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author
chris
<chris@web>
Thu, 26 Feb 2015 02:38:00 +0000
(21:38 -0500)
committer
Linux User
<ikiwiki@localhost.members.linode.com>
Thu, 26 Feb 2015 02:38:00 +0000
(21:38 -0500)
topics/_week5_system_F.mdwn
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diff --git
a/topics/_week5_system_F.mdwn
b/topics/_week5_system_F.mdwn
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--- a/
topics/_week5_system_F.mdwn
+++ b/
topics/_week5_system_F.mdwn
@@
-34,8
+34,7
@@
notational convention (which will last throughout the rest of the
course) that "<code>x:α</code>" represents an expression `x`
whose type is <code>α</code>.
course) that "<code>x:α</code>" represents an expression `x`
whose type is <code>α</code>.
-Then System F can be specified as follows (choosing notation that will
-match up with usage in O'Caml, whose type system is based on System F):
+Then System F can be specified as follows:
System F:
---------
System F:
---------
@@
-47,7
+46,7
@@
constants play the role in System F that base types play in the
simply-typed lambda calculus. So in a lingusitics context, type
constants might include `e` and `t`. "α" is a type variable. The
tick mark just indicates that the variable ranges over types rather
simply-typed lambda calculus. So in a lingusitics context, type
constants might include `e` and `t`. "α" is a type variable. The
tick mark just indicates that the variable ranges over types rather
-than over values; in various discussion below and later, type variable
+than over values; in various discussion below and later, type variable
s
can be distinguished by using letters from the greek alphabet
(α, β, etc.), or by using capital roman letters (X, Y,
etc.). "`τ1 -> τ2`" is the type of a function from expressions of
can be distinguished by using letters from the greek alphabet
(α, β, etc.), or by using capital roman letters (X, Y,
etc.). "`τ1 -> τ2`" is the type of a function from expressions of
@@
-57,7
+56,7
@@
universal type, since it universally quantifies over the type variable
have at least one free occurrence of `α` somewhere inside of it.
In the definition of the expressions, we have variables "`x`" as usual.
have at least one free occurrence of `α` somewhere inside of it.
In the definition of the expressions, we have variables "`x`" as usual.
-Abstracts "`λx:τ.
e`" are similar to abstracts in the simply-typed lambda
+Abstracts "`λx:τ.e`" are similar to abstracts in the simply-typed lambda
calculus, except that they have their shrug variable annotated with a
type. Applications "`e1 e2`" are just like in the simply-typed lambda calculus.
calculus, except that they have their shrug variable annotated with a
type. Applications "`e1 e2`" are just like in the simply-typed lambda calculus.