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Tries with Compression

This is the task corresponding to exercise 3. Tries with Compression.

Resources

Definitions File

```theory Defs
imports Main
begin

declare [[names_short]]
datatype bt = Lf bool | Nd bt bt

fun \<alpha> :: "bt \<Rightarrow> nat \<Rightarrow> bool list set" where
"\<alpha> (Lf b) d = (if b then {bs. length bs = d} else {})" |
"\<alpha> (Nd l r) d = Cons True ` \<alpha> l (d-1) \<union> Cons False ` \<alpha> r (d-1)"

fun ht :: "bt \<Rightarrow> nat" where
"ht (Lf _) = 0" |
"ht (Nd l r) = max (ht l) (ht r) + 1"

end```

Template File

```theory Submission
imports Defs
begin

fun isin :: "bt \<Rightarrow> bool list \<Rightarrow> bool" where
"isin _ = undefined"

fun inter :: "bt \<Rightarrow> bt \<Rightarrow> bt" where
"inter _ = undefined"

fun compressed :: "bt \<Rightarrow> bool" where
"compressed _ \<longleftrightarrow> undefined"

fun compress :: "bt \<Rightarrow> bt" where
"compress _ = undefined"

end```

Check File

```theory Check
imports Submission
begin

end```

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