## Traversing a tree inorder, filling an array

From Rustan Leino's tutorial on Dafny at VSTTE 2012

**Authors:** Jean-Christophe Filliâtre

**Topics:** Trees

**Tools:** Why3

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(* Traversing a tree inorder, filling an array with the elements (from Rustan Leino's tutorial on Dafny at VSTTE 2012) Author: Jean-Christophe Filliatre (CNRS) *) module Fill use import int.Int use import array.Array type elt type tree = Null | Node tree elt tree predicate contains (t: tree) (x: elt) = match t with | Null -> false | Node l y r -> contains l x || x = y || contains r x end let rec fill (t: tree) (a: array elt) (start: int) : int requires { 0 <= start <= length a } ensures { start <= result <= length a } ensures { forall i: int. 0 <= i < start -> a[i] = (old a)[i] } ensures { forall i: int. start <= i < result -> contains t a[i] } variant { t } = match t with | Null -> start | Node l x r -> let res = fill l a start in if res <> length a then begin a[res] <- x; fill r a (res + 1) end else res end end

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