--- a/src/HOL/ex/nbe.thy Fri Mar 03 19:30:20 2006 +0100
+++ b/src/HOL/ex/nbe.thy Fri Mar 03 19:30:30 2006 +0100
@@ -6,9 +6,82 @@
theory nbe
imports Main
begin
+ML"reset quick_and_dirty"
-(*ML"set Toplevel.timing"*)
-norm_by_eval "exp (Suc (Suc (Suc (Suc (Suc (Suc (Suc 0))))))) (Suc (Suc (Suc (Suc (Suc 0)))))"
+declare disj_assoc[code]
+
+norm_by_eval "(P | Q) | R"
+
+lemma[code]: "(P \<longrightarrow> P)=True" by blast
+norm_by_eval "P \<longrightarrow> P"
+norm_by_eval "True \<longrightarrow> P"
+
+
+datatype n = Z | S n
+consts
+ add :: "n \<Rightarrow> n \<Rightarrow> n"
+ add2 :: "n \<Rightarrow> n \<Rightarrow> n"
+ mul :: "n \<Rightarrow> n \<Rightarrow> n"
+ mul2 :: "n \<Rightarrow> n \<Rightarrow> n"
+ exp :: "n \<Rightarrow> n \<Rightarrow> n"
+primrec
+"add Z = id"
+"add (S m) = S o add m"
+primrec
+"add2 Z n = n"
+"add2 (S m) n = S(add2 m n)"
+
+lemma [code]: "add2 (add2 n m) k = add2 n (add2 m k)"
+by(induct n, auto)
+lemma [code]: "add2 n (S m) = S(add2 n m)"
+by(induct n, auto)
+lemma [code]: "add2 n Z = n"
+by(induct n, auto)
+
+norm_by_eval "add2 (add2 n m) k"
+norm_by_eval "add2 (add2 (S n) (S m)) (S k)"
+norm_by_eval "add2 (add2 (S n)(add2 (S m) Z)) (S k)"
+
+primrec
+"mul Z = (%n. Z)"
+"mul (S m) = (%n. add (mul m n) n)"
+primrec
+"mul2 Z n = Z"
+"mul2 (S m) n = add2 n (mul2 m n)"
+primrec
+"exp m Z = S Z"
+"exp m (S n) = mul (exp m n) m"
+
+
+norm_by_eval "mul2 (S(S(S(S(S(S(S Z))))))) (S(S(S(S(S Z)))))"
+norm_by_eval "mul (S(S(S(S(S(S(S Z))))))) (S(S(S(S(S Z)))))"
+norm_by_eval "exp (S(S(S(S(S(S(S Z))))))) (S(S(S(S(S Z)))))"
+
+norm_by_eval "[] @ []"
+norm_by_eval "[] @ xs"
+norm_by_eval "[a,b,c] @ xs"
+norm_by_eval "[%a. a, %b. b, c] @ xs"
+norm_by_eval "[%a. a, %b. b, c] @ [u,v]"
+norm_by_eval "map f [x,y,z]"
+norm_by_eval "map (%f. f True) [id,g,Not]"
+norm_by_eval "map (%f. f True) ([id,g,Not] @ fs)"
+norm_by_eval "rev[a,b,c]"
+norm_by_eval "rev(a#b#cs)"
+norm_by_eval "map map [f,g,h]"
+norm_by_eval "map (%F. F [a,b,c]) (map map [f,g,h])"
+norm_by_eval "map (%F. F ([a,b,c] @ ds)) (map map ([f,g,h]@fs))"
+norm_by_eval "map (%F. F [Z,S Z,S(S Z)]) (map map [S,add (S Z),mul (S(S Z)),id])"
+norm_by_eval "map (%x. case x of None \<Rightarrow> False | Some y \<Rightarrow> True) [None, Some ()]"
+norm_by_eval "case xs of [] \<Rightarrow> True | x#xs \<Rightarrow> False"
+norm_by_eval "case Z of Z \<Rightarrow> True | S x \<Rightarrow> False"
+norm_by_eval "map (%x. case x of None \<Rightarrow> False | Some y \<Rightarrow> True) xs"
+norm_by_eval "let x = y in [x,x]"
+norm_by_eval "Let y (%x. [x,x])"
+norm_by_eval "case n of Z \<Rightarrow> True | S x \<Rightarrow> False"
+norm_by_eval "(%(x,y). add x y) (S z,S z)"
+norm_by_eval "filter (%x. x) ([True,False,x]@xs)"
+norm_by_eval "filter Not ([True,False,x]@xs)"
+
norm_by_eval "0 + (n::nat)"
norm_by_eval "0 + Suc(n)"
norm_by_eval "Suc(n) + Suc m"
@@ -22,3 +95,15 @@
norm_by_eval "rev [a, b, c]"
end
+
+(*
+ML"set Toplevel.debug"
+norm_by_eval "case n of None \<Rightarrow> True | Some((x,y),(u,v)) \<Rightarrow> False"
+norm_by_eval "let ((x,y),(u,v)) = ((Z,Z),(Z,Z)) in add (add x y) (add u v)"
+norm_by_eval "(%((x,y),(u,v)). add (add x y) (add u v)) ((Z,Z),(Z,Z))"
+*)
+(* to be done
+norm_by_eval "max 0 (0::nat)"
+norm_by_eval "last[a,b,c]"
+ Numerals! *)
+