[[!toc]]
-Types, OCaml
-------------
+Polymorphic Types and System F
+------------------------------
+
+[Notes still to be added. Hope you paid attention during seminar.]
+
+<!--
+
+8. The simply-typed lambda calculus<p>
+9. Parametric polymorphism, System F, "type inference"<p>
+
+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
+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. [which paper?](http://rci.rutgers.edu/~jeffreck/pub.php)
+12. [Phil/ling application] King and Pryor on that clauses, predicates vs singular property-designators
+ Russell On Denoting / Kaplan on plexy
+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>
+
+6. Inductive types (numbers, lists)
+
+5. Unit type
+4. Zero/bottom types
+7. "Pattern-matching" or type unpacking<p>
+
+-->
+
+
+Types in OCaml
+--------------
OCaml has type inference: the system can often infer what the type of
an expression must be, based on the type of other known expressions.
`==` operator instead of the `=` operator. Later when we discuss mutation,
we'll discuss the difference between these two equality operations.
Scheme has a similar pair, which they name `eq?` and `equal?`. In Python,
-these are `is` and `==` respectively. It's unfortunate that OCaml uses `==` for the opposite operation that Python and many other languages use it for. In any case, OCaml will understand `(f) == f` even though it doesn't understand
+these are `is` and `==` respectively. It's unfortunate that OCaml uses `==` for the opposite operation that Python and many other languages use it for. In any case, OCaml will accept `(f) == f` even though it doesn't accept
`(f) = f`. However, don't expect it to figure out in general when two functions
-are identical. (That question is not Turing computable.)
+are equivalent. (That question is not Turing computable.)
# (f) == (fun x -> x + 3);;
- : bool = false
# test ();;
<Infinite loop, need to control-c to interrupt>
-We can use functions that take arguments of type unit to control
-execution. In Scheme parlance, functions on the unit type are called
+We can use functions that take arguments of type `unit` to control
+execution. In Scheme parlance, functions on the `unit` type are called
*thunks* (which I've always assumed was a blend of "think" and "chunk").
Question: why do thunks work? We know that `blackhole ()` doesn't terminate, so why do expressions like:
let rec blackhole x = blackhole x in 2 :: (blackhole 1);;
+By the way, what's the type of this:
+
let rec blackhole (x:'a) : 'a = blackhole x in blackhole
Towards Monads
--------------
-This has now been moved to [its own page](/towards_monads).
+This has now been moved to the start of [[week7]].