This is very sketchy at this point, but it should give a sense of our intended scope.
## Introduction ##
1. Declarative vs imperatival models of computation.
2. Variety of ways in which "order can matter."
3. Variety of meanings for "dynamic."
4. Schoenfinkel, Curry, Church: a brief history
5. Functions as "first-class values"
6. "Curried" functions
## The "pure" or untyped lambda calculus ##
1. Beta reduction
2. Substitution; using alpha-conversion and other strategies
3. Conversion versus reduction
4. Eta reduction and "extensionality"
5. Different evaluation strategies (call by name, call by value, etc.)
6. Strongly normalizing vs weakly normalizing vs non-normalizing; Church-Rosser Theorem(s)
6. Lambda calculus compared to combinatorial logic
7. Encoding pairs (and triples and ...)
8. Encoding booleans
9. Church-like encodings of numbers, defining addition and multiplication
10. Defining the predecessor function; alternate encodings for the numbers
11. Homogeneous sequences or "lists"; how they differ from pairs, triples, etc.
12. Representing lists as pairs
13. Representing lists as folds
14. Typical higher-order functions: map, filter, fold
15. Recursion exploiting the fold-like representation of numbers and lists ([deforestation](http://en.wikipedia.org/wiki/Deforestation_%28computer_science%29), [zippers](http://en.wikipedia.org/wiki/Zipper_%28data_structure%29))
16. General recursion using omega
17. The Y combinator(s); more on evaluation strategies
18. Introducing the notion of a "continuation", which technique we'll now already have used a few times
## Types ##
1. Product or record types, e.g. pairs and triples
2. Sum or variant types; tagged or "disjoint" unions
3. Maybe/option types; representing "out-of-band" values
4. Zero/bottom types
5. Unit type
6. Inductive types (numbers, lists)
7. "Pattern-matching" or type unpacking
8. The simply-typed lambda calculus
9. Parametric polymorphism, System F, "type inference"
10. [Phil/ling application] inner/outer domain semantics for positive free logic
11. [Phil/ling application] King vs Schiffer in King 2007, pp 103ff. [which paper?](http://rci.rutgers.edu/~jeffreck/pub.php)
12. [Phil/ling application] King and Pryor on that clauses, predicates vs singular property-designators
13. Possible excursion: [Frege's "On Concept and Object"](http://www.persiangig.com/pages/download/?dl=http://sahmir.persiangig.com/document/Frege%27s%20Articles/On%20Concept%20And%20object%20%28Jstore%29.pdf)
14. Curry-Howard isomorphism between simply-typed lambda and intuitionistic propositional logic
15. The types of continuations; continuations as first-class values
16. [Phil/ling application] Partee on whether NPs should be uniformly interpreted as generalized quantifiers, or instead "lifted" when necessary. Lifting = a CPS transform.
17. [Phil/ling application] Expletives
18. Some references:
* [de Groote on the lambda-mu calculus in linguistics](http://www.loria.fr/%7Edegroote/papers/amsterdam01.pdf)
* [on donkey anaphora and continuations](http://dx.doi.org/10.3765/sp.1.1)
* [Wadler on symmetric sequent calculi](http://homepages.inf.ed.ac.uk/wadler/papers/dual-reloaded/dual-reloaded.pdf)
19. Dependent types
## Side-effects and mutation ##
1. What difference imperativity makes
2. Monads we've already seen, and the "monadic laws" [computer science version: Wadler](http://homepages.inf.ed.ac.uk/wadler/papers/marktoberdorf/baastad.pdf)
3. Side-effects in a purely functional setting, via monads
4. The basis of monads in category theory
5. Other interesting monads: reader monad, continuation monad
6. [Phil/ling application] Monsters and context-shifting, e.g. Gillies/von Fintel on "ifs" [not sure which paper]
7. Montague / Ben-avi and Winter, [A modular approach to intensionality](http://citeseerx.ist.psu.edu/viewdocsummary?doi=10.1.1.73.6927)
8. Passing by reference
9. [Phil/ling application] Fine and Pryor on "coordinated contents" (see, e.g., [Hyper-Evaluativity](http://www.jimpryor.net/research/papers/Hyper-Evaluativity.txt))
## Continuations (continued) ##
1. Using CPS to handle abortive computations (think: presupposition failure, expressives)
2. Using CPS to do other handy things, e.g., coroutines
3. Making evaluation order explicit with continuations (could also be done earlier, but I think will be helpful to do after we've encountered mutation)
4. Delimited (quantifier scope) vs undelimited (expressives, presupposition) continuations
5. [Phil/ling application] [Barker/Shan on donkey anaphora](http://dx.doi.org/10.3765/sp.1.1)
## Preemptively parallel computing and linear logic ##
1. Basics of parallel programming: semaphores/mutexes
2. Contrasting "preemptive" parallelism to "cooperative" parallelism (coroutines, above)
3. Linear logic
4. [Phil/ling application] Barker on free choice, imperatives