
diff -r 50dd4fc40fcb -r 168f9a5824a8 src/HOL/Data_Structures/Time_Examples.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Data_Structures/Time_Examples.thy	Thu Feb 06 17:28:27 2025 +0100
@@ -0,0 +1,70 @@
+(*
+Author: Jonas Stahl
+
+Nonstandard examples of the time function definition commands.
+*)
+
+theory Time_Examples
+imports Define_Time_Function
+begin
+
+fun even :: "nat \<Rightarrow> bool"
+  and odd :: "nat \<Rightarrow> bool" where
+  "even 0 = True"
+| "odd 0 = False"
+| "even (Suc n) = odd n"
+| "odd (Suc n) = even n"
+time_fun even odd
+
+locale locTests =
+  fixes f :: "'a \<Rightarrow> 'b"
+   and  T_f :: "'a \<Rightarrow> nat"
+begin
+
+fun simple where
+  "simple a = f a"
+time_fun simple
+
+fun even :: "'a list \<Rightarrow> 'b list" and odd :: "'a list \<Rightarrow> 'b list" where
+  "even [] = []"
+| "odd [] = []"
+| "even (x#xs) = f x # odd xs"
+| "odd (x#xs) = even xs"
+time_fun even odd
+
+fun locSum :: "nat list \<Rightarrow> nat" where
+  "locSum [] = 0"
+| "locSum (x#xs) = x + locSum xs"
+time_fun locSum
+
+fun map :: "'a list \<Rightarrow> 'b list" where
+  "map [] = []"
+| "map (x#xs) = f x # map xs"
+time_fun map
+
+end
+
+definition "let_lambda a b c \<equiv> let lam = (\<lambda>a b. a + b) in lam a (lam b c)"
+time_fun let_lambda
+
+partial_function (tailrec) collatz :: "nat \<Rightarrow> bool" where
+  "collatz n = (if n \<le> 1 then True
+                else if n mod 2 = 0 then collatz (n div 2)
+                else collatz (3 * n + 1))"
+
+text \<open>This is the expected time function:\<close>
+partial_function (option) T_collatz' :: "nat \<Rightarrow> nat option" where
+  "T_collatz' n = (if n \<le> 1 then Some 0
+                else if n mod 2 = 0 then Option.bind (T_collatz' (n div 2)) (\<lambda>k. Some (Suc k))
+                else Option.bind (T_collatz' (3 * n + 1)) (\<lambda>k. Some (Suc k)))"
+time_fun_0 "(mod)"
+time_partial_function collatz
+
+text \<open>Proof that they are the same up to 20:\<close>
+lemma setIt: "P i \<Longrightarrow> \<forall>n \<in> {Suc i..j}. P n \<Longrightarrow> \<forall>n \<in> {i..j}. P n"
+  by (metis atLeastAtMost_iff le_antisym not_less_eq_eq)
+lemma "\<forall>n \<in> {2..20}. T_collatz n = T_collatz' n"
+  apply (rule setIt, simp add: T_collatz.simps T_collatz'.simps, simp)+
+  by (simp add: T_collatz.simps T_collatz'.simps)
+
+end
\ No newline at end of file




