X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=topics%2F_week5_system_F.mdwn;fp=topics%2F_week5_system_F.mdwn;h=e69eeb4d2447b9b4dcc89f1291519c345fbb8799;hp=ae0b7e056f75c12f353d55a2a6b9ceca22759dea;hb=de7e75d334623860b686900be73418598e5dccb7;hpb=b895ad012c22442151800347864a4b3f84f6de84 diff --git a/topics/_week5_system_F.mdwn b/topics/_week5_system_F.mdwn index ae0b7e05..e69eeb4d 100644 --- 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 "x:α" represents an expression `x` whose type is α. -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: --------- @@ -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 -than over values; in various discussion below and later, type variable +than over values; in various discussion below and later, type variables 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. -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.