comparing Different Languages
33 (20 Sept) Lecture notes for [[Week2]]; [[Assignment2]].
35 > Topics: Reduction and Convertibility; Combinators; Evaluation Strategies and Normalization; Decidability; [[Lists and Numbers]]
37 (27 Sept) Lecture notes for [[Week3]]; [[Assignment3]];
38 an evaluator with the definitions used for homework 3
39 preloaded is available at [[assignment 3 evaluator]].
41 > Topics: [[Evaluation Order]]; Recursion with Fixed Point Combinators
43 (4 Oct) Lecture notes for [[Week4]]; [[Assignment4]].
45 > Topics: More on Fixed Points; Sets; Aborting List Traversals; [[Implementing Trees]]
48 (18 Oct, 25 Oct) Lecture notes for [[Week5]] and [[Week6]]; [[Assignment5]].
50 > Topics: Types, Polymorphism, Unit and Bottom
52 (1 Nov) Lecture notes for [[Week7]]; [[Assignment6]].
54 > Topics: Monads; [[Reader Monad for Variable Binding]]; [[Reader Monad for Intensionality]]
56 (8 Nov) Lecture notes for [[Week8]].
58 (15 Nov) Lecture notes are coming; [[Assignment7]] is here.
65 > Topics: Version 4 lists, Monads in Category Theory
69 See [below](#installing) for how to get the programming languages running on your computer.
71 * Links for help [[learning Scheme]]
73 * Links for help [[learning OCaml]]
76 ##[[Offsite Reading]]##
78 There's lots of links here already to tutorials and encyclopedia entries about many of the notions we'll be dealing with.
84 The goal of this seminar is to introduce concepts and techniques from
85 theoretical computer science and show how they can provide insight
86 into established philosophical and linguistic problems.
88 This is not a seminar about any particular technology or software.
89 Rather, it's about a variety of conceptual/logical ideas that have been
90 developed in computer science and that linguists and philosophers ought to
91 know, or may already be unknowingly trying to reinvent.
93 Philosphers and linguists tend to reuse the same familiar tools in
94 ever more (sometime spectacularly) creative ways. But when your only
95 hammer is classical logic, every problem looks like modus ponens. In
96 contrast, computer scientists have invested considerable ingenuity in
97 studying tool design, and have made remarkable progress.
99 "Why shouldn't I reinvent some idea X for myself? It's intellectually
100 rewarding!" Yes it is, but it also takes time you might have better
101 spent elsewhere. After all, you can get anywhere you want to go by walking, but you can
102 accomplish more with a combination of walking and strategic subway
105 More importantly, the idiosyncrasies of your particular
106 implementation may obscure what's fundamental to the idea you're
107 working with. Your implementation may be buggy in corner cases you
108 didn't think of; it may be incomplete and not trivial to generalize; its
109 connection to existing literature and neighboring issues may go
110 unnoticed. For all these reasons you're better off understanding the
113 The theoretical tools we'll be introducing aren't very familiar to
114 everyday programmers, but they are prominent in academic computer science,
115 especially in the fields of functional programming and type theory.
117 Of necessity, this course will lay a lot of logical groundwork. But throughout
118 we'll be aiming to mix that groundwork with real cases
119 in our home subjects where these tools play central roles. Our aim for the
120 course is to enable you to make these tools your own; to have enough
121 understanding of them to recognize them in use, use them yourself at least
122 in simple ways, and to be able to read more about them when appropriate.
124 Once we get up and running, the central focii of the course will be
125 **continuations**, **types**, and **monads**. One of the on-going themes will
126 concern evaluation order and issues about how computations (inferences,
127 derivations) unfold in (for instance) time. The key analytic technique is to
128 form a static, order-independent model of a dynamic process. We'll be
129 discussing this in much more detail as the course proceeds.
131 The logical systems we'll be looking at include:
133 * the pure/untyped lambda calculus
134 * combinatorial logic
135 * the simply-typed lambda calculus
136 * polymorphic types with System F
137 * some discussion of dependent types
138 * if time permits, "indeterministic" or "preemptively parallel" computation and linear logic
143 recursion using the Y-combinator
144 evaluation-order stratgies
145 normalizing properties
146 the Curry-Howard isomorphism(s)
147 monads in category theory and computation
150 ## Who Can Participate? ##
152 The course will not presume previous experience with programming. We
153 will, however, discuss concepts embodied in specific programming
154 languages, and we will encourage experimentation with running,
155 modifying, and writing computer programs.
157 The course will not presume lots of mathematical or logical background, either.
158 However, it will demand a certain amount of comfort working with such material; as a result,
159 it will not be especially well-suited to be a first graduate-level course
160 in formal semantics or philosophy of language. If you have concerns about your
161 background, come discuss them with us.
163 This class will count as satisfying the logic requirement for Philosophy
164 PhD students; however if this would be your first or only serious
165 engagement with graduate-level formal work you should consider
166 carefully, and must discuss with us, (1) whether you'll be adequately
167 prepared for this course, and (2) whether you'd be better served by
168 taking a logic course (at a neighboring department, or at NYU next year)
169 with a more canonical syllabus.
172 Faculty and students from outside of NYU Linguistics and Philosophy are welcome
173 to audit, to the extent that this coheres well with the needs of our local
177 ## Recommended Software ##
179 During the course, we'll be encouraging you to try out various things in Scheme
180 and Caml, which are prominent *functional programming languages*. We'll explain
181 what that means during the course.
183 * **Scheme** is one of two major dialects of *Lisp*, which is a large family
184 of programming languages. Scheme
185 is the more clean and minimalistic dialect, and is what's mostly used in
187 Scheme itself has umpteen different "implementations", which share most of
188 their fundamentals, but have slightly different extensions and interact with
189 the operating system differently. One major implementation used to be called
190 PLT Scheme, and has just in the past few weeks changed their name to Racket.
191 This is what we recommend you use. (If you're already using or comfortable with
192 another Scheme implementation, though, there's no compelling reason to switch.)
194 Racket stands to Scheme in something like the relation Firefox stands to HTML.
196 * **Caml** is one of two major dialects of *ML*, which is another large
197 family of programming languages. Caml has only one active implementation,
198 OCaml, developed by the INRIA academic group in France.
200 * Those of you with some programming background may have encountered a third
201 prominent functional programming language, **Haskell**. This is also used a
202 lot in the academic contexts we'll be working through. Its surface syntax
203 differs from Caml, and there are various important things one can do in
204 each of Haskell and Caml that one can't (or can't as easily) do in the
205 other. But these languages also have a lot in common, and if you're
206 familiar with one of them, it's not difficult to move between it and the
209 <a name=installing></a>
210 [[How to get the programming languages running on your computer]]
212 [[Family tree of functional programming languages]]
215 ## Recommended Books ##
217 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.
219 * *An Introduction to Lambda Calculi for Computer Scientists*, by Chris
220 Hankin, currently $17 on
221 [Amazon](http://www.amazon.com/dp/0954300653).
223 * (Another good book covering the same ground as the Hankin book, but
224 more thoroughly, and in a more mathematical style, is *Lambda-Calculus and Combinators:
225 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
226 both the Hankin book and this book, you'll notice the authors made some different
227 terminological/notational choices. At first, this makes comprehension slightly slower,
228 but in the long run it's helpful because it makes the arbitrariness of those choices more salient.)
230 * (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.)
232 * *The Little Schemer, Fourth Edition*, by Daniel P. Friedman and Matthias
233 Felleisen, currently $23 on [Amazon](http://www.amazon.com/exec/obidos/ASIN/0262560992).
234 This is a classic text introducing the gentle art of programming, using the
235 functional programming language Scheme. Many people love this book, but it has
236 an unusual dialog format that is not to everybody's taste. **Of particular
237 interest for this course** is the explanation of the Y combinator, available as
238 a free sample chapter [at the MIT Press web page for the
239 book](http://www.ccs.neu.edu/home/matthias/BTLS/).
241 * *The Seasoned Schemer*, also by Daniel P. Friedman and Matthias Felleisen, currently $28
242 on [Amazon](http://www.amazon.com/Seasoned-Schemer-Daniel-P-Friedman/dp/026256100X)
244 * *The Little MLer*, by Matthias Felleisen and Daniel P. Friedman, currently $27
245 on [Amazon](http://www.amazon.com/Little-MLer-Matthias-Felleisen/dp/026256114X).
246 This covers some of the same introductory ground as The Little Schemer, but
247 this time in ML. It uses another dialect of ML (called SML), instead of OCaml, but there are only
248 superficial syntactic differences between these languages. [Here's a translation
249 manual between them](http://www.mpi-sws.org/~rossberg/sml-vs-ocaml.html).
255 All wikis are supposed to have a [[SandBox]], so this one does too.
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