X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week4.mdwn;h=b7ff879082a8bb7f11fe2907df3a59ed908977e1;hp=9175c4aeaf9d478cec36e04ce49ef7ad88965261;hb=6dffa91feff41dc4736d907bf59c3a76a3c8d50f;hpb=4acb0dcfac415c233c70e3125e333e07fa51a387 diff --git a/week4.mdwn b/week4.mdwn index 9175c4ae..b7ff8790 100644 --- a/week4.mdwn +++ b/week4.mdwn @@ -288,8 +288,8 @@ Version 1 type numerals are not a good choice for the simply-typed lambda calculus. The reason is that each different numberal has a different type! For instance, if zero has type σ, then `false` has type τ --> τ --> &tau, for some τ. Since one is -represented by the function `\x.x false 0`, one must have type `(τ ---> τ --> &tau) --> &sigma --> σ`. But this is a different +represented by the function `\x.x false 0`, one must have type (τ +--> τ --> τ) --> σ --> σ. But this is a different type than zero! Because each number has a different type, it becomes impossible to write arithmetic operations that can combine zero with one. We would need as many different addition operations as we had