Exercises/ex12/ex12.thy
 changeset 69842 985eb3b647ab parent 69841 d2283b15d2ca child 69848 5a47947a89db
equal inserted replaced
69841:d2283b15d2ca 69842:985eb3b647ab
`    22 "enq a (xs,ys) = balance (a#xs, ys)"`
`    22 "enq a (xs,ys) = balance (a#xs, ys)"`
`    23 `
`    23 `
`    24 fun deq :: "'a queue \<Rightarrow> 'a queue" where`
`    24 fun deq :: "'a queue \<Rightarrow> 'a queue" where`
`    25 "deq (xs,ys) = balance (xs, tl ys)"`
`    25 "deq (xs,ys) = balance (xs, tl ys)"`
`    26 `
`    26 `
`    27 text \<open>Note that we assume that the size computation in \<open>balance\<close> only takes constant time.`
`    27 text \<open>Again, we count only the newly allocated list cells.\<close>`
`    28 In reality the time is linear. How would you avoid that?\<close>`
`       `
`    29 `
`    28 `
`    30 fun t_enq :: "'a \<Rightarrow> 'a queue \<Rightarrow> nat" where`
`    29 fun t_enq :: "'a \<Rightarrow> 'a queue \<Rightarrow> nat" where`
`    31 "t_enq a (xs,ys) = 1 + (if size xs + 1 \<le> size ys then 0 else size xs + 1 + size ys)"`
`    30 "t_enq a (xs,ys) = 1 + (if size xs + 1 \<le> size ys then 0 else size xs + 1 + size ys)"`
`    32 `
`    31 `
`    33 fun t_deq :: "'a queue \<Rightarrow> nat" where`
`    32 fun t_deq :: "'a queue \<Rightarrow> nat" where`