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[lambda.git] / topics / _week5_system_F.mdwn

diff --git a/topics/_week5_system_F.mdwn b/topics/_week5_system_F.mdwn
index ae0b7e0..55f49ae 100644 (file)
--- 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:&alpha;</code>" represents an expression `x`
 whose type is <code>&alpha;</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:
        ---------
@@ -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
 (&alpha;, &beta;, 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.
 
@@ -117,15 +116,15 @@ however.  Here is one way, coded in
 System F|http://www.cis.upenn.edu/~bcpierce/tapl/index.html]] (the
 relevant evaluator is called "fullpoly"):
 
-    N = ∀α. (α->α)->α->α;
-    Pair = (N->N->N) -> N;
-    let zero = Λα. λs:α->α . λz:α. z in 
-    let fst = λx:N. λy:N . x in
-    let snd = λx:N. λy:N . y in
-    let pair = λx:N. λy:N . λz:N->N->N . z x y in
-    let suc = λn:N. λα . λlambda s:α->α . λz:α. s (n [α] s z) in
-    let shift = λp:Pair. pair (suc (p fst)) (p fst) in
-    let pre = λn:N. n [Pair] shift (pair zero zero) snd in
+    N = ∀α.(α->α)->α->α;
+    Pair = (N->N->N)->N;
+    let zero = Λα.λs:α->α.λz:α. z in 
+    let fst = λx:N.λy:N.x in
+    let snd = λx:N.λy:N.y in
+    let pair = λx:N.λy:N.λz:N->N->N.z x y in
+    let suc = λn:N.λα.λs:α->α.λz:α.s (n [α] s z) in
+    let shift = λp:Pair.pair (suc (p fst)) (p fst) in
+    let pre = λn:N.n [Pair] shift (pair zero zero) snd in
 
     pre (suc (suc (suc zero)));