ThreeIdem is only in the logic

examples/three_idem_ring.mlw

@@ -6,29 +6,24 @@
 module ThreeIdempotentRing
 
        use int.Int
-       type t
-       val constant zero : t
-       val function (+) t t : t
-       val function ( *) t t : t
 
-       clone import algebra.Ring as R with
-       	     type t = t, constant zero = zero, function (+) = (+), function ( *) = ( *),
+       clone export algebra.Ring with
        	     axiom .
 
        (** Define multiplication by an integer recursively *)
-       let rec function mul (x : t) (n : int) : t
+       let rec ghost function mul (x : t) (n : int) : t
        	   requires { n >= 0 }
        	   variant { n }
        =
-       	if n = 0 then zero else x + mul x (n-1)
+       	if n = 0 then pure{zero} else let r = mul x (n-1) in pure {x + r}
 
        (** We get lemmas from the why3 library *)
-       clone import int.Exponentiation as Mul with
-       	     type t = t, constant one = zero,
-	     function ( *) = (+), function power = mul, lemma .
+       clone int.Exponentiation with type t = t,
+       	     constant one = zero, function ( * ) = (+), function power = mul,
+       	     lemma .
 
 
-(** {2 General results about unitary rings} *)
+(** {2 General results about rings} *)
 
 (** First results : *)
 

examples/three_idem_ring/why3session.xml

@@ -13,19 +13,19 @@
  <goal name="VC mul" expl="VC for mul" proved="true">
  <proof prover="0"><result status="valid" time="0.03"/></proof>
  </goal>
- <goal name="Mul.Assoc" proved="true">
+ <goal name="Exponentiation.Assoc" proved="true">
  <proof prover="0"><result status="valid" time="0.01"/></proof>
  </goal>
- <goal name="Mul.Unit_def_l" proved="true">
+ <goal name="Exponentiation.Unit_def_l" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
- <goal name="Mul.Unit_def_r" proved="true">
+ <goal name="Exponentiation.Unit_def_r" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
- <goal name="Mul.Power_0" proved="true">
+ <goal name="Exponentiation.Power_0" proved="true">
  <proof prover="0"><result status="valid" time="0.01"/></proof>
  </goal>
- <goal name="Mul.Power_s" proved="true">
+ <goal name="Exponentiation.Power_s" proved="true">
  <proof prover="0"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="simpl_left" proved="true">
@@ -67,11 +67,9 @@
  <proof prover="0"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC mul_star_l" expl="VC for mul_star_l" proved="true">
- <proof prover="1"><result status="valid" time="1.02" steps="108"/></proof>
  <proof prover="4"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC mul_star_r" expl="VC for mul_star_r" proved="true">
- <proof prover="1"><result status="valid" time="3.46" steps="124"/></proof>
  <proof prover="4"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="null_star_l" proved="true">
@@ -143,14 +141,14 @@
   <proof prover="0"><result status="valid" time="0.02"/></proof>
   </goal>
   <goal name="null2_comm.2" proved="true">
-  <proof prover="0"><result status="valid" time="0.22"/></proof>
+  <proof prover="0"><result status="valid" time="0.42"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="swap_equality" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="swap_equality.0" proved="true">
-  <proof prover="0"><result status="valid" time="1.57"/></proof>
+  <proof prover="0"><result status="valid" time="2.30"/></proof>
   </goal>
   <goal name="swap_equality.1" proved="true">
   <proof prover="0"><result status="valid" time="0.01"/></proof>
@@ -171,7 +169,7 @@
   <proof prover="0"><result status="valid" time="0.35"/></proof>
   </goal>
   <goal name="swap_equality.7" proved="true">
-  <proof prover="0"><result status="valid" time="0.23"/></proof>
+  <proof prover="0"><result status="valid" time="0.42"/></proof>
   </goal>
   <goal name="swap_equality.8" proved="true">
   <proof prover="0"><result status="valid" time="0.02"/></proof>