From 93f9e689eb10f3cc3b05db934ac2c73f2146ac3c Mon Sep 17 00:00:00 2001 From: Jim Pryor Date: Wed, 15 Sep 2010 21:25:13 -0400 Subject: [PATCH] week1: tweaks Signed-off-by: Jim Pryor --- week1.mdwn | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/week1.mdwn b/week1.mdwn index 09ad8bd1..c1759a37 100644 --- a/week1.mdwn +++ b/week1.mdwn @@ -54,7 +54,9 @@ The notion of **function** that we'll be working with will be one that, by defau It's possible to enhance the lambda calculus so that functions do get identified when they map all the same inputs to the same outputs. This is called making the calculus **extensional**. Church called languages which didn't do this **intensional**. If you try to understand that kind of "intensionality" in terms of functions from worlds to extensions (an idea also associated with Church), you may hurt yourself. So too if you try to understand it in terms of mental stereotypes, another notion sometimes designated by "intension." -It's often said that dynamic systems are distinguished because they are the ones in which **order matters**. However, there are many ways in which order can matter. If we have a trivalent boolean system, for example---easily had in a purely functional calculus---we might choose TODO +It's often said that dynamic systems are distinguished because they are the ones in which **order matters**. However, there are many ways in which order can matter. If we have a trivalent boolean system, for example---easily had in a purely functional calculus---we might choose to give a truth-table like this for "and": + +true and true = true And then we'd notice that `* and false` has a different intepretation than `false and *`. (The same phenomenon is already present with the material conditional in bivalent logics; but seeing that a non-symmetric semantics for `and` is available even for functional languages is instructive.) -- 2.11.0