[[!toc]]
-Types, OCAML
+Types, OCaml
------------
-OCAML has type inference: the system can often infer what the type of
+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.
For instance, if we type
# (3) = 3;;
- : bool = true
-though OCAML, like many systems, refuses to try to prove whether two
+though OCaml, like many systems, refuses to try to prove whether two
functional objects may be identical:
# (f) = f;;
Oh well.
-Booleans in OCAML, and simple pattern matching
+Booleans in OCaml, and simple pattern matching
----------------------------------------------
Where we would write `true 1 2` in our pure lambda calculus and expect
-it to evaluate to `1`, in OCAML boolean types are not functions
+it to evaluate to `1`, in OCaml boolean types are not functions
(equivalently, are functions that take zero arguments). Selection is
accomplished as follows:
Unit and thunks
---------------
-All functions in OCAML take exactly one argument. Even this one:
+All functions in OCaml take exactly one argument. Even this one:
# let f x y = x + y;;
# f 2 3;;
After we've given our `f` one argument, it returns a function that is
still waiting for another argument.
-There is a special type in OCAML called `unit`. There is exactly one
+There is a special type in OCaml called `unit`. There is exactly one
object in this type, written `()`. So
# ();;
# (fun x -> true) omega;;
- : bool = true
-OCAML declined to try to evaluate the argument before applying the
+OCaml declined to try to evaluate the argument before applying the
functor. But remember that `omega` is a function too, so we can
reverse the order of the arguments:
So the integer division operation presupposes that its second argument
(the divisor) is not zero, upon pain of presupposition failure.
-Here's what my OCAML interpreter says:
+Here's what my OCaml interpreter says:
# 12/0;;
Exception: Division_by_zero.
So we want to explicitly allow for the possibility that
division will return something other than a number.
-We'll use OCAML's option type, which works like this:
+We'll use OCaml's option type, which works like this:
# type 'a option = None | Some of 'a;;
# None;;
Beautiful, just what we need: now we can try to divide by anything we
want, without fear that we're going to trigger any system errors.
-I prefer to line up the `match` alternatives by using OCAML's
+I prefer to line up the `match` alternatives by using OCaml's
built-in tuple type:
<pre>
doesn't trigger any presupposition of its own, so it is a shame that
it needs to be adjusted because someone else might make trouble.
-But we can automate the adjustment. The standard way in OCAML,
+But we can automate the adjustment. The standard way in OCaml,
Haskell, etc., is to define a `bind` operator (the name `bind` is not
well chosen to resonate with linguists, but what can you do):