list.Sorted generalized for elements of any type

.gitignore

@@ -164,4 +164,5 @@ why3.conf
 /modules/string/
 /modules/stack/
 /modules/queue/
+/modules/pqueue/
 

examples/programs/insertion_sort_list.mlw

@@ -5,7 +5,7 @@ module M
 
   use import int.Int
   use import list.Length
-  use import list.Sorted
+  use import list.SortedInt
   use import list.Permut
 
   let rec insert x l variant { length l } =

examples/programs/mergesort_list.mlw

@@ -5,7 +5,7 @@ module M
 
   use import int.Int
   use import list.Length
-  use import list.Sorted
+  use import list.SortedInt
   use import list.Append
   use import list.Permut
 

examples/programs/sorted_list.mlw

@@ -4,7 +4,7 @@ module FindInSortedList
 
   use import int.Int
   use import list.Mem
-  use import list.Sorted
+  use import list.SortedInt
 
   lemma Sorted_not_mem:
     forall x y : int, l : list int.

examples/programs/sorted_list/why3session.xml

 <?xml version="1.0" encoding="UTF-8"?>
 <!DOCTYPE why3session SYSTEM "why3session.dtd">
-<why3session name="programs/sorted_list/why3session.xml">
- <prover id="alt-ergo" name="Alt-Ergo" version="0.93"/>
- <prover id="coq" name="Coq" version="8.2pl1"/>
- <prover id="cvc3" name="CVC3" version="2.2"/>
- <prover id="gappa" name="Gappa" version="0.13.0"/>
- <prover id="simplify" name="Simplify" version="1.5.4"/>
- <prover id="z3" name="Z3" version="2.19"/>
- <file name="../sorted_list.mlw" verified="true" expanded="true">
-  <theory name="WP FindInSortedList" verified="true" expanded="true">
-   <goal name="Sorted_not_mem" sum="065ba337071029143930bed502bf4f54" proved="true" expanded="true" shape="amemV0aConsV1V2NIasortedaConsV1V2Iainfix <V0V1F">
-    <proof prover="alt-ergo" timelimit="20" edited="" obsolete="false">
-     <result status="valid" time="0.02"/>
+<why3session
+ name="examples/programs/sorted_list/why3session.xml">
+ <prover
+  id="alt-ergo"
+  name="Alt-Ergo"
+  version="0.93"/>
+ <prover
+  id="coq"
+  name="Coq"
+  version="8.3pl2"/>
+ <prover
+  id="cvc3"
+  name="CVC3"
+  version="2.2"/>
+ <prover
+  id="simplify"
+  name="Simplify"
+  version="1.5.4"/>
+ <prover
+  id="yices"
+  name="Yices"
+  version="1.0.27"/>
+ <prover
+  id="z3"
+  name="Z3"
+  version="2.19"/>
+ <file
+  name="../sorted_list.mlw"
+  verified="true"
+  expanded="true">
+  <theory
+   name="WP FindInSortedList"
+   verified="true"
+   expanded="true">
+   <goal
+    name="Sorted_not_mem"
+    sum="0e5b025f01157d802e4968ce08ccd4c4"
+    proved="true"
+    expanded="true"
+    shape="amemV0aConsV1V2NIasortedaConsV1V2Iainfix <V0V1F">
+    <proof
+     prover="alt-ergo"
+     timelimit="20"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="0.01"/>
     </proof>
    </goal>
-   <goal name="WP_parameter find" expl="parameter find" sum="3088f11d3e64fa3492117d9f16ba16b0" proved="true" expanded="true" shape="CV1aNilamemV0V1qfaConsVVamemV0V1qainfix =V4aTrueAainfix >V0V2Oainfix =V0V2IamemV0V3qainfix =V4aTrueFAasortedV3IasortedV1FF">
-    <proof prover="alt-ergo" timelimit="20" edited="" obsolete="false">
+   <goal
+    name="WP_parameter find"
+    expl="parameter find"
+    sum="d06791b94cf6be238e76a7a9c8c63a80"
+    proved="true"
+    expanded="true"
+    shape="CV1aNilamemV0V1qfaConsVVamemV0V1qainfix =V4aTrueAainfix >V0V2Oainfix =V0V2IamemV0V3qainfix =V4aTrueFAasortedV3IasortedV1FF">
+    <proof
+     prover="alt-ergo"
+     timelimit="20"
+     edited=""
+     obsolete="false">
      <result status="valid" time="0.03"/>
     </proof>
    </goal>

modules/queue.mlw

@@ -25,7 +25,7 @@ module Queue
                           | Cons x t -> result = x /\ q.elts = t end }
     | Empty -> { q.elts = old q.elts = Nil }
 
-  val top:
+  val peek:
     q: t 'a ->
     {}
     'a
@@ -35,7 +35,7 @@ module Queue
 
   val clear: q: t 'a -> {} unit writes q {q.elts = Nil }
 
-  val copy: q: t 'a -> {} t 'a { result = q }
+  val copy: q: t 'a -> {} t 'a reads q { result = q }
 
   val is_empty:
     q: t 'a -> {} bool reads q { result=True <-> q.elts = Nil }
@@ -61,9 +61,9 @@ module Test
   let test1 () =
     let s = Queue.create () in
     Queue.push 1 s;
-    let x = Queue.top s in assert { x = 1 };
+    let x = Queue.peek s in assert { x = 1 };
     Queue.push 2 s;
-    let x = Queue.top s in assert { x = 1 };
+    let x = Queue.peek s in assert { x = 1 };
     ()
 
 end

theories/list.why

@@ -132,22 +132,31 @@ end
 theory Sorted
 
   use export List
-  use import int.Int
 
-  inductive sorted (l: list int) =
+  type t
+  predicate le t t
+
+  inductive sorted (l: list t) =
     | Sorted_Nil:
         sorted Nil
     | Sorted_One:
-        forall x: int. sorted (Cons x Nil)
+        forall x: t. sorted (Cons x Nil)
     | Sorted_Two:
-        forall x y: int, l: list int.
-        x <= y -> sorted (Cons y l) -> sorted (Cons x (Cons y l))
+        forall x y: t, l: list t.
+        le x y -> sorted (Cons y l) -> sorted (Cons x (Cons y l))
 
   use import Mem
 
-  lemma Sorted_mem:
-    forall x: int, l: list int.
-    (forall y: int. mem y l -> x <= y) /\ sorted l <-> sorted (Cons x l)
+  lemma sorted_mem:
+    forall x: t, l: list t.
+    (forall y: t. mem y l -> le x y) /\ sorted l <-> sorted (Cons x l)
+
+end
+
+theory SortedInt
+
+  use import int.Int
+  clone export Sorted with type t = int, predicate le = (<=)
 
 end