added Curry-Howard

[lambda.git] / index.mdwn

# Seminar in Semantics / Philosophy of Language #

or: **What Philosophers and Linguists Can Learn From Theoretical Computer Science But Didn't Know To Ask**

This course will be 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."


## Announcements ##

*       The seminar meets on Mondays from 4-6, in 
the Linguistics building at 10 Washington Place, in room 104 (back of the first floor).

*       One student session will be held every Wednesday from 3-4. The other will
be arranged to fit the schedule of those who'd like to attend but can't
make the Wednesday time. (We first proposed Tuesdays from 11-12, but this
time turns out not to be so helpful.) 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.

*       Henceforth, unless we say otherwise, every homework will be "due" by
Sunday morning after the Monday 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.

##[[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.


## Lecture Notes and Assignments ##

(13 Sept) Lecture notes for [[Week1]]; [[Assignment1]].

>       Topics: [[Applications]], including [[Damn]]; Basics of Lambda Calculus; Comparing Different Languages

(20 Sept) Lecture notes for [[Week2]]; [[Assignment2]].

>       Topics: Reduction and Convertibility; Combinators; Evaluation Strategies and Normalization; Decidability; [[Lists and Numbers]]

(27 Sept) Lecture notes for [[Week3]];  [[Assignment3]];
an evaluator with the definitions used for homework 3
preloaded is available at [[assignment 3 evaluator]]. 

>       Topics: [[Evaluation Order]]; Recursion with Fixed Point Combinators

(4 Oct) Lecture notes for [[Week4]]; [[Assignment4]].

>       Topics: More on Fixed Points; Sets; Aborting List Traversals; [[Implementing Trees]] 


(18 Oct) Lecture notes for [[Week5]] (in progress).

>       Topics: Types, Polymorphism

[[Upcoming topics]]

[Advanced Lambda Calculus Topics](/advanced_lambda)

##Scheme and OCaml##

See [below](#installing) for how to get the programming languages running on your computer.

*       Links for help [[learning Scheme]]

*       Links for help [[learning OCaml]]


##[[Offsite Reading]]##

There's lots of links here already to tutorials and encyclopedia entries about many of the notions we'll be dealing with.



## Course Overview ##

The 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.

Philosphers 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
studying tool design, and have made remarkable progress.

"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
spent elsewhere. After all, you can get anywhere you want to go by walking, but you can
accomplish more with a combination of walking and strategic subway
rides.

More importantly, the idiosyncrasies of your particular
implementation may obscure what's fundamental to the idea you're
working with. Your implementation may be buggy in corner cases you
didn't think of; it may be incomplete and not trivial to generalize; its
connection to existing literature and neighboring issues may go
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
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. 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
-->

## Who Can Participate? ##

The course will not presume previous experience with programming.  We
will, however, discuss concepts embodied in specific programming
languages, and we will encourage experimentation with running,
modifying, and writing computer programs.

The course will not presume lots of mathematical or logical background, either.
However, it will demand a certain amount of comfort working with such material; as a result,
it will not be especially well-suited to be a first graduate-level course
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
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)
with a more canonical syllabus.


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
students.


## Recommended Software ##

During the course, we'll be encouraging you to try out various things in Scheme
and Caml, which are prominent *functional programming languages*. We'll explain
what that means during the course.

*       **Scheme** is one of two 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
academic circles.
Scheme itself has umpteen different "implementations", which share most of
their fundamentals, but have slightly different extensions and interact with
the operating system differently. One major implementation used to be called
PLT Scheme, and has just in the past few weeks changed their name to Racket.
This 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.

*       **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.

*       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.

<a name=installing></a>
[[How to get the programming languages running on your computer]]

[[Family tree of functional programming languages]]


## Recommended Books ##

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.

*       *An Introduction to Lambda Calculi for Computer Scientists*, by Chris
Hankin, currently $17 on
[Amazon](http://www.amazon.com/dp/0954300653).

*       (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 $52 on [Amazon](http://www.amazon.com/dp/0521898854). 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 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.)

*   *The Little Schemer, Fourth Edition*, by Daniel P. Friedman and Matthias
Felleisen, currently $23 on [Amazon](http://www.amazon.com/exec/obidos/ASIN/0262560992).
This is a classic text introducing the gentle art of programming, using the
functional programming language Scheme. Many people love this book, but it has
an unusual dialog format that is not to everybody's taste. **Of particular
interest for this course** is the explanation of the Y combinator, available as
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 $28
on [Amazon](http://www.amazon.com/Seasoned-Schemer-Daniel-P-Friedman/dp/026256100X)

*       *The Little MLer*, by Matthias Felleisen and Daniel P. Friedman, currently $27
on [Amazon](http://www.amazon.com/Little-MLer-Matthias-Felleisen/dp/026256114X).
This covers some of the same introductory ground as The Little Schemer, but
this time in ML. It uses another dialect of ML (called SML), instead of OCaml, but there are only
superficial syntactic differences between these languages. [Here's a translation
manual between them](http://www.mpi-sws.org/~rossberg/sml-vs-ocaml.html).



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