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]]; [[Intensionality Monad]]
61 > Topics: Version 4 lists, Monads in Category Theory
65 See [below](#installing) for how to get the programming languages running on your computer.
67 * Links for help [[learning Scheme]]
69 * Links for help [[learning OCaml]]
72 ##[[Offsite Reading]]##
74 There's lots of links here already to tutorials and encyclopedia entries about many of the notions we'll be dealing with.
80 The goal of this seminar is to introduce concepts and techniques from
81 theoretical computer science and show how they can provide insight
82 into established philosophical and linguistic problems.
84 This is not a seminar about any particular technology or software.
85 Rather, it's about a variety of conceptual/logical ideas that have been
86 developed in computer science and that linguists and philosophers ought to
87 know, or may already be unknowingly trying to reinvent.
89 Philosphers and linguists tend to reuse the same familiar tools in
90 ever more (sometime spectacularly) creative ways. But when your only
91 hammer is classical logic, every problem looks like modus ponens. In
92 contrast, computer scientists have invested considerable ingenuity in
93 studying tool design, and have made remarkable progress.
95 "Why shouldn't I reinvent some idea X for myself? It's intellectually
96 rewarding!" Yes it is, but it also takes time you might have better
97 spent elsewhere. After all, you can get anywhere you want to go by walking, but you can
98 accomplish more with a combination of walking and strategic subway
101 More importantly, the idiosyncrasies of your particular
102 implementation may obscure what's fundamental to the idea you're
103 working with. Your implementation may be buggy in corner cases you
104 didn't think of; it may be incomplete and not trivial to generalize; its
105 connection to existing literature and neighboring issues may go
106 unnoticed. For all these reasons you're better off understanding the
109 The theoretical tools we'll be introducing aren't very familiar to
110 everyday programmers, but they are prominent in academic computer science,
111 especially in the fields of functional programming and type theory.
113 Of necessity, this course will lay a lot of logical groundwork. But throughout
114 we'll be aiming to mix that groundwork with real cases
115 in our home subjects where these tools play central roles. Our aim for the
116 course is to enable you to make these tools your own; to have enough
117 understanding of them to recognize them in use, use them yourself at least
118 in simple ways, and to be able to read more about them when appropriate.
120 Once we get up and running, the central focii of the course will be
121 **continuations**, **types**, and **monads**. One of the on-going themes will
122 concern evaluation order and issues about how computations (inferences,
123 derivations) unfold in (for instance) time. The key analytic technique is to
124 form a static, order-independent model of a dynamic process. We'll be
125 discussing this in much more detail as the course proceeds.
127 The logical systems we'll be looking at include:
129 * the pure/untyped lambda calculus
130 * combinatorial logic
131 * the simply-typed lambda calculus
132 * polymorphic types with System F
133 * some discussion of dependent types
134 * if time permits, "indeterministic" or "preemptively parallel" computation and linear logic
139 recursion using the Y-combinator
140 evaluation-order stratgies
141 normalizing properties
142 the Curry-Howard isomorphism(s)
143 monads in category theory and computation
146 ## Who Can Participate? ##
148 The course will not presume previous experience with programming. We
149 will, however, discuss concepts embodied in specific programming
150 languages, and we will encourage experimentation with running,
151 modifying, and writing computer programs.
153 The course will not presume lots of mathematical or logical background, either.
154 However, it will demand a certain amount of comfort working with such material; as a result,
155 it will not be especially well-suited to be a first graduate-level course
156 in formal semantics or philosophy of language. If you have concerns about your
157 background, come discuss them with us.
159 This class will count as satisfying the logic requirement for Philosophy
160 PhD students; however if this would be your first or only serious
161 engagement with graduate-level formal work you should consider
162 carefully, and must discuss with us, (1) whether you'll be adequately
163 prepared for this course, and (2) whether you'd be better served by
164 taking a logic course (at a neighboring department, or at NYU next year)
165 with a more canonical syllabus.
168 Faculty and students from outside of NYU Linguistics and Philosophy are welcome
169 to audit, to the extent that this coheres well with the needs of our local
173 ## Recommended Software ##
175 During the course, we'll be encouraging you to try out various things in Scheme
176 and Caml, which are prominent *functional programming languages*. We'll explain
177 what that means during the course.
179 * **Scheme** is one of two major dialects of *Lisp*, which is a large family
180 of programming languages. Scheme
181 is the more clean and minimalistic dialect, and is what's mostly used in
183 Scheme itself has umpteen different "implementations", which share most of
184 their fundamentals, but have slightly different extensions and interact with
185 the operating system differently. One major implementation used to be called
186 PLT Scheme, and has just in the past few weeks changed their name to Racket.
187 This is what we recommend you use. (If you're already using or comfortable with
188 another Scheme implementation, though, there's no compelling reason to switch.)
190 Racket stands to Scheme in something like the relation Firefox stands to HTML.
192 * **Caml** is one of two major dialects of *ML*, which is another large
193 family of programming languages. Caml has only one active implementation,
194 OCaml, developed by the INRIA academic group in France.
196 * Those of you with some programming background may have encountered a third
197 prominent functional programming language, **Haskell**. This is also used a
198 lot in the academic contexts we'll be working through. Its surface syntax
199 differs from Caml, and there are various important things one can do in
200 each of Haskell and Caml that one can't (or can't as easily) do in the
201 other. But these languages also have a lot in common, and if you're
202 familiar with one of them, it's not difficult to move between it and the
205 <a name=installing></a>
206 [[How to get the programming languages running on your computer]]
208 [[Family tree of functional programming languages]]
211 ## Recommended Books ##
213 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.
215 * *An Introduction to Lambda Calculi for Computer Scientists*, by Chris
216 Hankin, currently $17 on
217 [Amazon](http://www.amazon.com/dp/0954300653).
219 * (Another good book covering the same ground as the Hankin book, but
220 more thoroughly, and in a more mathematical style, is *Lambda-Calculus and Combinators:
221 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
222 both the Hankin book and this book, you'll notice the authors made some different
223 terminological/notational choices. At first, this makes comprehension slightly slower,
224 but in the long run it's helpful because it makes the arbitrariness of those choices more salient.)
226 * (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.)
228 * *The Little Schemer, Fourth Edition*, by Daniel P. Friedman and Matthias
229 Felleisen, currently $23 on [Amazon](http://www.amazon.com/exec/obidos/ASIN/0262560992).
230 This is a classic text introducing the gentle art of programming, using the
231 functional programming language Scheme. Many people love this book, but it has
232 an unusual dialog format that is not to everybody's taste. **Of particular
233 interest for this course** is the explanation of the Y combinator, available as
234 a free sample chapter [at the MIT Press web page for the
235 book](http://www.ccs.neu.edu/home/matthias/BTLS/).
237 * *The Seasoned Schemer*, also by Daniel P. Friedman and Matthias Felleisen, currently $28
238 on [Amazon](http://www.amazon.com/Seasoned-Schemer-Daniel-P-Friedman/dp/026256100X)
240 * *The Little MLer*, by Matthias Felleisen and Daniel P. Friedman, currently $27
241 on [Amazon](http://www.amazon.com/Little-MLer-Matthias-Felleisen/dp/026256114X).
242 This covers some of the same introductory ground as The Little Schemer, but
243 this time in ML. It uses another dialect of ML (called SML), instead of OCaml, but there are only
244 superficial syntactic differences between these languages. [Here's a translation
245 manual between them](http://www.mpi-sws.org/~rossberg/sml-vs-ocaml.html).
251 All wikis are supposed to have a [[SandBox]], so this one does too.
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