or: **What Philosophers and Linguists Can Learn From Theoretical Computer Science But Didn't Know To Ask**
-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"
-The seminar meets in spring 2015 on Thursdays from 4 until a bit before 7 (with a short break in the middle), in
+This course is co-taught by [Chris Barker](http://homepages.nyu.edu/~cb125/) and [Jim Pryor](http://www.jimpryor.net/). Linguistics calls it "LING-GA 3340" and Philosophy calls it "PHIL-GA 2296".
+The seminar meets in spring 2015 on Thursdays from 4 until a bit before 7 (with a short break in the middle), in
the Linguistics building at 10 Washington Place, in room 103 (front of the first floor).
<!--
-One student session will be held every Wednesday from 3-4 on the
-fourth floor at 10 Washington Place.
+One student session will be held every Wednesday from XX-YY at WHERE.
-->
+## [[Index of Content (lecture notes and more)|content]] ##
## Announcements ##
-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
-we taught this course, and iron out various technical wrinkles. Please be patient.
+* 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
+we taught this course, and iron out various technical wrinkles. Please be patient. When you sit down to read the wiki, it's a good idea to always hit "Refresh" in your browser to make sure you're reading the latest additions and refinements of the website. (Sometimes these will be tweaks, other times very substantial. Updates will happen at miscellaneous hours, sometimes many times in a given day.)
-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
-the text and links there haven't been updated.
+ 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
+the text and links there haven't been updated. And/or you can get started on installing the software and ordering some of the books.
-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.
+* 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.
-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.
+* 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.
-Here is information about [[How to get the programming languages running on your computer]].
+<!--
+One student session will be held every Wednesday from XX-YY at WHERE.
+
+For those who'd like to attend the section but can't make the
+Wednesday time: If you're one of the students who
+wants to meet for Q&A at some other time in the week, let us know.
+
+You should see the student sessions as opportunities to clear up lingering
+issues from material we've discussed, and help get a better footing for what
+we'll be doing the next week. It would be smart to make a serious start on that
+week's homework, for instance, before the session.
+-->
+
+* Here is information about [[How to get the programming languages running on your computer|installing]].
+
+* Henceforth, unless we say otherwise, every homework will be "due" by
+Wednesday morning after the Thursday seminar in which we refer to it.
+(Usually we'll post the assignment shortly before the seminar, but don't
+rely on this.) However, for every assignment there will be a "grace
+period" of one further week for you to continue working on it if you
+have trouble and aren't able to complete the assignment to your
+satisfaction by the due date. You shouldn't hesitate to talk to us---or
+each other!---about the assignments when you do have trouble. We don't
+mind so much if you come across answers to the assignment when browsing
+the web, or the Little Schemer book, or anywhere. So long as you can
+reason yourself through the solutions and experience for yourself the
+insights they embody.
+
+ We reserve the privilege to ruthlessly require you to
+explain your solutions in conversations at any point, in section or in
+class.
+
+ You should always *aim* to complete the assignments by the "due" date,
+as this will fit best with the progress of the seminar.
+
+ The assignments will tend to be quite challenging. Again, you should by
+all means talk amongst yourselves, and to us, about strategies and
+questions that come up when working through them.
+
+ We will not always be able to predict accurately which problems are
+easy and which are hard. If we misjudge, and choose a problem that is
+too hard for you to complete to your own satisfaction, it is still
+very much worthwhile (and very much appreciated) if you would explain
+what is difficult, what you tried, why what you tried didn't work, and
+what you think you need in order to solve the problem.
+
+
+
+
+(**Week 1**) Thursday 29 Jan 2015
+
+> Topics:
+[[Order in programming languages and natural language|topics/week1 order]];
+[[Introduction to functional programming|topics/week1]];
+[[Homework|exercises/assignment1]];
+[[Advanced notes|topics/week1 advanced notes]]
+
+
+<!--
+[[Lambda Evaluator]]: Usable in your browser. It can help you check whether your answer to some of the homework questions works correctly. There is also now a [library](/lambda_library) of lambda-calculus arithmetical and list operations, some relatively advanced.
+
+We've added a [[Monad Library]] for OCaml.
+We've posted a [[State Monad Tutorial]].
+-->
## Course Overview ##
-The goal of this seminar is to introduce concepts and techniques from
+The overarching goal of this seminar is to introduce concepts and techniques from
theoretical computer science and show how they can provide insight
into established philosophical and linguistic problems.
This is not a seminar about any particular technology or software.
-
Rather, it's about a variety of conceptual/logical ideas that have been
developed in computer science and that linguists and philosophers ought to
know, or may already be unknowingly trying to reinvent.
ever more (sometime spectacularly) creative ways. But when your only
hammer is classical logic, every problem looks like modus ponens. In
contrast, computer scientists have invested considerable ingenuity in
-studying tool design, and have made remarkable progress.
+studying the design of their conceptual tools (among other things), and they've made much progress that we can benefit from.
"Why shouldn't I reinvent some idea X for myself? It's intellectually
rewarding!" Yes it is, but it also takes time you might have better
unnoticed. For all these reasons you're better off understanding the
state of the art.
-The theoretical tools we'll be introducing aren't very familiar to
+The theoretical tools we'll be introducing aren't part of the diet of most
everyday programmers, but they are prominent in academic computer science,
especially in the fields of functional programming and type theory.
Of necessity, this course will lay a lot of logical groundwork. But throughout
we'll be aiming to mix that groundwork with real cases
-in our home subjects where these tools play central roles.
+in our home subjects where these tools can (or already do, covertly) play central roles.
Our aim for the
course is to enable you to make these tools your own; to have enough
understanding of them to recognize them in use, use them yourself at least
in simple ways, and to be able to read more about them when appropriate.
-<!--
-Once we get up and running, the central focii of the course will be
-**continuations**, **types**, and **monads**. One of the on-going themes will
-concern evaluation order and issues about how computations (inferences,
-derivations) unfold in (for instance) time. The key analytic technique is to
-form a static, order-independent model of a dynamic process. We'll be
-discussing this in much more detail as the course proceeds.
-
-The logical systems we'll be looking at include:
-
-* the pure/untyped lambda calculus
-* combinatorial logic
-* the simply-typed lambda calculus
-* polymorphic types with System F
-* some discussion of dependent types
-* if time permits, "indeterministic" or "preemptively parallel" computation and linear logic
-
-
-Other keywords:
- recursion using the Y-combinator
- evaluation-order stratgies
- normalizing properties
- the Curry-Howard isomorphism(s)
- monads in category theory and computation
--->
+[[More about the topics and larger themes of the course|overview]]
+
## Who Can Participate? ##
in formal semantics or philosophy of language. If you have concerns about your
background, come discuss them with us.
-<!--
-This class will count as satisfying the logic requirement for Philosophy
-PhD students; however if this would be your first or only serious
+If you hope to have the class satisfy the logic requirement for Philosophy PhD students, this needs to be discussed with us and approved in advance. If this would be
+your first or only serious
engagement with graduate-level formal work you should consider
carefully, and must discuss with us, (1) whether you'll be adequately
prepared for this course, and (2) whether you'd be better served by
-taking a logic course (at a neighboring department, or at NYU next year)
+taking a logic course
with a more canonical syllabus.
--->
+This term you could take PHIL-GA 1003, [Logic for Philosophers](http://jdh.hamkins.org), offered by Joel Hamkins on Wednesdays 12-2.
Faculty and students from outside of NYU Linguistics and Philosophy are welcome
to audit, to the extent that this coheres well with the needs of our local
time to explain. We'll get clearer on this during the course. Another term used roughly the same as "functional"
is "declarative." At a first pass, "functional" or "declarative" programming is primarily focused on complex
expressions that get computationally evaluated to some (usually simpler) result. In class I gave the examples
-of `1+2` (which gets evaluated in arithmetic to 3), `1+2 < 5` (which gets evaluated in arithmetic to 'true), and `1`
-(which gets evaluated in arithmetic to 1). Also Google search strings, which get evaluated by Google servers to a
+of `1+2` (which gets evaluated in arithmetic to `3`), `1+2 < 5` (which gets evaluated in arithmetic to a truth-value), and `1`
+(which gets evaluated in arithmetic to `1`). Also Google search strings, which get evaluated by Google servers to a
list of links.
The dominant contrasting class of programming languages (the great majority of what's used
-in industry) are called "imperatival" languages, meaning they have more to do with following a sequence of commands (what we
+in industry) are called "imperatival" languages, meaning they have more to do with following a sequence of commands (generating what we
called in class "side-effects", though sometimes what they're *alongside* is not that interesting, and all the focus is instead
-on the effect). Programming languages like C and Python and JavaScript and so on are all of this sort.
+on the effects). Programming languages like C and Python and JavaScript and so on are predominantly of this sort.
+
+In truth, nothing that gets marketed as a "programming language" is really completely 100% functional/declarative, and even the
+languages I called "imperatival" will have some "functional" *fragments* (they evaluate `1+2` to `3`, also). So these labels aren't
+strictly exclusive. The labels are better thought of as concerning different
+*styles* or *idioms* of programming. Languages like Scheme and OCaml and especially Haskell get called "functional languages" because
+of the extent to which they emphasize, and are designed around those idioms. Languages like Python and JavaScript are sometimes themselves
+described as "more functional" than other languages, like C.
-In fact, nothing that gets marketed as a "programming language" is really completely 100% functional/declarative, and even the
-imperatival languages will have purely functional fragments (they evaluate `1+2` to 3, also). So these labels are really
-more about *styles* or *idioms* of programming, and languages like Scheme and OCaml and especially Haskell get called "functional languages" because
-of the extent to which they emphasize, and are designed around those idioms. Even languages like Python and JavaScript are sometimes
-described as "more functional" than some other languages. The language C is about as non-functional as you can get.
+In any case, here is some more context for the three languages we will be focusing on.
-* **Scheme** is one of two major dialects of *Lisp*, which is a large family
+* **Scheme** is one of two or three major dialects of *Lisp*, which is a large family
of programming languages. Scheme
-is the more clean and minimalistic dialect, and is what's mostly used in
+is the more clean and minimalist dialect of Lisp, and is what's mostly used in
academic circles.
Scheme itself has umpteen different "implementations", which share most of
their fundamentals, but have slightly different extensions and interact with
and that is what we recommend you use. If you're already using or comfortable with
another Scheme implementation, though, there's no compelling reason to switch.
- Racket stands to Scheme in something like the relation Firefox stands to HTML.
+ <!-- Racket doesn't have R7RS-small, and won't anytime soon. :-( Perhaps prefer Chicken? -->
-(Wikipedia on [Lisp](http://en.wikipedia.org/wiki/Lisp_%28programming_language%29),
+ Racket stands to Scheme in something like the relation Firefox stands to HTML.
+
+ (Wikipedia on [Lisp](http://en.wikipedia.org/wiki/Lisp_%28programming_language%29),
[Scheme](http://en.wikipedia.org/wiki/Scheme_%28programming_language%29),
and [Racket](http://en.wikipedia.org/wiki/Racket_%28programming_language%29).)
-* **Caml** is one of two major dialects of *ML*, which is another large
+* **Caml** is one of two major dialects of *ML*, which is another large
family of programming languages. Caml has only one active "implementation",
OCaml, developed by the INRIA academic group in France. Sometimes we may refer to Caml or ML
more generally; but you can assume that what we're talking about always works more
specifically in OCaml.
-(Wikipedia on [ML](http://en.wikipedia.org/wiki/ML_%28programming_language%29),
+ (Wikipedia on [ML](http://en.wikipedia.org/wiki/ML_%28programming_language%29),
[Caml](http://en.wikipedia.org/wiki/Caml),
and [OCaml](http://en.wikipedia.org/wiki/OCaml).)
-* Those of you with some programming background may have encountered a third
+* Those of you with some programming background may have encountered a third
prominent functional programming language, **Haskell**. This is also used a
lot in the academic contexts we'll be working through. Its surface syntax
differs from Caml, and there are various important things one can do in
each of Haskell and Caml that one can't (or can't as easily) do in the
-other. But these languages also have a lot in common, and if you're
-familiar with one of them, it's not difficult to move between it and the
+other. But these languages also have *a lot* in common, and if you're
+familiar with one of them, it's generally not hard to move between it and the
other.
-(Wikipedia on [Haskell](http://en.wikipedia.org/wiki/Haskell_%28programming_language%29).)
+ (Wikipedia on [Haskell](http://en.wikipedia.org/wiki/Haskell_%28programming_language%29).)
<a name=installing></a>
-[[How to get the programming languages running on your computer]]
-
-<!--
-[[Family tree of functional programming languages]]
-
-[[Translating between OCaml Scheme and Haskell]]
-
-## What is Functional Programming? ##
+[[How to get the programming languages running on your computer|installing]]
-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.
-
-Read more about the [uptake of Haskell](http://steve-yegge.blogspot.com/2010/12/haskell-researchers-announce-discovery.html) among programmers in the street.
--->
## Recommended Books ##
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.
-* *An Introduction to Lambda Calculi for Computer Scientists*, by Chris
+* *An Introduction to Lambda Calculi for Computer Scientists*, by Chris
Hankin, currently $18 paperback on
[Amazon](http://www.amazon.com/dp/0954300653).
a free sample chapter [at the MIT Press web page for the
book](http://www.ccs.neu.edu/home/matthias/BTLS/).
-* *The Seasoned Schemer*, also by Daniel P. Friedman and Matthias Felleisen, currently $29 paperback
+* *The Seasoned Schemer*, also by Daniel P. Friedman and Matthias Felleisen, currently $29 paperback
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.
-* *The Little MLer*, by Matthias Felleisen and Daniel P. Friedman, currently $31 paperback / $29 kindle
+* *The Little MLer*, by Matthias Felleisen and Daniel P. Friedman, currently $31 paperback / $29 kindle
on [Amazon](http://www.amazon.com/Little-MLer-Matthias-Felleisen/dp/026256114X).
This covers much of the same introductory ground as The Little Schemer, but
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.
([Here's a translation manual between them](http://www.mpi-sws.org/~rossberg/sml-vs-ocaml.html).)
-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.
+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.
-* Another good book covering the same ground as the Hankin book, but
+* Another good book covering the same ground as the Hankin book, but
more thoroughly, and in a more mathematical style, is *Lambda-Calculus and Combinators:
an Introduction*, by J. Roger Hindley and Jonathan P. Seldin, currently $74 hardback / $65 kindle on [Amazon](http://www.amazon.com/dp/0521898854).
-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.
+This book is substantial; and although 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.
If you choose to read both the Hankin book and this book, you'll notice the authors made some different
terminological/notational choices. At first, this makes comprehension slightly slower,
but in the long run it's helpful because it makes the arbitrariness of those choices more salient.
-* 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.
+* 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.
----
All wikis are supposed to have a [[SandBox]], so this one does too.
This wiki is powered by [[ikiwiki]].
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