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Commit 13bbd6e2 authored by Martin Clochard's avatar Martin Clochard
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new example (to be completed): finger trees

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examples/finger_trees.mlw 0 → 100644
View file @ 13bbd6e2
module FingerTrees
use import int.Int
use import list.List
use import list.Length
use import list.Append
type digit 'a =
| One 'a
| Two 'a 'a
| Three 'a 'a 'a
| Four 'a 'a 'a 'a
function d_m (b:digit 'a) : list 'a = match b with
| One x -> Cons x Nil
| Two y x -> Cons y (Cons x Nil)
| Three z y x -> Cons z (Cons y (Cons x Nil))
| Four u z y x -> Cons u (Cons z (Cons y (Cons x Nil)))
end
type node 'a =
| Node2 'a 'a
| Node3 'a 'a 'a
function node_cons (nd:node 'a) (l:list 'a) : list 'a = match nd with
| Node2 x y -> Cons x (Cons y l)
| Node3 x y z -> Cons x (Cons y (Cons z l))
end
let lemma node_cons_app (nd:node 'a) (p q:list 'a)
ensures { node_cons nd (p++q) = node_cons nd p ++ q }
= match nd with Node2 _ _ -> "keep_on_simp" () | _ -> () end
function flatten (l:list (node 'a)) : list 'a = match l with
| Nil -> Nil
| Cons nd q -> node_cons nd (flatten q)
end
type t 'a =
| Empty
| Single (digit 'a)
| Deep (digit 'a) (t (node 'a)) (digit 'a)
function t_m (t:t 'a) : list 'a = match t with
| Empty -> Nil
| Single x -> d_m x
| Deep l m r -> d_m l ++ flatten (t_m m) ++ d_m r
end
let d_cons (x:'a) (d:digit 'a) : (digit 'a,list (node 'a))
returns { (b,o) -> Cons x (d_m d) = d_m b ++ flatten o /\ length o <= 1 }
= match d with
| One y -> (Two x y , Nil)
| Two y z -> (Three x y z , Nil)
| Three y z t -> (Four x y z t , Nil)
| Four y z t u -> (Two x y , Cons (Node3 z t u) Nil)
end
let rec cons (x:'a) (t:t 'a) : t 'a
ensures { t_m result = Cons x (t_m t) }
variant { t }
= match t with
| Empty -> Single (One x)
| Single d -> Deep (One x) Empty d
| Deep lf md rg -> let (lf2 , rem) = d_cons x lf in
match rem with
| Nil -> Deep lf2 md rg
| Cons x q -> assert { q = Nil };
Deep lf2 (cons x md) rg
end
end
end
examples/finger_trees/why3session.xml 0 → 100644
View file @ 13bbd6e2
<?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="5" memlimit="1000"/>
<prover id="1" name="CVC3" version="2.4.1" timelimit="5" memlimit="1000"/>
<prover id="2" name="CVC4" version="1.4" timelimit="5" memlimit="1000"/>
<file name="../finger_trees.mlw" expanded="true">
<theory name="FingerTrees" sum="c53ab3527c4f3a9462387424b3a2842d" expanded="true">
<goal name="WP_parameter node_cons_app" expl="VC for node_cons_app">
<transf name="split_goal_wp">
<goal name="WP_parameter node_cons_app.1" expl="1. postcondition">
<proof prover="0"><result status="valid" time="0.04" steps="74"/></proof>
</goal>
<goal name="WP_parameter node_cons_app.2" expl="2. postcondition">
<proof prover="0"><result status="valid" time="0.04" steps="80"/></proof>
</goal>
</transf>
</goal>
<goal name="WP_parameter d_cons" expl="VC for d_cons">
<transf name="split_goal_wp">
<goal name="WP_parameter d_cons.1" expl="1. postcondition">
<proof prover="0"><result status="valid" time="0.03" steps="70"/></proof>
</goal>
<goal name="WP_parameter d_cons.2" expl="2. postcondition">
<proof prover="0"><result status="valid" time="0.04" steps="75"/></proof>
</goal>
<goal name="WP_parameter d_cons.3" expl="3. postcondition">
<proof prover="0"><result status="valid" time="0.03" steps="80"/></proof>
</goal>
<goal name="WP_parameter d_cons.4" expl="4. postcondition">
<proof prover="1"><result status="valid" time="0.03"/></proof>
<proof prover="2"><result status="valid" time="0.31"/></proof>
</goal>
</transf>
</goal>
<goal name="WP_parameter cons" expl="VC for cons" expanded="true">
<transf name="split_goal_wp" expanded="true">
<goal name="WP_parameter cons.1" expl="1. postcondition">
<proof prover="0"><result status="valid" time="0.02" steps="29"/></proof>
</goal>
<goal name="WP_parameter cons.2" expl="2. postcondition">
<proof prover="0"><result status="valid" time="0.07" steps="151"/></proof>
</goal>
<goal name="WP_parameter cons.3" expl="3. postcondition">
<proof prover="0"><result status="valid" time="0.18" steps="184"/></proof>
</goal>
<goal name="WP_parameter cons.4" expl="4. assertion">
<proof prover="0"><result status="valid" time="0.11" steps="140"/></proof>
</goal>
<goal name="WP_parameter cons.5" expl="5. variant decrease">
<proof prover="0"><result status="valid" time="0.02" steps="28"/></proof>
</goal>
<goal name="WP_parameter cons.6" expl="6. postcondition" expanded="true">
<metas
expanded="true">
<ts_pos name="real" arity="0" id="2"
ip_theory="BuiltIn">
<ip_library name="why3"/>
<ip_library name="BuiltIn"/>
<ip_qualid name="real"/>
</ts_pos>
<ts_pos name="bool" arity="0" id="3"
ip_theory="Bool">
<ip_library name="why3"/>
<ip_library name="Bool"/>
<ip_qualid name="bool"/>
</ts_pos>
<ts_pos name="tuple0" arity="0" id="20"
ip_theory="Tuple0">
<ip_library name="why3"/>
<ip_library name="Tuple0"/>
<ip_qualid name="tuple0"/>
</ts_pos>
<ts_pos name="unit" arity="0" id="21"
ip_theory="Unit">
<ip_library name="why3"/>
<ip_library name="Unit"/>
<ip_qualid name="unit"/>
</ts_pos>
<ts_pos name="&apos;mark" arity="0" id="61"
ip_theory="Mark">
<ip_library name="why3"/>
<ip_library name="Mark"/>
<ip_qualid name="&apos;mark"/>
</ts_pos>
<ts_pos name="tuple2" arity="2" id="863"
ip_theory="Tuple2">
<ip_library name="why3"/>
<ip_library name="Tuple2"/>
<ip_qualid name="tuple2"/>
</ts_pos>
<ls_pos name="infix =" id="10"
ip_theory="BuiltIn">
<ip_library name="why3"/>
<ip_library name="BuiltIn"/>
<ip_qualid name="infix ="/>
</ls_pos>
<ls_pos name="zero" id="147"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="zero"/>
</ls_pos>
<ls_pos name="one" id="148"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="one"/>
</ls_pos>
<ls_pos name="infix &lt;" id="149"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="infix &lt;"/>
</ls_pos>
<ls_pos name="infix &gt;" id="152"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="infix &gt;"/>
</ls_pos>
<ls_pos name="infix +" id="1318"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="infix +"/>
</ls_pos>
<ls_pos name="prefix -" id="1319"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="prefix -"/>
</ls_pos>
<ls_pos name="infix *" id="1320"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="infix *"/>
</ls_pos>
<ls_pos name="infix -" id="1368"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="infix -"/>
</ls_pos>
<ls_pos name="infix &gt;=" id="1388"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="infix &gt;="/>
</ls_pos>
<ls_pos name="mem" id="2121"
ip_theory="Mem">
<ip_library name="list"/>
<ip_qualid name="mem"/>
</ls_pos>
<pr_pos name="Assoc" id="1321"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CommutativeGroup"/>
<ip_qualid name="Assoc"/>
</pr_pos>
<pr_pos name="Unit_def_l" id="1328"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CommutativeGroup"/>
<ip_qualid name="Unit_def_l"/>
</pr_pos>
<pr_pos name="Unit_def_r" id="1331"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CommutativeGroup"/>
<ip_qualid name="Unit_def_r"/>
</pr_pos>
<pr_pos name="Inv_def_l" id="1334"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CommutativeGroup"/>
<ip_qualid name="Inv_def_l"/>
</pr_pos>
<pr_pos name="Inv_def_r" id="1337"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CommutativeGroup"/>
<ip_qualid name="Inv_def_r"/>
</pr_pos>
<pr_pos name="Comm" id="1340"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CommutativeGroup"/>
<ip_qualid name="Comm"/>
<ip_qualid name="Comm"/>
</pr_pos>
<pr_pos name="Assoc" id="1345"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Assoc"/>
<ip_qualid name="Assoc"/>
</pr_pos>
<pr_pos name="Mul_distr_l" id="1352"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Mul_distr_l"/>
</pr_pos>
<pr_pos name="Mul_distr_r" id="1359"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Mul_distr_r"/>
</pr_pos>
<pr_pos name="Comm" id="1377"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Comm"/>
<ip_qualid name="Comm"/>
</pr_pos>
<pr_pos name="Unitary" id="1382"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Unitary"/>
</pr_pos>
<pr_pos name="NonTrivialRing" id="1385"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="NonTrivialRing"/>
</pr_pos>
<pr_pos name="Refl" id="1397"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Refl"/>
</pr_pos>
<pr_pos name="Trans" id="1400"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Trans"/>
</pr_pos>
<pr_pos name="Antisymm" id="1407"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Antisymm"/>
</pr_pos>
<pr_pos name="Total" id="1412"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Total"/>
</pr_pos>
<pr_pos name="ZeroLessOne" id="1417"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="ZeroLessOne"/>
</pr_pos>
<pr_pos name="CompatOrderAdd" id="1418"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CompatOrderAdd"/>
</pr_pos>
<pr_pos name="CompatOrderMult" id="1425"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CompatOrderMult"/>
</pr_pos>
<pr_pos name="Length_nonnegative" id="2114"
ip_theory="Length">
<ip_library name="list"/>
<ip_qualid name="Length_nonnegative"/>
</pr_pos>
<pr_pos name="Length_nil" id="2117"
ip_theory="Length">
<ip_library name="list"/>
<ip_qualid name="Length_nil"/>
</pr_pos>
<pr_pos name="Append_l_nil" id="3506"
ip_theory="Append">
<ip_library name="list"/>
<ip_qualid name="Append_l_nil"/>
</pr_pos>
<pr_pos name="Append_length" id="3509"
ip_theory="Append">
<ip_library name="list"/>
<ip_qualid name="Append_length"/>
</pr_pos>
<pr_pos name="mem_append" id="3514"
ip_theory="Append">
<ip_library name="list"/>
<ip_qualid name="mem_append"/>
</pr_pos>
<pr_pos name="mem_decomp" id="3521"
ip_theory="Append">
<ip_library name="list"/>
<ip_qualid name="mem_decomp"/>
</pr_pos>
<meta name="remove_logic">
<meta_arg_ls id="10"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="147"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="148"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="149"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="152"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="1318"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="1319"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="1320"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="1368"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="1388"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="2121"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1321"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1328"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1331"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1334"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1337"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1340"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1345"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1352"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1359"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1377"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1382"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1385"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1397"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1400"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1407"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1412"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1417"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1418"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="1425"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="2114"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="2117"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="3506"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="3509"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="3514"/>
</meta>
<meta name="remove_prop">
<meta_arg_pr id="3521"/>
</meta>
<meta name="remove_type">
<meta_arg_ts id="2"/>
</meta>
<meta name="remove_type">
<meta_arg_ts id="3"/>
</meta>
<meta name="remove_type">
<meta_arg_ts id="20"/>
</meta>
<meta name="remove_type">
<meta_arg_ts id="21"/>
</meta>
<meta name="remove_type">
<meta_arg_ts id="61"/>
</meta>
<meta name="remove_type">
<meta_arg_ts id="863"/>
</meta>
<goal name="WP_parameter cons.6" expl="6. postcondition" expanded="true">
<transf name="eliminate_builtin" expanded="true">
<goal name="WP_parameter cons.6.1" expl="1. postcondition" expanded="true">
<proof prover="0"><result status="valid" time="0.10" steps="271"/></proof>
</goal>
</transf>
</goal>
</metas>
</goal>
</transf>
</goal>
</theory>
</file>
</why3session>
examples/random_access_list.mlw
View file @ 13bbd6e2
......@@ -38,9 +38,6 @@ module RandomAccessList
| Nil -> ()
end
(*lemma length_flatten:
forall l: list ('a, 'a). length (flatten l) = 2 * length l*)
function elements (l: ral 'a) : list 'a
= match l with
| Empty -> Nil
......
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