## The "pure" or untyped lambda calculus ##
1. Beta reduction
-2. Subtitution; using alpha-conversion and other strategies
-3. Conversion versus Reduction
-4. Eta reduction and "extensionality"
-5. Different evaluation strategies
-6. Strongly normalizing vs weakly normalizing vs non-normalizing; Church-Rosser Theorem(s)
-
-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
-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
+1. Substitution; using alpha-conversion and other strategies
+1. Conversion versus reduction
+1. Eta reduction and "extensionality"
+1. Different evaluation strategies (call by name, call by value, etc.)
+1. Strongly normalizing vs weakly normalizing vs non-normalizing; Church-Rosser Theorem(s)
+1. Lambda calculus compared to combinatorial logic<p>
+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<p>
+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<p>
+1. Introducing the notion of a "continuation", which technique we'll now already have used a few times
## Types ##
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"
-
+7. "Pattern-matching" or type unpacking<p>
+8. The simply-typed lambda calculus<p>
+9. Parametric polymorphism, System F, "type inference"<p>
10. [Phil/ling application] inner/outer domain semantics for positive free logic
- <!-- <http://philosophy.ucdavis.edu/antonelli/papers/pegasus-JPL.pdf> -->
-
-11. [Phil/ling application] King vs Schiffer in King 2007, pp 103ff.
+ <!-- <http://philosophy.ucdavis.edu/antonelli/papers/pegasus-JPL.pdf> --><p>
+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"
-
-14. Curry-Howard isomorphism between simply-typed lambda and intuitionistic propositional logic
-
+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)<p>
+14. Curry-Howard isomorphism between simply-typed lambda and intuitionistic propositional logic<p>
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. Dependent types
+17. [Phil/ling application] Expletives<p>
+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 seen, and the "monadic laws" (computer science version)
+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"
-7. Montague / Yoad Winter? (just have this written down in my notes, I assume Chris will remember the reference)
-
+5. Other interesting monads: reader monad, continuation monad<p>
+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)<p>
8. Passing by reference
-9. [Phil/ling application] Fine and Pryor or "coordinated contents"
-
+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
+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 continuations
-5. [Phil/ling application] Barker/Shan on donkey anaphora
-
+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
+4. [Phil/ling application] Barker on free choice, imperatives