a few tests

tests/test-ind.why

+
+theory T
+
+type list 'a = Nil | Cons 'a (list 'a)
+
+function app (l1:list 'a) (l2:list 'a) : (list 'a) =
+  match l1 with
+  | Nil -> l2
+  | Cons x r -> Cons x (app r l2) 
+  end
+
+lemma app_nil : forall l:list 'a. app l Nil = l
+
+type tree = Leaf int | Node tree tree
+
+end
+

tests/test-ind/why3session.xml

+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE why3session SYSTEM "/usr/local/share/why3/why3session.dtd">
+<why3session
+ name="test-ind/why3session.xml" shape_version="2">
+ <file
+  name="../test-ind.why"
+  verified="false"
+  expanded="true">
+  <theory
+   name="T"
+   locfile="test-ind/../test-ind.why"
+   loclnum="2" loccnumb="7" loccnume="8"
+   verified="false"
+   expanded="true">
+   <goal
+    name="app_nil"
+    locfile="test-ind/../test-ind.why"
+    loclnum="12" loccnumb="6" loccnume="13"
+    sum="57a6eece27d97fc131ecc13471649486"
+    proved="false"
+    expanded="true"
+    shape="ainfix =aappV0aNilV0F">
+   </goal>
+  </theory>
+ </file>
+</why3session>

tests/test-settheory.why

+
+theory TestOverriding
+
+  use import settheory.Relation
+  use import settheory.InverseDomRan
+  use import settheory.Overriding
+  use import settheory.Function
+
+  constant f : rel int int = singleton (3,4)
+  constant g : rel int int = f <+ (singleton (5,6))
+  constant h : rel int int = g <+ (singleton (3,7))
+
+  goal testdom1: mem 3 (dom g)
+  goal testdom2: mem 3 (dom h)
+
+  goal testapply1: apply f 3 = 4
+
+  goal testapply2: apply g 3 = 4
+  goal testapply3: apply g 5 = 6
+
+  goal testapply4: apply h 3 = 7
+  goal testapply5: apply h 5 = 6
+
+  goal testapply_smoke1: apply h 3 = 8
+  goal testapply_smoke2: apply h 5 = 9
+
+end
+
+theory TestCompose
+
+  use import settheory.Relation
+  use import settheory.InverseDomRan
+  use import settheory.Composition
+  use import settheory.Function
+
+  constant f : rel int int = singleton (3,4)
+  constant g : rel int int = singleton (4,6)
+  constant h : rel int int = semicolon f g
+
+  use import settheory.Interval
+
+  constant fun_int_int : set (rel int int) = integer +-> integer
+
+(*
+  lemma f_is_fun : mem f fun_int_int
+
+  lemma g_is_fun : mem g fun_int_int
+
+  lemma h_is_fun : mem h fun_int_int
+*)
+
+  goal test1: mem (apply h 3) (Interval.mk 0 10)
+
+  goal test2: 0 <= apply h 3 <= 10
+
+  goal test3: apply h 3 = 6
+
+
+end
+