--- a/src/HOL/ex/NormalForm.thy Mon Jan 21 08:43:33 2008 +0100
+++ b/src/HOL/ex/NormalForm.thy Mon Jan 21 08:43:34 2008 +0100
@@ -64,29 +64,29 @@
lemma "case Z of Z \<Rightarrow> True | S x \<Rightarrow> False" by normalization
lemma "[] @ [] = []" by normalization
-normal_form "map f [x,y,z::'x] = [f x, f y, f z]"
-normal_form "[a, b, c] @ xs = a # b # c # xs"
+lemma "map f [x,y,z::'x] = [f x, f y, f z]" by normalization rule+
+lemma "[a, b, c] @ xs = a # b # c # xs" by normalization rule+
lemma "[] @ xs = xs" by normalization rule
-normal_form "map f [x,y,z::'x] = [f x, f y, f z]"
-normal_form "map (%f. f True) [id, g, Not] = [True, g True, False]"
-normal_form "map (%f. f True) ([id, g, Not] @ fs) = [True, g True, False] @ map (%f. f True) fs"
-normal_form "rev [a, b, c] = [c, b, a]"
+lemma "map (%f. f True) [id, g, Not] = [True, g True, False]" by normalization rule+
+lemma "map (%f. f True) ([id, g, Not] @ fs) = [True, g True, False] @ map (%f. f True) fs" by normalization rule+
+lemma "rev [a, b, c] = [c, b, a]" by normalization rule+
normal_form "rev (a#b#cs) = rev cs @ [b, a]"
normal_form "map (%F. F [a,b,c::'x]) (map map [f,g,h])"
normal_form "map (%F. F ([a,b,c] @ ds)) (map map ([f,g,h]@fs))"
normal_form "map (%F. F [Z,S Z,S(S Z)]) (map map [S,add (S Z),mul (S(S Z)),id])"
-normal_form "map (%x. case x of None \<Rightarrow> False | Some y \<Rightarrow> True) [None, Some ()]"
+lemma "map (%x. case x of None \<Rightarrow> False | Some y \<Rightarrow> True) [None, Some ()] = [False, True]"
+ by normalization
normal_form "case xs of [] \<Rightarrow> True | x#xs \<Rightarrow> False"
-normal_form "map (%x. case x of None \<Rightarrow> False | Some y \<Rightarrow> True) xs"
-normal_form "let x = y::'x in [x,x]"
-normal_form "Let y (%x. [x,x])"
+normal_form "map (%x. case x of None \<Rightarrow> False | Some y \<Rightarrow> True) xs = P"
+lemma "let x = y in [x, x] = [y, y]" by normalization rule+
+lemma "Let y (%x. [x,x]) = [y, y]" by normalization rule+
normal_form "case n of Z \<Rightarrow> True | S x \<Rightarrow> False"
-normal_form "(%(x,y). add x y) (S z,S z)"
+lemma "(%(x,y). add x y) (S z,S z) = S (add z (S z))" by normalization rule+
normal_form "filter (%x. x) ([True,False,x]@xs)"
normal_form "filter Not ([True,False,x]@xs)"
-normal_form "[x,y,z] @ [a,b,c] = [x, y, z, a, b ,c]"
-normal_form "(%(xs, ys). xs @ ys) ([a, b, c], [d, e, f]) = [a, b, c, d, e, f]"
+lemma "[x,y,z] @ [a,b,c] = [x, y, z, a, b ,c]" by normalization rule+
+lemma "(%(xs, ys). xs @ ys) ([a, b, c], [d, e, f]) = [a, b, c, d, e, f]" by normalization rule+
lemma "map (%x. case x of None \<Rightarrow> False | Some y \<Rightarrow> True) [None, Some ()] = [False, True]" by normalization
lemma "last [a, b, c] = c" by normalization rule
@@ -111,11 +111,11 @@
lemma "(42::rat) / 1704 = 1 / 284 + 3 / 142" by normalization
normal_form "Suc 0 \<in> set ms"
-normal_form "f"
-normal_form "f x"
-normal_form "(f o g) x"
-normal_form "(f o id) x"
-normal_form "\<lambda>x. x"
+lemma "f = f" by normalization rule+
+lemma "f x = f x" by normalization rule+
+lemma "(f o g) x = f (g x)" by normalization rule+
+lemma "(f o id) x = f x" by normalization rule+
+normal_form "(\<lambda>x. x)"
(* Church numerals: *)
@@ -124,4 +124,3 @@
normal_form "(%m n. n m) (%f x. f(f(f(x)))) (%f x. f(f(f(x))))"
end
-