1. Church-like encodings of numbers, defining addition and multiplication 1. Defining the predecessor function; alternate encodings for the numbers 1. Homogeneous sequences or "lists"; how they differ from pairs, triples, etc. 1. Representing lists as pairs 1. Representing lists as folds 1. Typical higher-order functions: map, filter, fold

1. Recursion exploiting the fold-like representation of numbers and lists ([[!wikipedia Deforestation (computer science)]], [[!wikipedia Zipper (data structure)]]) 1. General recursion using omega 1. The Y combinator(s); more on evaluation strategies

1. 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