examples(wip): 2wp_gen

examples/in_progress/2wp_gen/Makefile

 SHELL=/bin/bash
 REPLAY=why3 replay -L .
-MLW=base choice ho_set ho_rel fn order transfinite game
+MLW=base choice ho_set ho_rel fn order transfinite game game_fmla
 
 replay:
 	@exe() { echo "$$0 $$@"; "$$@"; };\

examples/in_progress/2wp_gen/base/why3session.xml

@@ -2,13 +2,13 @@
 <!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="1.00.prv" timelimit="5" steplimit="1" memlimit="1000"/>
+<prover id="1" name="Alt-Ergo" version="1.01" timelimit="5" steplimit="1" memlimit="1000"/>
 <file name="../base.mlw">
 <theory name="Fun" sum="d41d8cd98f00b204e9800998ecf8427e">
 </theory>
 <theory name="FunExt" sum="74d4af5538daa9eb9ddee6284a05e5bf">
  <goal name="WP_parameter extensional" expl="VC for extensional">
- <proof prover="0"><result status="valid" time="0.00" steps="2"/></proof>
+ <proof prover="1"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
 </theory>
 <theory name="FunCategory" sum="d41d8cd98f00b204e9800998ecf8427e">
@@ -19,34 +19,34 @@
   <goal name="ext.1" expl="1.">
   <transf name="inline_goal">
    <goal name="ext.1.1" expl="1.">
-   <proof prover="0"><result status="valid" time="0.00" steps="2"/></proof>
+   <proof prover="1"><result status="valid" time="0.00" steps="2"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="ext.2" expl="2.">
-  <proof prover="0"><result status="valid" time="0.00" steps="3"/></proof>
+  <proof prover="1"><result status="valid" time="0.00" steps="3"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="assoc">
- <proof prover="0"><result status="valid" time="0.00" steps="4"/></proof>
+ <proof prover="1"><result status="valid" time="0.00" steps="4"/></proof>
  </goal>
  <goal name="neutral">
- <proof prover="0"><result status="valid" time="0.00" steps="9"/></proof>
+ <proof prover="1"><result status="valid" time="0.00" steps="9"/></proof>
  </goal>
  <goal name="FunExt.extensionality">
- <proof prover="0"><result status="valid" time="0.00" steps="2"/></proof>
+ <proof prover="1"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
  <goal name="FunCategory.assoc">
- <proof prover="0"><result status="valid" time="0.00" steps="2"/></proof>
+ <proof prover="1"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
  <goal name="FunCategory.neutral">
- <proof prover="0"><result status="valid" time="0.01" steps="10"/></proof>
+ <proof prover="1"><result status="valid" time="0.01" steps="10"/></proof>
  </goal>
 </theory>
 <theory name="Set" sum="8dc39e2ae96fd0498b0d50bb47f235eb">
  <goal name="sext_is_ext">
- <proof prover="0"><result status="valid" time="0.00" steps="4"/></proof>
+ <proof prover="1"><result status="valid" time="0.00" steps="4"/></proof>
  </goal>
 </theory>
 <theory name="Rel" sum="d41d8cd98f00b204e9800998ecf8427e">
@@ -63,66 +63,66 @@
  <goal name="extensionality">
  <transf name="split_goal_wp">
   <goal name="extensionality.1" expl="1.">
-  <proof prover="0"><result status="valid" time="0.01" steps="4"/></proof>
+  <proof prover="1"><result status="valid" time="0.01" steps="4"/></proof>
   </goal>
   <goal name="extensionality.2" expl="2.">
-  <proof prover="0"><result status="valid" time="0.01" steps="4"/></proof>
+  <proof prover="1"><result status="valid" time="0.01" steps="4"/></proof>
   </goal>
   <goal name="extensionality.3" expl="3.">
-  <proof prover="0"><result status="valid" time="0.00" steps="3"/></proof>
+  <proof prover="1"><result status="valid" time="0.00" steps="3"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="assoc">
  <transf name="compute_specified">
   <goal name="assoc.1" expl="1.">
-  <proof prover="0"><result status="valid" time="0.01" steps="12"/></proof>
+  <proof prover="1"><result status="valid" time="0.01" steps="12"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="reverse_antimorphism">
- <proof prover="0"><result status="valid" time="0.01" steps="27"/></proof>
+ <proof prover="1"><result status="valid" time="0.01" steps="27"/></proof>
  </goal>
  <goal name="reverse_antimorphism_id">
- <proof prover="0"><result status="valid" time="0.01" steps="9"/></proof>
+ <proof prover="1"><result status="valid" time="0.01" steps="9"/></proof>
  </goal>
  <goal name="reverse_involution">
- <proof prover="0"><result status="valid" time="0.01" steps="5"/></proof>
+ <proof prover="1"><result status="valid" time="0.01" steps="5"/></proof>
  </goal>
  <goal name="neutral">
  <transf name="compute_specified">
   <goal name="neutral.1" expl="1.">
-  <proof prover="0"><result status="valid" time="0.00" steps="14"/></proof>
+  <proof prover="1"><result status="valid" time="0.00" steps="14"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="RelExt.extensionality">
- <proof prover="0"><result status="valid" time="0.01" steps="2"/></proof>
+ <proof prover="1"><result status="valid" time="0.01" steps="2"/></proof>
  </goal>
  <goal name="RelCategory.assoc">
- <proof prover="0"><result status="valid" time="0.01" steps="2"/></proof>
+ <proof prover="1"><result status="valid" time="0.01" steps="2"/></proof>
  </goal>
  <goal name="RelCategory.reverse_antimorphism">
- <proof prover="0"><result status="valid" time="0.01" steps="2"/></proof>
+ <proof prover="1"><result status="valid" time="0.01" steps="2"/></proof>
  </goal>
  <goal name="RelCategory.reverse_antimorphism_id">
- <proof prover="0"><result status="valid" time="0.00" steps="2"/></proof>
+ <proof prover="1"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
  <goal name="RelCategory.reverse_involution">
- <proof prover="0"><result status="valid" time="0.01" steps="2"/></proof>
+ <proof prover="1"><result status="valid" time="0.01" steps="2"/></proof>
  </goal>
  <goal name="RelCategory.neutral">
- <proof prover="0"><result status="valid" time="0.01" steps="11"/></proof>
+ <proof prover="1"><result status="valid" time="0.01" steps="11"/></proof>
  </goal>
 </theory>
 <theory name="SubsetOrder" sum="d41d8cd98f00b204e9800998ecf8427e">
 </theory>
 <theory name="SetProofs" sum="0be5aa0fe01aa313571b5c5ef55cb77b">
  <goal name="anti_subset">
- <proof prover="0"><result status="valid" time="0.00" steps="7"/></proof>
+ <proof prover="1"><result status="valid" time="0.00" steps="7"/></proof>
  </goal>
  <goal name="SubsetOrder.subset_order">
- <proof prover="0"><result status="valid" time="0.02" steps="65"/></proof>
+ <proof prover="1"><result status="valid" time="0.02" steps="65"/></proof>
  </goal>
 </theory>
 <theory name="Image" sum="d41d8cd98f00b204e9800998ecf8427e">

examples/in_progress/2wp_gen/choice/why3session.xml

@@ -2,14 +2,14 @@
 <!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="1.00.prv" timelimit="5" steplimit="1" memlimit="1000"/>
+<prover id="1" name="Alt-Ergo" version="1.01" timelimit="5" steplimit="1" memlimit="1000"/>
 <file name="../choice.mlw">
 <theory name="Choice" sum="7c1ca533a0ae37f3bd6e59347ceef0bd">
  <goal name="WP_parameter choose" expl="VC for choose">
- <proof prover="0"><result status="valid" time="0.00" steps="3"/></proof>
+ <proof prover="1"><result status="valid" time="0.00" steps="3"/></proof>
  </goal>
  <goal name="WP_parameter choose_if" expl="VC for choose_if">
- <proof prover="0"><result status="valid" time="0.00" steps="2"/></proof>
+ <proof prover="1"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
 </theory>
 </file>

examples/in_progress/2wp_gen/fn/why3session.xml

@@ -7,5 +7,7 @@
 </theory>
 <theory name="Category" sum="d41d8cd98f00b204e9800998ecf8427e" expanded="true">
 </theory>
+<theory name="Image" sum="d41d8cd98f00b204e9800998ecf8427e" expanded="true">
+</theory>
 </file>
 </why3session>

examples/in_progress/2wp_gen/game.mlw

@@ -1993,123 +1993,3 @@ module StratProofs
 
 end
 
-(*
-
-  lemma absurdity : forall sc:section 'a 'b,dmn.
-    section_hypothesis sc ->
-    let evl = evolve sc dmn in
-    let bs = basic sc in
-    let st = fixpoint_above sc.sd evl bs in
-    let angb = sim_angel sc in
-    let winb = rel_map sc.r sc.win in
-    (forall x. st.h_total x -> not winb x) /\
-    not win_at sc.g2 winb angb dmn st.h_total ->
-    false
-    by let o1 = sc.g1.progress in let o2 = sc.g2.progress in
-      let op = oprod o1 o2 in
-      let pr = sup op st.h_pair in
-      let (a,b) = pr in
-      let nst = evl st in
-      tr_reach sc.sd evl bs st
-      so coherent sc dmn st
-      so maximum sc.sd (tr_reach sc.sd evl bs) st
-      so if not maximum op st.h_pair pr
-      then nst.h_pair pr so chain op st.h_pair
-        so (exists y. supremum op st.h_pair y)
-        so supremum op st.h_pair pr
-        so upper_bound op st.h_pair pr so false
-      else let s0 = sc.anga a st.h_proj in
-        if st.i_dmn s0 <> None \/ not sc.g1.transition a s0
-        then (* This is the point where we use the fact that
-          'a-angel must win. *)
-          let dmna = \x. match st.i_dmn x with
-            | None -> default
-            | Some a -> a
-            end
-          in
-          compat st.i_dmn dmna
-          so reconstructed sc st dmna
-          so (forall x. st.h_proj x -> not (sc.win x
-            so exists y. st.h_pair (x,y) so sc.r x y
-            so rel_map_witness sc.r sc.win y x so winb y
-            so st.h_total y))
-          so (maximum o1 st.h_proj a by forall u. st.h_proj u ->
-            o1 u a by exists v. st.h_pair (u,v) so op (u,v) (a,b))
-          so supremum o1 st.h_proj a
-          so a = sup o1 st.h_proj
-          so (sc.g1.transition a s0 -> dmna s0 = a /\ s0 (dmna s0)
-            by match st.i_dmn s0 with
-            | None -> false
-            | Some u -> s0 u /\ u = a
-            end)
-          so let nxt = strat_next sc.g1 sc.anga dmna in
-            nxt st.h_proj = a
-          so pext (extends_ch o1 nxt st.h_proj) st.h_proj
-          so maximum (subchain o1)
-               (tr_reach (subchain o1) (extends_ch o1 nxt) ((=) sc.basea))
-               st.h_proj
-          so (not win_against sc.g1 sc.basea sc.win sc.anga dmna
-            by forall ch. reach_ch o1 nxt ((=) sc.basea) ch ->
-              win_at sc.g1 sc.win sc.anga dmna ch -> false
-              by exists x. maximum o1 ch x /\
-                (sc.win x \/ let a = sc.anga x ch in sc.g1.transition x a /\
-                  not a (dmna a))
-              so not (sc.win x so subchain o1 ch st.h_proj so st.h_proj x)
-              so supremum o1 ch x
-              so x = sup o1 ch
-              so nxt ch = x
-              so ext (extends_ch o1 nxt ch) ch
-              so maximum (subchain o1)
-                   (tr_reach (subchain o1) (extends_ch o1 nxt) ((=) sc.basea))
-                   ch
-              so ch = st.h_proj
-              so false)
-          so not winning_strat sc.g1 sc.basea sc.win sc.anga
-          so false
-        else false by let target = rel_map sc.r s0 in
-          let bl = sup o2 st.h_local in
-          if target bl
-          then let al = choice (rel_map_witness  sc.r s0 bl) in
-            nst.i_dmn s0 = Some al so false
-          else let iang = iangel sc b target in
-            let nxt = strat_next sc.g2 iang dmn in
-            nst.h_local = extends_ch o2 nxt st.h_local
-            so if win_at sc.g2 winb angb dmn st.h_total then true else
-              not (nst.h_local = st.h_local
-              so locally_winning sc dmn st
-              so reach_ch o2 nxt ((=) b) st.h_local
-              so maximum (subchain o2)
-                      (tr_reach (subchain o2) (extends_ch o2 nxt) ((=) b))
-                      st.h_local
-              so (not win_against sc.g2 b target iang dmn
-                by forall ch. reach_ch o2 nxt ((=) b) ch ->
-                  win_at sc.g2 target iang dmn ch -> false
-                  by exists x. maximum o2 ch x /\
-                    (target x \/ let a = iang x ch in sc.g2.transition x a /\
-                      not a (dmn a))
-                  so (supremum o2 st.h_local bl
-                    by exists y. supremum o2 st.h_local y)
-                  so not (target x so subchain o2 ch st.h_local so st.h_local x
-                    so maximum o2 st.h_local x
-                    so supremum o2 st.h_local x
-                    so x = bl)
-                  so supremum o2 ch x
-                  so x = sup o2 ch
-                  so nxt ch = x
-                  so ext (extends_ch o2 nxt ch) ch
-                  so maximum (subchain o2)
-                       (tr_reach (subchain o2) (extends_ch o2 nxt) ((=) b))
-                       ch
-                  so ch = st.h_local
-                  so x = bl
-                  so maximum o2 st.h_total bl
-                  so maximal_witness sc st.h_total st dmn
-                  so any_max_witness sc st.h_total st
-                  so st = choice (any_max_witness sc st.h_total)
-                  so iang bl ch = angb bl st.h_total)
-              so not winning_strat sc.g2 b target iang
-              so sc.r a b
-              so exists ang. winning_strat sc.g2 b target ang)
-            so false
-
-end*)