X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=topics%2F_week5_system_F.mdwn;h=0dcb0957803ffa0855c51e792a0c0979a4590683;hp=4bde11e08fbdec51ebd083d13cc5fdd2c9089a48;hb=4d9fe4645917a4966694c7c4bf8edde8b243745f;hpb=447c097435042d6895c2cf7e861ec119a2f20b63 diff --git a/topics/_week5_system_F.mdwn b/topics/_week5_system_F.mdwn index 4bde11e0..0dcb0957 100644 --- a/topics/_week5_system_F.mdwn +++ b/topics/_week5_system_F.mdwn @@ -9,23 +9,6 @@ simply-typed lambda calculus as a way of expressing natural language meaning. So we will need to get more sophisticated about types. The next step in that journey will be to consider System F. -In the simply-typed lambda calculus, we write types like σ --> τ. This looks like logical implication. We'll take -that resemblance seriously when we discuss the Curry-Howard -correspondence. In the meantime, note that types respect modus -ponens: - -
-Expression    Type      Implication
------------------------------------
-fn            α -> β    α ⊃ β
-arg           α         α
-------        ------    --------
-(fn arg)      β         β
-
- -The implication in the right-hand column is modus ponens, of course. - System F was discovered by Girard (the same guy who invented Linear Logic), but it was independently proposed around the same time by Reynolds, who called his version the *polymorphic lambda calculus*.