Add query to readme

Author: krishnangovindraj

sudoku/readme.md

@@ -54,7 +54,10 @@ The file would contain:
 ```
 
 ## Approach
-We declare a variable corresponding to each position in the sudoku 
+The work is done in the `solution-rule`.
+
+Each row, column and box is constrained to be a permutation of the numbers 1 to 6.
+We have one variable corresponding to each position in the sudoku. 
 
 | - | a | b | c | d | e | f |
 |---|---|---|---|---|---|---|
@@ -65,42 +68,73 @@ We declare a variable corresponding to each position in the sudoku
 | 5 |$a5|$b5|$c5|$d5|$e5|$f5|
 | 6 |$a6|$b6|$c6|$d6|$e6|$f6|
 
-The work is done in the `solution-rule`.
-Each row, column and box is constrained to be a permutation of the numbers 1 to 6.
-
+ 
 ```typeql
-# Each row must be a valid permutation 
-(mem: $a1, mem: $b1, mem: $c1, mem: $d1, mem: $e1, mem: $f1) isa permutation;
-(mem: $a2, mem: $b2, mem: $c2, mem: $d2, mem: $e2, mem: $f2) isa permutation;
-(mem: $a3, mem: $b3, mem: $c3, mem: $d3, mem: $e3, mem: $f3) isa permutation;
-(mem: $a4, mem: $b4, mem: $c4, mem: $d4, mem: $e4, mem: $f4) isa permutation;
-(mem: $a5, mem: $b5, mem: $c5, mem: $d5, mem: $e5, mem: $f5) isa permutation;
-(mem: $a6, mem: $b6, mem: $c6, mem: $d6, mem: $e6, mem: $f6) isa permutation;
-
-# Each column must be a valid permutation
-(mem: $a1, mem: $a2, mem: $a3, mem: $a4, mem: $a5, mem: $a6) isa permutation;
-(mem: $b1, mem: $b2, mem: $b3, mem: $b4, mem: $b5, mem: $b6) isa permutation;
-(mem: $c1, mem: $c2, mem: $c3, mem: $c4, mem: $c5, mem: $c6) isa permutation;
-(mem: $d1, mem: $d2, mem: $d3, mem: $d4, mem: $d5, mem: $d6) isa permutation;
-(mem: $e1, mem: $e2, mem: $e3, mem: $e4, mem: $e5, mem: $e6) isa permutation;
-(mem: $f1, mem: $f2, mem: $f3, mem: $f4, mem: $f5, mem: $f6) isa permutation;
-
-# Each box must be a valid permutation
-(mem: $a1, mem: $b1, mem: $c1, mem: $a2, mem: $b2, mem: $c2) isa permutation;
-(mem: $a3, mem: $b3, mem: $c3, mem: $a4, mem: $b4, mem: $c4) isa permutation;
-(mem: $a5, mem: $b5, mem: $c5, mem: $a6, mem: $b6, mem: $c6) isa permutation;
-(mem: $d1, mem: $e1, mem: $f1, mem: $d2, mem: $e2, mem: $f2) isa permutation;
-(mem: $d3, mem: $e3, mem: $f3, mem: $d4, mem: $e4, mem: $f4) isa permutation;
-(mem: $d5, mem: $e5, mem: $f5, mem: $d6, mem: $e6, mem: $f6) isa permutation;
+rule solution-rule:
+when {
+    # Each row must be a valid permutation 
+    (mem: $a1, mem: $b1, mem: $c1, mem: $d1, mem: $e1, mem: $f1) isa permutation;
+    (mem: $a2, mem: $b2, mem: $c2, mem: $d2, mem: $e2, mem: $f2) isa permutation;
+    (mem: $a3, mem: $b3, mem: $c3, mem: $d3, mem: $e3, mem: $f3) isa permutation;
+    (mem: $a4, mem: $b4, mem: $c4, mem: $d4, mem: $e4, mem: $f4) isa permutation;
+    (mem: $a5, mem: $b5, mem: $c5, mem: $d5, mem: $e5, mem: $f5) isa permutation;
+    (mem: $a6, mem: $b6, mem: $c6, mem: $d6, mem: $e6, mem: $f6) isa permutation;
+    
+    # Each column must be a valid permutation
+    (mem: $a1, mem: $a2, mem: $a3, mem: $a4, mem: $a5, mem: $a6) isa permutation;
+    (mem: $b1, mem: $b2, mem: $b3, mem: $b4, mem: $b5, mem: $b6) isa permutation;
+    (mem: $c1, mem: $c2, mem: $c3, mem: $c4, mem: $c5, mem: $c6) isa permutation;
+    (mem: $d1, mem: $d2, mem: $d3, mem: $d4, mem: $d5, mem: $d6) isa permutation;
+    (mem: $e1, mem: $e2, mem: $e3, mem: $e4, mem: $e5, mem: $e6) isa permutation;
+    (mem: $f1, mem: $f2, mem: $f3, mem: $f4, mem: $f5, mem: $f6) isa permutation;
+    
+    # Each box must be a valid permutation
+    (mem: $a1, mem: $b1, mem: $c1, mem: $a2, mem: $b2, mem: $c2) isa permutation;
+    (mem: $a3, mem: $b3, mem: $c3, mem: $a4, mem: $b4, mem: $c4) isa permutation;
+    (mem: $a5, mem: $b5, mem: $c5, mem: $a6, mem: $b6, mem: $c6) isa permutation;
+    (mem: $d1, mem: $e1, mem: $f1, mem: $d2, mem: $e2, mem: $f2) isa permutation;
+    (mem: $d3, mem: $e3, mem: $f3, mem: $d4, mem: $e4, mem: $f4) isa permutation;
+    (mem: $d5, mem: $e5, mem: $f5, mem: $d6, mem: $e6, mem: $f6) isa permutation;
+} then {
+  (
+    pos11: $a1, pos12: $b1, pos13: $c1, pos14: $d1, pos15: $e1, pos16: $f1,
+    pos21: $a2, pos22: $b2, pos23: $c2, pos24: $d2, pos25: $e2, pos26: $f2,
+    pos31: $a3, pos32: $b3, pos33: $c3, pos34: $d3, pos35: $e3, pos36: $f3,
+    pos41: $a4, pos42: $b4, pos43: $c4, pos44: $d4, pos45: $e4, pos46: $f4,
+    pos51: $a5, pos52: $b5, pos53: $c5, pos54: $d5, pos55: $e5, pos56: $f5,
+    pos61: $a6, pos62: $b6, pos63: $c6, pos64: $d6, pos65: $e6, pos66: $f6
+  ) isa solution;
+};
 ```
 
 In our database, we have a single permutation instance inserted as follows:
 ```typeql
+insert 
 $v1 = 1 isa number;
 $v2 = 2 isa number;
 $v3 = 3 isa number;
 $v4 = 4 isa number;
 $v5 = 5 isa number;
 $v6 = 6 isa number;
 (mem: $v1, mem: $v2, mem: $v3, mem: $v4, mem: $v5, mem: $v6) isa permutation;
+```
+
+
+To query it, We add a statement for the variables which we know the value of (e.g. `$v13 = 3 isa number;`) and query the rule:
+```typeql
+match
+    $v13 = 3 isa number;
+    $v15 = 1 isa number;
+    # ...
+    $v62 = 4 isa number;
+    $v64 = 1 isa number;
+    (
+        pos11: $v11, pos12: $v12, pos13: $v13, pos14: $v14, pos15: $v15, pos16: $v16,
+        pos21: $v21, pos22: $v22, pos23: $v23, pos24: $v24, pos25: $v25, pos26: $v26,
+        pos31: $v31, pos32: $v32, pos33: $v33, pos34: $v34, pos35: $v35, pos36: $v36,
+        pos41: $v41, pos42: $v42, pos43: $v43, pos44: $v44, pos45: $v45, pos46: $v46,
+        pos51: $v51, pos52: $v52, pos53: $v53, pos54: $v54, pos55: $v55, pos56: $v56,
+        pos61: $v61, pos62: $v62, pos63: $v63, pos64: $v64, pos65: $v65, pos66: $v66
+    ) isa solution;
+    limit 1;
 ```