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" and Philosophy calls it "G83.2296"
6 The seminar meets in spring 2015 on Thursdays from 4 until a bit before 7 (with a short break in the middle), in
7 the Linguistics building at 10 Washington Place, in room 103 (front of the first floor).
10 One student session will be held every Wednesday from 3-4 on the
11 fourth floor at 10 Washington Place.
17 This wiki will be undergoing lots of changes throughout the semester, and particularly in these first few days as we get it set up, migrate over some of the content from the previous time
18 we taught this course, and iron out various technical wrinkles. Please be patient.
20 If you've eager to learn, though, you don't have to wait on us to be ready to serve you. You can go look at the [archived first version](http://lambda1.jimpryor.net) of this course. Just keep in mind that
21 the text and links there haven't been updated.
23 As we mentioned in class, if you're following the course and would like to be emailed occasionally, send an email to <mailto:jim.pryor@nyu.edu>, saying "lambda" in the subject line. Most often, we will just post announcements to this website, rather than emailing you. But occasionally an email might be more appropriate.
25 As we mentioned in class, we're also going to schedule a session to discuss the weekly homeworks. If you'd like to participate in this, please complete [this Doodle poll](http://doodle.com/7xrf4w8xq4i9e5za). It asks when you are available on Tuesdays and Wednesdays.
27 Here is information about [[How to get the programming languages running on your computer]].
32 The goal of this seminar is to introduce concepts and techniques from
33 theoretical computer science and show how they can provide insight
34 into established philosophical and linguistic problems.
36 This is not a seminar about any particular technology or software.
38 Rather, it's about a variety of conceptual/logical ideas that have been
39 developed in computer science and that linguists and philosophers ought to
40 know, or may already be unknowingly trying to reinvent.
42 Philosphers and linguists tend to reuse the same familiar tools in
43 ever more (sometime spectacularly) creative ways. But when your only
44 hammer is classical logic, every problem looks like modus ponens. In
45 contrast, computer scientists have invested considerable ingenuity in
46 studying tool design, and have made remarkable progress.
48 "Why shouldn't I reinvent some idea X for myself? It's intellectually
49 rewarding!" Yes it is, but it also takes time you might have better
50 spent elsewhere. After all, you can get anywhere you want to go by walking, but you can
51 accomplish more with a combination of walking and strategic subway
54 More importantly, the idiosyncrasies of your particular
55 implementation may obscure what's fundamental to the idea you're
56 working with. Your implementation may be buggy in corner cases you
57 didn't think of; it may be incomplete and not trivial to generalize; its
58 connection to existing literature and neighboring issues may go
59 unnoticed. For all these reasons you're better off understanding the
62 The theoretical tools we'll be introducing aren't very familiar to
63 everyday programmers, but they are prominent in academic computer science,
64 especially in the fields of functional programming and type theory.
66 Of necessity, this course will lay a lot of logical groundwork. But throughout
67 we'll be aiming to mix that groundwork with real cases
68 in our home subjects where these tools play central roles.
71 course is to enable you to make these tools your own; to have enough
72 understanding of them to recognize them in use, use them yourself at least
73 in simple ways, and to be able to read more about them when appropriate.
76 Once we get up and running, the central focii of the course will be
77 **continuations**, **types**, and **monads**. One of the on-going themes will
78 concern evaluation order and issues about how computations (inferences,
79 derivations) unfold in (for instance) time. The key analytic technique is to
80 form a static, order-independent model of a dynamic process. We'll be
81 discussing this in much more detail as the course proceeds.
83 The logical systems we'll be looking at include:
85 * the pure/untyped lambda calculus
87 * the simply-typed lambda calculus
88 * polymorphic types with System F
89 * some discussion of dependent types
90 * if time permits, "indeterministic" or "preemptively parallel" computation and linear logic
94 recursion using the Y-combinator
95 evaluation-order stratgies
96 normalizing properties
97 the Curry-Howard isomorphism(s)
98 monads in category theory and computation
101 ## Who Can Participate? ##
103 The course will not presume previous experience with programming. We
104 will, however, discuss concepts embodied in specific programming
105 languages, and we will encourage experimentation with running,
106 modifying, and writing computer programs.
108 The course will not presume lots of mathematical or logical background, either.
109 However, it will demand a certain amount of comfort working with such material; as a result,
110 it will not be especially well-suited to be a first graduate-level course
111 in formal semantics or philosophy of language. If you have concerns about your
112 background, come discuss them with us.
115 This class will count as satisfying the logic requirement for Philosophy
116 PhD students; however if this would be your first or only serious
117 engagement with graduate-level formal work you should consider
118 carefully, and must discuss with us, (1) whether you'll be adequately
119 prepared for this course, and (2) whether you'd be better served by
120 taking a logic course (at a neighboring department, or at NYU next year)
121 with a more canonical syllabus.
124 Faculty and students from outside of NYU Linguistics and Philosophy are welcome
125 to audit, to the extent that this coheres well with the needs of our local
129 ## Recommended Software ##
131 During the course, we'll be encouraging you to try out various things in Scheme
132 and OCaml. Occasionally we will also make remarks about Haskell. All three of these
133 are prominent *functional programming languages*. The term "functional" here means they have
134 a special concern with functions, not just that they aren't broken. But what precisely is
135 meant by "functional" is somewhat fuzzy and even its various precisifications take some
136 time to explain. We'll get clearer on this during the course. Another term used roughly the same as "functional"
137 is "declarative." At a first pass, "functional" or "declarative" programming is primarily focused on complex
138 expressions that get computationally evaluated to some (usually simpler) result. In class I gave the examples
139 of `1+2` (which gets evaluated in arithmetic to 3), `1+2 < 5` (which gets evaluated in arithmetic to 'true), and `1`
140 (which gets evaluated in arithmetic to 1). Also Google search strings, which get evaluated by Google servers to a
143 The dominant contrasting class of programming languages (the great majority of what's used
144 in industry) are called "imperatival" languages, meaning they have more to do with following a sequence of commands (what we
145 called in class "side-effects", though sometimes what they're *alongside* is not that interesting, and all the focus is instead
146 on the effect). Programming languages like C and Python and JavaScript and so on are all of this sort.
148 In fact, nothing that gets marketed as a "programming language" is really completely 100% functional/declarative, and even the
149 imperatival languages will have purely functional fragments (they evaluate `1+2` to 3, also). So these labels are really
150 more about *styles* or *idioms* of programming, and languages like Scheme and OCaml and especially Haskell get called "functional languages" because
151 of the extent to which they emphasize, and are designed around those idioms. Even languages like Python and JavaScript are sometimes
152 described as "more functional" than some other languages. The language C is about as non-functional as you can get.
154 * **Scheme** is one of two major dialects of *Lisp*, which is a large family
155 of programming languages. Scheme
156 is the more clean and minimalistic dialect, and is what's mostly used in
158 Scheme itself has umpteen different "implementations", which share most of
159 their fundamentals, but have slightly different extensions and interact with
160 the operating system differently. One major implementation is called Racket,
161 and that is what we recommend you use. If you're already using or comfortable with
162 another Scheme implementation, though, there's no compelling reason to switch.
164 Racket stands to Scheme in something like the relation Firefox stands to HTML.
166 (Wikipedia on [Lisp](http://en.wikipedia.org/wiki/Lisp_%28programming_language%29),
167 [Scheme](http://en.wikipedia.org/wiki/Scheme_%28programming_language%29),
168 and [Racket](http://en.wikipedia.org/wiki/Racket_%28programming_language%29).)
170 * **Caml** is one of two major dialects of *ML*, which is another large
171 family of programming languages. Caml has only one active "implementation",
172 OCaml, developed by the INRIA academic group in France. Sometimes we may refer to Caml or ML
173 more generally; but you can assume that what we're talking about always works more
174 specifically in OCaml.
176 (Wikipedia on [ML](http://en.wikipedia.org/wiki/ML_%28programming_language%29),
177 [Caml](http://en.wikipedia.org/wiki/Caml),
178 and [OCaml](http://en.wikipedia.org/wiki/OCaml).)
181 * Those of you with some programming background may have encountered a third
182 prominent functional programming language, **Haskell**. This is also used a
183 lot in the academic contexts we'll be working through. Its surface syntax
184 differs from Caml, and there are various important things one can do in
185 each of Haskell and Caml that one can't (or can't as easily) do in the
186 other. But these languages also have a lot in common, and if you're
187 familiar with one of them, it's not difficult to move between it and the
190 (Wikipedia on [Haskell](http://en.wikipedia.org/wiki/Haskell_%28programming_language%29).)
193 <a name=installing></a>
194 [[How to get the programming languages running on your computer]]
197 [[Family tree of functional programming languages]]
199 [[Translating between OCaml Scheme and Haskell]]
201 ## What is Functional Programming? ##
203 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.
205 Read more about the [uptake of Haskell](http://steve-yegge.blogspot.com/2010/12/haskell-researchers-announce-discovery.html) among programmers in the street.
208 ## Recommended Books ##
210 It's not *mandatory* 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. We especially recommend the first three of them.
212 * *An Introduction to Lambda Calculi for Computer Scientists*, by Chris
213 Hankin, currently $18 paperback on
214 [Amazon](http://www.amazon.com/dp/0954300653).
216 * *The Little Schemer, Fourth Edition*, by Daniel P. Friedman and Matthias
217 Felleisen, currently $29 paperback on [Amazon](http://www.amazon.com/exec/obidos/ASIN/0262560992).
218 This is a classic text introducing the gentle art of programming, using the
219 functional programming language Scheme. Many people love this book, but it has
220 an unusual dialog format that is not to everybody's taste. **Of particular
221 interest for this course** is the explanation of the Y combinator, available as
222 a free sample chapter [at the MIT Press web page for the
223 book](http://www.ccs.neu.edu/home/matthias/BTLS/).
225 * *The Seasoned Schemer*, also by Daniel P. Friedman and Matthias Felleisen, currently $29 paperback
226 on [Amazon](http://www.amazon.com/Seasoned-Schemer-Daniel-P-Friedman/dp/026256100X). This is a sequel to The Little Schemer, and it focuses on mutation and continuations in Scheme. We will be covering those topics in the second half of the course.
228 * *The Little MLer*, by Matthias Felleisen and Daniel P. Friedman, currently $31 paperback / $29 kindle
229 on [Amazon](http://www.amazon.com/Little-MLer-Matthias-Felleisen/dp/026256114X).
230 This covers much of the same introductory ground as The Little Schemer, but
231 this time in a dialect of ML. It doesn't use OCaml, the dialect we'll be working with, but instead another dialect of ML called SML. The syntactic differences between these languages is slight.
232 ([Here's a translation manual between them](http://www.mpi-sws.org/~rossberg/sml-vs-ocaml.html).)
233 Still, that does add an extra layer of interpretation, and you might as well just use The Little Schemer instead. Those of you who are already more comfortable with OCaml (or with Haskell) than with Scheme might consider working through this book instead of The Little Schemer; for the rest of you, or those of you who *want* practice with Scheme, go with The Little Schemer.
235 * Another good book covering the same ground as the Hankin book, but
236 more thoroughly, and in a more mathematical style, is *Lambda-Calculus and Combinators:
237 an Introduction*, by J. Roger Hindley and Jonathan P. Seldin, currently $74 hardback / $65 kindle on [Amazon](http://www.amazon.com/dp/0521898854).
238 This book is substantial and though it doesn't presuppose any specific mathematical background knowledge, it will be a good choice only if you're already comfortable reading advanced math textbooks.
239 If you choose to read both the Hankin book and this book, you'll notice the authors made some different
240 terminological/notational choices. At first, this makes comprehension slightly slower,
241 but in the long run it's helpful because it makes the arbitrariness of those choices more salient.
243 * Another good book, covering some of the same ground as the Hankin, and the Hindley & Seldin, but delving deeper into typed lambda calculi, is *Types and Programming Languages*, by Benjamin Pierce, currently $77 hardback / $68 kindle on [Amazon](http://www.amazon.com/dp/0262162091). This book has many examples in OCaml.
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