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 XX-YY at WHERE.
--->
+One student session to discuss homeworks will be held every Wednesday from 5-6, in Linguistics room 104 (back of the first floor).
-## [[Index of Content (lecture notes and more)|content]] ##
+## [[Index of Main Content|content]] (lecture notes and more) ##
+
+## [[Offsite Readings|readings]] ##
## Announcements ##
+* [[Untyped lambda calculus evaluator|code/lambda_evaluator]] on this site
+
* 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
+ If you're 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, 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.
+-->
-<!--
-One student session will be held every Wednesday from XX-YY at WHERE.
+* The student session has been scheduled for Wednesdays from 5-6, in Linguistics room 104 (back of the first floor).
-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.
+ Those of you interested in additional Q&A but who can't make that time, let us know.
-You should see the student sessions as opportunities to clear up lingering
+ You should see these 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.
--->
+we'll be doing the next week. It's expected you'll have made at least a serious start on that
+week's homework (due the following day) before the session.
-* Here is information about [[How to get the programming languages running on your computer|installing]].
+* Here is information about [[How to get the programming languages running on your computer|installing]]. If those instructions seem overwhelming, note that it should be possible to do a lot of this course using only demonstration versions of these languages [[that run in your web browser|browser]].
* Henceforth, unless we say otherwise, every homework will be "due" by
Wednesday morning after the Thursday seminar in which we refer to it.
> Topics:
[[Order in programming languages and natural language|topics/week1 order]];
-[[Introduction to functional programming|topics/week1]];
+[[Introduction to functional programming|topics/week1 kapulet intro]];
[[Homework|exercises/assignment1]];
-[[Advanced notes|topics/week1 advanced notes]]
+[[Advanced notes|topics/week1 kapulet advanced]]
+
+(**Intermezzo**)
+> Help on [[learning Scheme]], [[OCaml|learning OCaml]], and [[Haskell|learning Haskell]];
+The [[differences between our made-up language and Scheme, OCaml, and Haskell|rosetta1]];
+[[What do words like "interpreter" and "compiler" mean?|ecosystem]] (in progress)
+
+(**[[Lambda Evaluator|code/lambda evaluator]]**) Usable in your browser. It can help you check whether your answer to some of the (upcoming) homework questions works correctly.
+<!--
+ There is also now a [library](/lambda library) of lambda-calculus arithmetical and list operations, some relatively advanced.
+-->
+
+(**Week 2**) Thursday 5 February 2015
+> Topics:
+[[Intro to the Lambda Calculus|topics/week2 lambda intro]];
+[[Advanced notes|topics/week2 lambda advanced]];
+[[Encoding Booleans, Tuples, Lists, and Numbers|topics/week2 encodings]];
+[[Homework|exercises/assignment2]]
+
+> Also, if you're reading the Hankin book, try reading Chapters 1-3. You will most likely need to come back again and read it multiple times; but this would be a good time to make the first attempt.
+
+> We posted [[answers to Week 1's homework|exercises/assignment1_answers]].
+
+(**Week 3**) Thursday 12 February 2015
+*We will continue to develop these notes over the next few days.*
+
+> Topics:
+[[Arithmetic with Church numbers|topics/week3_church_arithmetic]];
+[[More on Lists|topics/week3 lists]] (expanded on Sunday);
+[[What is computation?|topics/week3_what_is_computation]];
+[[Reduction Strategies and Normal Forms|topics/week3_evaluation_order]] (posted on Monday 23 Feb);
+[[Unit and its usefulness|topics/week3 unit]] (posted on Wednesday);
+[[Combinatory Logic|topics/week3 combinatory logic]] (revised on Monday and Tuesday);
+[[Homework|exercises/assignment3]]
+
+> Also, by this point you should be able to handle all of *The Little Schemer* except for Chapters 9 and 10. Chapter 9 covers what is going on under the hood with `letrec`, and that will be our topic for next week. You can also read Chapter 4 of Hankin on Combinatory Logic.
+
+> We posted [[answers to Week 2's homework|exercises/assignment2_answers]].
+
+(**Week 4**) Thursday 19 February 2015
+
+> Topics: [[!img images/tabletop_roleplaying.png size="240x240" alt="Hey, no recursing"]]
+[[Yes, recursing|topics/week4_fixed_point_combinators]];
+[[More about fixed point combinators|topics/week4_more_about_fixed_point_combinators]];
+Towards types (in progress);
+[[Homework|exercises/assignment4]]
+
+> Now you can read Sections 3.1 and 6.1 of Hankin; and browse the rest of Hankin Chapter 6, which should look somewhat familiar.
+
+> If you're reading along in the Pierce book, we've now covered much of the material in his Chapters 1-7.
+
+> We posted [[answers to Week 3's homework|exercises/assignment3_answers]].
+
+(**Week 5**) Thursday 26 February 2015
+
+> *Note*: Jim will be updating and expanding the lecture notes by Tuesday, but doesn't want to delay any longer letting you have access to the drafts we (in part) presented from in seminar. But do come back and re-read the pages when the expanded versions are posted.
+> Topics:
+[[Simply-typed lambda calculus|topics/week5 simply typed]];
+[[System F|topics/week5 system F]];
+Types in OCaml and Haskell;
+Practical advice for working with OCaml and/or Haskell (all will be posted soon);
+[[Homework|exercises/assignment5]]
+
+> *There is some assigned reading for our next meeting.* This comes in two batches. The first batch consists of [[this footnote|readings/kaplan-plexy.pdf]] from Kaplan's *Demonstratives*. Also recommended, but not mandatory, is [[this selection|readings/king-on-schiffer.pdf]] from Chapter 4 of Jeff King's 2007 book *The Nature and Structure of Content*. The second batch consists of [[this paper|readings/rieppel-beingsthg.pdf]] from Michael Rieppel, a recent Berkeley Philosophy PhD, on Frege's "concept horse" problem. Also recommended, but not mandatory, is [[this selection|readings/king-on-logicism.pdf]] from Chapter 5 of King's book. (It reviews and elaborates his paper "[Designating propositions](http://philpapers.org/rec/KINDP)".)
+
+> If you're interested in the scholarly background on Frege's "concept horse" problem, here is [an entry point](http://philpapers.org/rec/PROWIF).
+
+> If you're reading along in Hankin, you can look at Chapter 7.
+
+> If you're reading along in the Pierce book, the chapters most relevant to this week's discussion are 22 and 23; though for context we also recommend at least Chapters 8, 9, 11, 20, and 29. We don't expect most of you to follow these recommendations now, or even to be comfortable enough yet with the material to be able to. We're providing the pointers as references that some might conceivably pursue now, and others later.
+
+(**Week 6**) Thursday March 5
+
+> We will be discussing the readings posted above.
+
+> Topics: [[Kaplan on Plexy|topics/week6_plexy]]; King on that-clauses and "the proposition that P"; Rieppel on Frege and the concept HORSE
+
+(**Week 7**) Thursday March 12
+
+> Topics: [[Combinatory evaluator|topics/week7_combinatory_evaluator]]; Interpreter for Lambda terms; [[Introducing Monads|topics/week7_introducing_monads]]; [[Homework|exercises/assignment7]]
<!--
-[[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.
+(**Week 8**) Thursday March 26
+-->
+<!--
We've added a [[Monad Library]] for OCaml.
We've posted a [[State Monad Tutorial]].
-->
developed in computer science and that linguists and philosophers ought to
know, or may already be unknowingly trying to reinvent.
-Philosphers and linguists tend to reuse the same familiar tools in
+Philosophers and linguists tend to reuse the same familiar tools in
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
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.
-[[More about the topics and larger themes of the course| overview]]
+"Computer Science is no more about computers than astronomy is about telescopes." -- [E. W. Dijkstra](https://en.wikipedia.org/wiki/Edsger_W._Dijkstra) <small>(or Hal Abelson, or Michael Fellows; the quote's <a href="https://en.wikiquote.org/wiki/Computer_science">origins are murky</a>)</small>
+
+
+[[More about the topics and larger themes of the course|overview]]
## Who Can Participate? ##
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 any case, here is some more context for the three languages we will be focusing on.
+In any case, here is
+<a name=installing></a>
+[[How to get the programming languages running on your computer|installing]].
+And here is some more context for the three languages we will be focusing on:
* **Scheme** is one of two or three major dialects of *Lisp*, which is a large family
of programming languages. Scheme
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 doesn't have R7RS-small, and won't anytime soon. :-( Perhaps prefer Chicken? -->
+ Another good Scheme implementation is Chicken. For our purposes, this is in some
+respects superior to Racket, and in other respects inferior. <!--
+Racket doesn't have R7RS-small, and won't anytime soon. :-(
+Also Chicken's library collection seems stronger, or at least better organized and maintained.
+Other R7RS-friendly: [Gauche](http://practical-scheme.net/gauche), [Chibi](https://code.google.com/p/chibi-scheme).
+-->
- Racket stands to Scheme in something like the relation Firefox stands to HTML.
+ Racket and Chicken stand to Scheme in something like the relation Firefox stands to HTML.
- (Wikipedia on [Lisp](http://en.wikipedia.org/wiki/Lisp_%28programming_language%29),
+ (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).)
+[Racket](http://en.wikipedia.org/wiki/Racket_%28programming_language%29), and
+[Chicken](http://en.wikipedia.org/wiki/CHICKEN_%28Scheme_implementation%29).)
+ (Help on [[Learning Scheme]])
* **Caml** is one of two major dialects of *ML*, which is another large
family of programming languages. Caml has only one active "implementation",
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),
-[Caml](http://en.wikipedia.org/wiki/Caml),
-and [OCaml](http://en.wikipedia.org/wiki/OCaml).)
+ (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).)
+ (Help on [[Learning OCaml]])
-* Those of you with some programming background may have encountered a third
-prominent functional programming language, **Haskell**. This is also used a
+* **Haskell** 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
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).)
+ Like Scheme, Haskell has a couple of different implementations. The
+dominant one, and the one we recommend you install, is called GHC, short
+for "Glasgow Haskell Compiler".
+ (Wikipedia on
+[Haskell](http://en.wikipedia.org/wiki/Haskell_%28programming_language%29) and
+[GHC](https://en.wikipedia.org/wiki/Glasgow_Haskell_Compiler).)
+ (Help on [[Learning Haskell]])
+
+<!--
+[Helium](https://www.haskell.org/pipermail/haskell/2003-January/011071.html) is a simplified Haskell for teaching (no typeclasses)
+-->
-<a name=installing></a>
-[[How to get the programming languages running on your computer|installing]]
## Recommended Books ##
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.
+* *The Haskell Road to Logic, Math and Programming*, by Kees Doets and Jan van Eijck, currently $22 on [Amazon](http://www.amazon.com/dp/0954300696) is a textbook teaching the parts of math and logic we cover in the first few weeks of Logic for Philosophers. (Notions like validity, proof theory for predicate logic, sets, sequences, relations, functions, inductive proofs and recursive definitions, and so on.) The math here should be accessible and familiar to all of you. What is novel about this book is that it integrates the exposition of these notions with a training in (part of) Haskell. It only covers the rudiments of Haskell's type system, and doesn't cover monads; but if you wanted to review this material and become comfortable with core pieces of Haskell in the process, this could be a good read.
+(The book also seems to be available online [here](http://fldit-www.cs.uni-dortmund.de/~peter/PS07/HR.pdf).)
+
+
+The rest of these are a bit more advanced, and are also looser suggestions:
+
+* *Computational Semantics with Functional Programming*, by Jan van Eijck and Christina Unger, currently $42 on [Amazon](http://www.amazon.com/dp/0521757606). We own this but haven't read it yet. It *looks* like it's doing the same kind of thing this seminar aims to do: exploring how natural language meanings can be understood to be "computed". The text uses Haskell, and is aimed at linguists and philosophers as well as computer scientists. Definitely worth a look.
+<!--
+It deals with both denotational meaning (where meaning
+comes from knowing the conditions of truth in situations), and
+operational meaning (where meaning is an instruction for performing
+cognitive action).
+-->
+
* 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).
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 a bit of the same ground as the Hankin and the Hindley & Seldin, but focusing especially on 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. It seems to be the standard textbook for CS students learning type theory.
+
+* The next two books focus on the formal semantics of typed programming languages, both in the "denotational" form that most closely corresponds to what we mean by semantics, and in the "operational" form very often used in CS. These are: *The Formal Semantics of Programming Languages*, by Glynn Winskel, currently $38 on [Amazon](http://www.amazon.com/dp/0262731037), and *Semantics of Programming Languages*, by Carl Gunter, currently $41 on [Amazon](http://www.amazon.com/dp/0262071436).
----