--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/ex/NormalForm.thy Fri Jun 09 12:17:37 2006 +0200
@@ -0,0 +1,118 @@
+(* ID: $Id$
+ Authors: Klaus Aehlig, Tobias Nipkow
+
+Test of normalization function
+*)
+
+theory NormalForm
+imports Main
+begin
+
+normal_form "True \<longrightarrow> p"
+
+(* FIXME Eventually the code generator should be able to handle this
+by re-generating the existing code for "or":
+
+declare disj_assoc[code]
+
+normal_form "(P | Q) | R"
+
+*)
+
+
+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)
+
+normal_form "add2 (add2 n m) k"
+normal_form "add2 (add2 (S n) (S m)) (S k)"
+normal_form "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"
+
+normal_form "mul2 (S(S(S(S(S(S(S Z))))))) (S(S(S(S(S Z)))))"
+normal_form "mul (S(S(S(S(S(S(S Z))))))) (S(S(S(S(S Z)))))"
+normal_form "exp (S(S Z)) (S(S(S(S(S Z)))))"
+
+normal_form "[] @ []"
+normal_form "[] @ xs"
+normal_form "[] @ (xs:: 'b list)"
+normal_form "[a::'d,b,c] @ xs"
+normal_form "[%a::'x. a, %b. b, c] @ xs"
+normal_form "[%a::'x. a, %b. b, c] @ [u,v]"
+normal_form "map f (xs::'c list)"
+normal_form "map f [x,y,z::'x]"
+normal_form "map (%f. f True) [id,g,Not]"
+normal_form "map (%f. f True) ([id,g,Not] @ fs)"
+normal_form "rev[a,b,c]"
+normal_form "rev(a#b#cs)"
+normal_form "map map [f,g,h]"
+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 ()]"
+normal_form "case xs of [] \<Rightarrow> True | x#xs \<Rightarrow> False"
+normal_form "case Z of Z \<Rightarrow> True | S x \<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 "case n of Z \<Rightarrow> True | S x \<Rightarrow> False"
+normal_form "(%(x,y). add x y) (S z,S z)"
+normal_form "filter (%x. x) ([True,False,x]@xs)"
+normal_form "filter Not ([True,False,x]@xs)"
+
+normal_form "0 + (n::nat)"
+normal_form "0 + Suc(n)"
+normal_form "0::nat"
+normal_form "Suc(n) + Suc m"
+normal_form "[] @ xs"
+normal_form "(x#xs) @ ys"
+normal_form "[x,y,z] @ [a,b,c]"
+normal_form "%(xs, ys). xs @ ys"
+normal_form "(%(xs, ys). xs @ ys) ([a, b, c], [d, e, f])"
+normal_form "%x. case x of None \<Rightarrow> False | Some y \<Rightarrow> True"
+normal_form "map (%x. case x of None \<Rightarrow> False | Some y \<Rightarrow> True) [None, Some ()]"
+
+normal_form "case n of None \<Rightarrow> True | Some((x,y),(u,v)) \<Rightarrow> False"
+normal_form "let ((x,y),(u,v)) = ((Z,Z),(Z,Z)) in add (add x y) (add u v)"
+normal_form "(%((x,y),(u,v)). add (add x y) (add u v)) ((Z,Z),(Z,Z))"
+normal_form "last[a,b,c]"
+normal_form "last([a,b,c]@xs)"
+normal_form " (0::nat) < (0::nat)"
+
+(* FIXME
+ won't work since it relies on
+ polymorphically used ad-hoc overloaded function:
+ normal_form "max 0 (0::nat)"
+*)
+
+text {*
+ Numerals still take their time\<dots>
+*}
+
+end
--- a/src/HOL/ex/nbe.thy Thu Jun 08 17:04:49 2006 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,122 +0,0 @@
-(* ID: $Id$
-
-Temporary test of nbe module.
-*)
-
-theory nbe
-imports Main
-begin
-
-ML "reset quick_and_dirty"
-
-norm_by_eval "True \<longrightarrow> p"
-
-(* FIXME Eventually the code generator should be able to handle this
-by re-generating the existing code for "or":
-
-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 Z)) (S(S(S(S(S Z)))))"
-
-norm_by_eval "[] @ []"
-norm_by_eval "[] @ xs"
-norm_by_eval "[] @ (xs:: 'b list)"
-norm_by_eval "[a::'d,b,c] @ xs"
-norm_by_eval "[%a::'x. a, %b. b, c] @ xs"
-norm_by_eval "[%a::'x. a, %b. b, c] @ [u,v]"
-norm_by_eval "map f (xs::'c list)"
-norm_by_eval "map f [x,y,z::'x]"
-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::'x]) (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::'x 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 "0::nat"
-norm_by_eval "Suc(n) + Suc m"
-norm_by_eval "[] @ xs"
-norm_by_eval "(x#xs) @ ys"
-norm_by_eval "[x,y,z] @ [a,b,c]"
-norm_by_eval "%(xs, ys). xs @ ys"
-norm_by_eval "(%(xs, ys). xs @ ys) ([a, b, c], [d, e, f])"
-norm_by_eval "%x. case x of None \<Rightarrow> False | Some y \<Rightarrow> True"
-norm_by_eval "map (%x. case x of None \<Rightarrow> False | Some y \<Rightarrow> True) [None, Some ()]"
-
-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))"
-norm_by_eval "last[a,b,c]"
-norm_by_eval "last([a,b,c]@xs)"
-norm_by_eval " (0::nat) < (0::nat)"
-
-(* FIXME
- won't work since it relies on
- polymorphically used ad-hoc overloaded function:
- norm_by_eval "max 0 (0::nat)"
-*)
-
-text {*
- Numerals still take their time\<dots>
-*}
-
-end