Makefile and a couple of examples.

Sudoku/Makefile

+
+DKCHECK=dkcheck
+
+all : empty easy medium hardest
+
+empty  : solve_empty.dko
+easy   : solve_easy.dko
+medium : solve_medium.dko
+hardest: solve_hardest.dko
+
+sudoku.dko : sudoku.dk
+	$(DKCHECK) -nl -e sudoku.dk
+
+%.dko: %.dk sudoku.dko
+	$(DKCHECK) $<
+
+clean:
+	rm -rf *.dko

Sudoku/solve_easy.dk

+
+def 1 := sudoku.1.
+def 2 := sudoku.2.
+def 3 := sudoku.3.
+def 4 := sudoku.4.
+def 5 := sudoku.5.
+def 6 := sudoku.6.
+def 7 := sudoku.7.
+def 8 := sudoku.8.
+def 9 := sudoku.9.
+def X := sudoku.X.
+
+def l := sudoku.l.
+def c := sudoku.c.
+
+
+def sudoku :=
+c (l X X X   2 6 X   7 X 1)
+  (l 6 8 X   X 7 X   X 9 X)
+  (l 1 9 X   X X 4   5 X X)
+
+  (l 8 2 X   1 X X   X 4 X)
+  (l X X 4   6 X 2   9 X X)
+  (l X 5 X   X X 3   X 2 8)
+
+  (l X X 9   3 X X   X 7 4)
+  (l X 4 X   X 5 X   X 3 6)
+  (l 7 X 3   X 1 8   X X X).
+
+#EVAL sudoku.solve_sudo sudoku.

Sudoku/solve_empty.dk

+
+#EVAL sudoku.solve_sudo sudoku.empty_sudo.
+
+(;
+c (l 1 2 3   4 5 6   7 8 9)
+  (l 4 5 6   7 8 9   1 2 3)
+  (l 7 8 9   1 2 3   4 5 6)
+ 
+  (l 2 1 4   3 6 5   8 9 7)
+  (l 3 6 5   8 9 7   2 1 4)
+  (l 8 9 7   2 1 4   3 6 5)
+ 
+  (l 5 3 1   6 4 2   9 7 8)
+  (l 6 4 2   9 7 8   5 3 1)
+  (l 9 7 8   5 3 1   6 4 2)
+;)

Sudoku/solve_hardest.dk

+
+def 1 := sudoku.1.
+def 2 := sudoku.2.
+def 3 := sudoku.3.
+def 4 := sudoku.4.
+def 5 := sudoku.5.
+def 6 := sudoku.6.
+def 7 := sudoku.7.
+def 8 := sudoku.8.
+def 9 := sudoku.9.
+def X := sudoku.X.
+
+def l := sudoku.l.
+def c := sudoku.c.
+
+
+def sudoku :=
+ c (l 8 X X   X X X   X X X)
+   (l X X 3   6 X X   X X X)
+   (l X 7 X   X 9 X   2 X X)
+
+   (l X 5 X   X X 7   X X X)
+   (l X X X   X 4 5   7 X X)
+   (l X X X   1 X X   X 3 X)
+
+   (l X X 1   X X X   X 6 8)
+   (l X X 8   5 X X   X 1 X)
+   (l X 9 X   X X X   4 X X).
+
+#EVAL sudoku.solve_sudo sudoku.

Sudoku/solve_medium.dk

+
+def 1 := sudoku.1.
+def 2 := sudoku.2.
+def 3 := sudoku.3.
+def 4 := sudoku.4.
+def 5 := sudoku.5.
+def 6 := sudoku.6.
+def 7 := sudoku.7.
+def 8 := sudoku.8.
+def 9 := sudoku.9.
+def X := sudoku.X.
+
+def l := sudoku.l.
+def c := sudoku.c.
+
+
+def sudoku :=
+c (l X 2 X   6 X 8   X X X)
+  (l 5 8 X   X X 9   7 X X)
+  (l X X X   X 4 X   X X X)
+
+  (l 3 7 X   X X X   6 X X)
+  (l 6 X X   X X X   X X 4)
+  (l X X 8   X X X   X 1 3)
+
+  (l X X X   X 2 X   X X X)
+  (l X X 9   8 X X   X 3 6)
+  (l X X X   3 X 6   X 9 X).
+
+#EVAL sudoku.solve_sudo sudoku.

Sudoku/sudoku.dk

-
-
-
-
 ind : Type.
 1 : ind.
 2 : ind.
@@ -37,11 +33,15 @@ def S : ind -> ind.
 [] S 9 --> X.
 
 def trunc3 : ind -> ind.
-[]  trunc3 X --> X.
-[]  trunc3 1 --> 1.
-[]  trunc3 4 --> 1.
-[]  trunc3 7 --> 1.
-[i] trunc3 i --> P i.
+[]  trunc3 1 --> 1
+[]  trunc3 2 --> 1
+[]  trunc3 3 --> 1
+[]  trunc3 4 --> 4
+[]  trunc3 5 --> 4
+[]  trunc3 6 --> 4
+[]  trunc3 7 --> 7
+[]  trunc3 8 --> 7
+[]  trunc3 9 --> 7.
 
 bool : Type.
 T : bool.
@@ -64,37 +64,73 @@ def eq : ind -> ind -> bool.
 [x,y] eq x y --> F.
 
 
-def ite : A : Type -> bool -> A -> A -> A.
-[A,x] ite A T x _ --> x
-[A,x] ite A F _ x --> x.
 
 
-ind_list : Type.
-Empty' : ind_list.
-Cons' : ind -> ind_list -> ind_list.
+line : Type.
+l : ind -> ind -> ind -> ind -> ind -> ind -> ind -> ind -> ind -> line.
 
-sudo : Type.
-Empty : sudo.
-Cons : ind_list -> sudo -> sudo.
+def sudo : Type.
+def c : line -> line -> line -> line -> line -> line -> line -> line -> line -> sudo.
+
+def getl : ind -> line -> ind.
+[x] getl 1 (l x _ _ _ _ _ _ _ _) --> x
+[x] getl 2 (l _ x _ _ _ _ _ _ _) --> x
+[x] getl 3 (l _ _ x _ _ _ _ _ _) --> x
+[x] getl 4 (l _ _ _ x _ _ _ _ _) --> x
+[x] getl 5 (l _ _ _ _ x _ _ _ _) --> x
+[x] getl 6 (l _ _ _ _ _ x _ _ _) --> x
+[x] getl 7 (l _ _ _ _ _ _ x _ _) --> x
+[x] getl 8 (l _ _ _ _ _ _ _ x _) --> x
+[x] getl 9 (l _ _ _ _ _ _ _ _ x) --> x.
+
+def getc : ind -> sudo -> line.
+[x] getc 1 (c x _ _ _ _ _ _ _ _) --> x
+[x] getc 2 (c _ x _ _ _ _ _ _ _) --> x
+[x] getc 3 (c _ _ x _ _ _ _ _ _) --> x
+[x] getc 4 (c _ _ _ x _ _ _ _ _) --> x
+[x] getc 5 (c _ _ _ _ x _ _ _ _) --> x
+[x] getc 6 (c _ _ _ _ _ x _ _ _) --> x
+[x] getc 7 (c _ _ _ _ _ _ x _ _) --> x
+[x] getc 8 (c _ _ _ _ _ _ _ x _) --> x
+[x] getc 9 (c _ _ _ _ _ _ _ _ x) --> x.
+
+
+
+
+def setl : ind -> ind -> line -> line.
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setl 1 k (l x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l k  x2 x3 x4 x5 x6 x7 x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setl 2 k (l x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l x1 k  x3 x4 x5 x6 x7 x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setl 3 k (l x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l x1 x2 k  x4 x5 x6 x7 x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setl 4 k (l x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l x1 x2 x3 k  x5 x6 x7 x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setl 5 k (l x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l x1 x2 x3 x4 k  x6 x7 x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setl 6 k (l x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l x1 x2 x3 x4 x5 k  x7 x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setl 7 k (l x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l x1 x2 x3 x4 x5 x6 k  x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setl 8 k (l x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l x1 x2 x3 x4 x5 x6 x7 k  x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setl 9 k (l x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l x1 x2 x3 x4 x5 x6 x7 x8 k ).
+
+def setc : ind -> (line -> line) -> sudo -> sudo.
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setc 1 k (c x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (c (k x1) x2 x3 x4 x5 x6 x7 x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setc 2 k (c x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (c x1 (k x2) x3 x4 x5 x6 x7 x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setc 3 k (c x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (c x1 x2 (k x3) x4 x5 x6 x7 x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setc 4 k (c x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (c x1 x2 x3 (k x4) x5 x6 x7 x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setc 5 k (c x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (c x1 x2 x3 x4 (k x5) x6 x7 x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setc 6 k (c x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (c x1 x2 x3 x4 x5 (k x6) x7 x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setc 7 k (c x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (c x1 x2 x3 x4 x5 x6 (k x7) x8 x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setc 8 k (c x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (c x1 x2 x3 x4 x5 x6 x7 (k x8) x9)
+[k,x1,x2,x3,x4,x5,x6,x7,x8,x9] setc 9 k (c x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (c x1 x2 x3 x4 x5 x6 x7 x8 (k x9) ).
 
-def E : ind_list :=
-	Cons' X (Cons' X (Cons' X (Cons' X (Cons' X (Cons' X (Cons' X (Cons' X (Cons' X Empty')))))))).
-def empty_sudo : sudo :=
-	Cons  E (Cons  E (Cons  E (Cons  E (Cons  E (Cons  E (Cons  E (Cons  E (Cons  E Empty )))))))).
-	
-def set' : ind -> ind -> ind_list -> ind_list.
-[j,k,a,l] set' j k (Cons' a l) --> ite ind_list (eq j 1) (Cons' k l) (Cons' a (set' (P j) k l)).
 
-def set : ind -> ind -> ind -> sudo -> sudo.
-[i,j,k,a,l] set i j k (Cons a l) --> ite sudo (eq i 1) (Cons (set' j k a) l) (Cons a (set (P i) j k l)).
 
 
-def get' : ind -> ind_list -> ind.
-[j,a,l] get' j (Cons' a l) --> ite ind (eq j 1) a (get' (P j) l).
+def E : line := l X X X X X X X X X.
+def empty_sudo : sudo := c E E E E E E E E E.
+
 
 def get : ind -> ind -> sudo -> ind.
-[i,j,a,l] get i j (Cons a l) --> ite ind (eq i 1) (get' j a) (get (P i) j l).
+[i,j,s] get i j s --> getl j (getc i s).
 
+def set : ind -> ind -> ind -> sudo -> sudo.
+[i,j,k,s] set i j k s --> setc i (setl j k) s.
 
 
 def exists' : (ind -> bool) -> ind -> bool.
@@ -104,6 +140,7 @@ def exists' : (ind -> bool) -> ind -> bool.
 def exists : (ind -> bool) -> bool := f => exists' f 1.
 
 
+
 def mem_line : ind -> ind -> ind -> sudo -> bool.
 [i,j,k,s] mem_line i j k s --> exists (i' => eq (get i' j s) k).
 
@@ -114,20 +151,19 @@ def mem_squ  : ind -> ind -> ind -> sudo -> bool.
 [i,j,k,s] mem_squ i j k s -->
   (i':ind =>
    j':ind =>
-     or (or (eq (get i'         j'         s) k)
-        (or (eq (get (S i')     j'         s) k)
-	        (eq (get (S (S i')) j'         s) k)))
-    (or (or (eq (get i'         (S j')     s) k)
-	    (or (eq (get (S i')     (S j')     s) k)
-	        (eq (get (S (S i')) (S j')     s) k)))
-        (or (eq (get i'         (S (S j')) s) k)
-	    (or (eq (get (S i')     (S (S j')) s) k)
-	        (eq (get (S (S i')) (S (S j')) s) k))))
+    (or (eq (get i'         j'         s) k)
+    (or (eq (get (S i')     j'         s) k)
+	(or (eq (get (S (S i')) j'         s) k)
+    (or (eq (get i'         (S j')     s) k)
+	(or (eq (get (S i')     (S j')     s) k)
+	(or (eq (get (S (S i')) (S j')     s) k)
+    (or (eq (get i'         (S (S j')) s) k)
+	(or (eq (get (S i')     (S (S j')) s) k)
+	    (eq (get (S (S i')) (S (S j')) s) k)))))))))
   )
   (trunc3 i) (trunc3 j).
 
 
-
 def check : ind -> ind -> ind -> sudo -> bool :=
 i => j => k => s =>
      and (not (mem_line i j k s))
@@ -140,6 +176,10 @@ success : sudo -> solution.
 fail : solution.
 
 
+def ite : bool -> solution -> solution -> solution.
+[x] ite T x _ --> x
+[x] ite F _ x --> x.
+
 def iffail : solution -> solution -> solution.
 [x] iffail (success x) _ --> success x
 [d] iffail fail     d --> d.
@@ -149,9 +189,9 @@ def solve : ind -> ind -> ind -> sudo -> solution.
 [  s]     solve X _ _ s --> success s.
 [i,j,s]   solve i j X s --> fail.
 [i,j,k,s] solve i j k s -->
-  ite solution
+  ite
     (eq (get i j s) X)
-    (ite solution
+    (ite
       (check i j k s)
       (iffail
         (solve i (S j) 1 (set i j k s))
@@ -163,13 +203,3 @@ def solve : ind -> ind -> ind -> sudo -> solution.
 
 
 def solve_sudo : sudo -> solution := s => solve 1 1 1 s.
-
-
-def extract_sol : solution -> sudo.
-[x] extract_sol (success x) --> x.
-
-
-
-def sol := solve_sudo empty_sudo.
-#EVAL sol.
-

Sudoku/sudoku2.dk → Sudoku/sudoku_old.dk

+
+
+
+
 ind : Type.
 1 : ind.
 2 : ind.
@@ -33,15 +37,11 @@ def S : ind -> ind.
 [] S 9 --> X.
 
 def trunc3 : ind -> ind.
-[]  trunc3 1 --> 1
-[]  trunc3 2 --> 1
-[]  trunc3 3 --> 1
-[]  trunc3 4 --> 4
-[]  trunc3 5 --> 4
-[]  trunc3 6 --> 4
-[]  trunc3 7 --> 7
-[]  trunc3 8 --> 7
-[]  trunc3 9 --> 7.
+[]  trunc3 X --> X.
+[]  trunc3 1 --> 1.
+[]  trunc3 4 --> 1.
+[]  trunc3 7 --> 1.
+[i] trunc3 i --> P i.
 
 bool : Type.
 T : bool.
@@ -69,43 +69,32 @@ def ite : A : Type -> bool -> A -> A -> A.
 [A,x] ite A F _ x --> x.
 
 
-list : A : Type -> Type.
-l : A : Type -> A -> A -> A -> A -> A -> A -> A -> A -> A -> list A.
+ind_list : Type.
+Empty' : ind_list.
+Cons' : ind -> ind_list -> ind_list.
 
-def get' : A : Type -> ind -> list A -> A.
-[A,x] get' A 1 (l A x _ _ _ _ _ _ _ _) --> x
-[A,x] get' A 2 (l A _ x _ _ _ _ _ _ _) --> x
-[A,x] get' A 3 (l A _ _ x _ _ _ _ _ _) --> x
-[A,x] get' A 4 (l A _ _ _ x _ _ _ _ _) --> x
-[A,x] get' A 5 (l A _ _ _ _ x _ _ _ _) --> x
-[A,x] get' A 6 (l A _ _ _ _ _ x _ _ _) --> x
-[A,x] get' A 7 (l A _ _ _ _ _ _ x _ _) --> x
-[A,x] get' A 8 (l A _ _ _ _ _ _ _ x _) --> x
-[A,x] get' A 9 (l A _ _ _ _ _ _ _ _ x) --> x.
+sudo : Type.
+Empty : sudo.
+Cons : ind_list -> sudo -> sudo.
 
-def set' : A : Type -> ind -> (A -> A) -> list A -> list A.
-[A,k,x1,x2,x3,x4,x5,x6,x7,x8,x9] set' A 1 k (l A x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l A (k x1) x2 x3 x4 x5 x6 x7 x8 x9)
-[A,k,x1,x2,x3,x4,x5,x6,x7,x8,x9] set' A 2 k (l A x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l A x1 (k x2) x3 x4 x5 x6 x7 x8 x9)
-[A,k,x1,x2,x3,x4,x5,x6,x7,x8,x9] set' A 3 k (l A x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l A x1 x2 (k x3) x4 x5 x6 x7 x8 x9)
-[A,k,x1,x2,x3,x4,x5,x6,x7,x8,x9] set' A 4 k (l A x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l A x1 x2 x3 (k x4) x5 x6 x7 x8 x9)
-[A,k,x1,x2,x3,x4,x5,x6,x7,x8,x9] set' A 5 k (l A x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l A x1 x2 x3 x4 (k x5) x6 x7 x8 x9)
-[A,k,x1,x2,x3,x4,x5,x6,x7,x8,x9] set' A 6 k (l A x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l A x1 x2 x3 x4 x5 (k x6) x7 x8 x9)
-[A,k,x1,x2,x3,x4,x5,x6,x7,x8,x9] set' A 7 k (l A x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l A x1 x2 x3 x4 x5 x6 (k x7) x8 x9)
-[A,k,x1,x2,x3,x4,x5,x6,x7,x8,x9] set' A 8 k (l A x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l A x1 x2 x3 x4 x5 x6 x7 (k x8) x9)
-[A,k,x1,x2,x3,x4,x5,x6,x7,x8,x9] set' A 9 k (l A x1 x2 x3 x4 x5 x6 x7 x8 x9) --> (l A x1 x2 x3 x4 x5 x6 x7 x8 (k x9) ).
+def E : ind_list :=
+	Cons' X (Cons' X (Cons' X (Cons' X (Cons' X (Cons' X (Cons' X (Cons' X (Cons' X Empty')))))))).
+def empty_sudo : sudo :=
+	Cons  E (Cons  E (Cons  E (Cons  E (Cons  E (Cons  E (Cons  E (Cons  E (Cons  E Empty )))))))).
+	
+def set' : ind -> ind -> ind_list -> ind_list.
+[j,k,a,l] set' j k (Cons' a l) --> ite ind_list (eq j 1) (Cons' k l) (Cons' a (set' (P j) k l)).
 
+def set : ind -> ind -> ind -> sudo -> sudo.
+[i,j,k,a,l] set i j k (Cons a l) --> ite sudo (eq i 1) (Cons (set' j k a) l) (Cons a (set (P i) j k l)).
 
-def sudo : Type := list (list ind).
-
-def E : list ind := l ind X X X X X X X X X.
-def empty_sudo : sudo := l (list ind) E E E E E E E E E.
 
+def get' : ind -> ind_list -> ind.
+[j,a,l] get' j (Cons' a l) --> ite ind (eq j 1) a (get' (P j) l).
 
 def get : ind -> ind -> sudo -> ind.
-[i,j,s] get i j s --> (get' ind j (get' (list ind) i s)).
+[i,j,a,l] get i j (Cons a l) --> ite ind (eq i 1) (get' j a) (get (P i) j l).
 
-def set : ind -> ind -> ind -> sudo -> sudo.
-[i,j,k,s] set i j k s --> set' (list ind) i (set' ind j (x => k)) s.
 
 
 def exists' : (ind -> bool) -> ind -> bool.
@@ -115,7 +104,6 @@ def exists' : (ind -> bool) -> ind -> bool.
 def exists : (ind -> bool) -> bool := f => exists' f 1.
 
 
-
 def mem_line : ind -> ind -> ind -> sudo -> bool.
 [i,j,k,s] mem_line i j k s --> exists (i' => eq (get i' j s) k).
 
@@ -123,29 +111,23 @@ def mem_col  : ind -> ind -> ind -> sudo -> bool.
 [i,j,k,s] mem_col i j k s --> exists (j' => eq (get i j' s) k).
 
 def mem_squ  : ind -> ind -> ind -> sudo -> bool.
-[i,j,k,s] mem_squ i j k s --> F.
-
-
-
-
-
-def mem_squ2  : ind -> ind -> ind -> sudo -> bool.
-[i,j,k,s] mem_squ2 i j k s -->
+[i,j,k,s] mem_squ i j k s -->
   (i':ind =>
    j':ind =>
-    (or (eq (get i'         j'         s) k)
-    (or (eq (get (S i')     j'         s) k)
-	(or (eq (get (S (S i')) j'         s) k)
-    (or (eq (get i'         (S j')     s) k)
-	(or (eq (get (S i')     (S j')     s) k)
-	(or (eq (get (S (S i')) (S j')     s) k)
-    (or (eq (get i'         (S (S j')) s) k)
-	(or (eq (get (S i')     (S (S j')) s) k)
-	    (eq (get (S (S i')) (S (S j')) s) k)))))))))
+     or (or (eq (get i'         j'         s) k)
+        (or (eq (get (S i')     j'         s) k)
+	        (eq (get (S (S i')) j'         s) k)))
+    (or (or (eq (get i'         (S j')     s) k)
+	    (or (eq (get (S i')     (S j')     s) k)
+	        (eq (get (S (S i')) (S j')     s) k)))
+        (or (eq (get i'         (S (S j')) s) k)
+	    (or (eq (get (S i')     (S (S j')) s) k)
+	        (eq (get (S (S i')) (S (S j')) s) k))))
   )
   (trunc3 i) (trunc3 j).
 
 
+
 def check : ind -> ind -> ind -> sudo -> bool :=
 i => j => k => s =>
      and (not (mem_line i j k s))
@@ -191,8 +173,3 @@ def extract_sol : solution -> sudo.
 def sol := solve_sudo empty_sudo.
 #EVAL sol.
 
-#EVAL[SNF,1] get 2 2 (extract_sol sol).
-#EVAL[SNF,2] get 2 2 (extract_sol sol).
-#EVAL[SNF,3] get 2 2 (extract_sol sol).
-
-#EVAL[WHNF,4] mem_squ2 2 2 3 (extract_sol sol).