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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 55f49ae..a7b4bb9 100644 (file)
--- a/topics/_week5_system_F.mdwn
+++ b/topics/_week5_system_F.mdwn
@@ -118,13 +118,14 @@ 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.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
+
+    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)));
 
@@ -137,7 +138,7 @@ lambda).
 
 The key to the extra expressive power provided by System F is evident
 in the typing imposed by the definition of `pre`.  The variable `n` is
-typed as a Church number, i.e., as `∀ α . (α->α)->α->α`.  The type
+typed as a Church number, i.e., as `∀α.(α->α)->α->α`.  The type
 application `n [Pair]` instantiates `n` in a way that allows it to
 manipulate ordered pairs: `n [Pair]: (Pair->Pair)->Pair->Pair`.  In
 other words, the instantiation turns a Church number into a
@@ -164,14 +165,14 @@ Typing ω
 In fact, unlike in the simply-typed lambda calculus, 
 it is even possible to give a type for ω in System F. 
 
-<code>&omega; = λlambda x:(∀ α. α->α) . x [∀ α . α->α] x</code>
+<code>&omega; = λx:(∀α.α->α). x [∀α.α->α] x</code>
 
 In order to see how this works, we'll apply &omega; to the identity
 function.  
 
 <code>&omega; id ==</code>
 
-    (λx:(∀α. α->α) . x [∀α.α->α] x) (Λα.λx:α. x)
+    (λx:(∀α.α->α). x [∀α.α->α] x) (Λα.λx:α.x)
 
 Since the type of the identity function is `∀α.α->α`, it's the
 right type to serve as the argument to &omega;.  The definition of