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Why3
why3
Commits
4e039176
Commit
4e039176
authored
Nov 24, 2015
by
Jean-Christophe Filliâtre
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gallery: new example tree_height
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examples/tree_height.mlw
examples/tree_height.mlw
+74
-0
examples/tree_height/why3session.xml
examples/tree_height/why3session.xml
+61
-0
examples/tree_height/why3shapes.gz
examples/tree_height/why3shapes.gz
+0
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examples/tree_height.mlw
0 → 100644
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4e039176
(** Computing the height of a tree in CPS style
(author: Jean-Christophe Filliâtre) *)
module HeightCPS
use import int.Int
use import int.MinMax
use import bintree.Tree
use import bintree.Height
use HighOrd
function height_cps (t: tree 'a) (k: int -> 'b) : 'b =
match t with
| Empty -> k 0
| Node l _ r ->
height_cps l (\ hl.
height_cps r (\ hr.
k (1 + max hl hr)))
end
function height1 (t: tree 'a) : int = height_cps t (\ h. h)
lemma height_cps_correct:
forall t: tree 'a, k: int -> 'b. height_cps t k = k (height t)
lemma height1_correct:
forall t: tree 'a. height1 t = height t
end
(** Computing the height of a tree with an explicit stack
(code: Andrei Paskevich / proof: Jean-Christophe Filliâtre) *)
module HeightStack
use import int.Int
use import int.MinMax
use import list.List
use import bintree.Tree
use import bintree.Size
use import bintree.Height
type stack 'a = list (int, tree 'a)
function heights (s: stack 'a) : int =
match s with
| Nil -> 0
| Cons (h, t) s' -> max (h + height t) (heights s')
end
function sizes (s: stack 'a) : int =
match s with
| Nil -> 0
| Cons (_, t) s' -> size t + sizes s'
end
lemma sizes_nonneg: forall s: stack 'a. sizes s >= 0
let rec height_stack (m: int) (s: stack 'a) : int
requires { m >= 0 }
variant { sizes s, s }
ensures { result = max m (heights s) }
= match s with
| Nil -> m
| Cons (h, Empty) s' -> height_stack (max m h) s'
| Cons (h, Node l _ r) s' -> height_stack m (Cons (h+1,l) (Cons (h+1,r) s'))
end
let height1 (t: tree 'a) : int
ensures { result = height t }
= height_stack 0 (Cons (0, t) Nil)
end
examples/tree_height/why3session.xml
0 → 100644
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4e039176
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session
shape_version=
"4"
>
<prover
id=
"0"
name=
"Alt-Ergo"
version=
"0.99.1"
timelimit=
"6"
memlimit=
"1000"
/>
<prover
id=
"1"
name=
"CVC4"
version=
"1.4"
timelimit=
"6"
memlimit=
"1000"
/>
<prover
id=
"3"
name=
"Eprover"
version=
"1.8-001"
timelimit=
"6"
memlimit=
"1000"
/>
<prover
id=
"4"
name=
"Vampire"
version=
"0.6"
timelimit=
"6"
memlimit=
"1000"
/>
<file
name=
"../tree_height.mlw"
>
<theory
name=
"HeightCPS"
sum=
"bf5f8a1bb7474cc558d4defd10f63945"
>
<goal
name=
"height_cps_correct"
>
<transf
name=
"induction_ty_lex"
>
<goal
name=
"height_cps_correct.1"
expl=
"1."
>
<proof
prover=
"0"
><result
status=
"valid"
time=
"0.02"
steps=
"20"
/></proof>
</goal>
</transf>
</goal>
<goal
name=
"height1_correct"
>
<proof
prover=
"0"
><result
status=
"valid"
time=
"0.01"
steps=
"3"
/></proof>
</goal>
</theory>
<theory
name=
"HeightStack"
sum=
"9eefeb26becfef0638674737a4335571"
>
<goal
name=
"sizes_nonneg"
>
<transf
name=
"induction_ty_lex"
>
<goal
name=
"sizes_nonneg.1"
expl=
"1."
>
<proof
prover=
"3"
><result
status=
"valid"
time=
"0.10"
/></proof>
<proof
prover=
"4"
><result
status=
"valid"
time=
"0.23"
/></proof>
</goal>
</transf>
</goal>
<goal
name=
"WP_parameter height_stack"
expl=
"VC for height_stack"
>
<transf
name=
"split_goal_wp"
>
<goal
name=
"WP_parameter height_stack.1"
expl=
"1. postcondition"
>
<proof
prover=
"0"
><result
status=
"valid"
time=
"0.01"
steps=
"5"
/></proof>
</goal>
<goal
name=
"WP_parameter height_stack.2"
expl=
"2. variant decrease"
>
<proof
prover=
"0"
><result
status=
"valid"
time=
"0.00"
steps=
"36"
/></proof>
</goal>
<goal
name=
"WP_parameter height_stack.3"
expl=
"3. precondition"
>
<proof
prover=
"0"
><result
status=
"valid"
time=
"0.02"
steps=
"8"
/></proof>
</goal>
<goal
name=
"WP_parameter height_stack.4"
expl=
"4. postcondition"
>
<proof
prover=
"1"
><result
status=
"valid"
time=
"0.03"
/></proof>
</goal>
<goal
name=
"WP_parameter height_stack.5"
expl=
"5. variant decrease"
>
<proof
prover=
"0"
><result
status=
"valid"
time=
"0.02"
steps=
"51"
/></proof>
</goal>
<goal
name=
"WP_parameter height_stack.6"
expl=
"6. precondition"
>
<proof
prover=
"0"
><result
status=
"valid"
time=
"0.00"
steps=
"4"
/></proof>
</goal>
<goal
name=
"WP_parameter height_stack.7"
expl=
"7. postcondition"
>
<proof
prover=
"1"
><result
status=
"valid"
time=
"0.04"
/></proof>
</goal>
</transf>
</goal>
<goal
name=
"WP_parameter height1"
expl=
"VC for height1"
>
<proof
prover=
"1"
><result
status=
"valid"
time=
"0.02"
/></proof>
</goal>
</theory>
</file>
</why3session>
examples/tree_height/why3shapes.gz
0 → 100644
View file @
4e039176
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