+1. Encoding pairs (and triples and ...) +1. Encoding booleans +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 + +