docs(frontend): Proposal with constant

frontends/concrete-python/examples/levenshtein_distance/levenshtein_distance.py

@@ -56,6 +56,10 @@ def mix(is_equal, if_equal, case_1, case_2, case_3):
 
         return fhe.if_then_else(is_equal, if_equal, 1 + min_123)
 
+    @fhe.function({"x": "clear"})
+    def constant(x):
+        return fhe.zero() + x
+
     # There is a single output in mix: it can go to
     #   - input 1 of mix
     #   - input 2 of mix
@@ -71,6 +75,10 @@ def mix(is_equal, if_equal, case_1, case_2, case_3):
             fhe.Wire(fhe.AllOutputs(mix), fhe.Input(mix, 2)),
             fhe.Wire(fhe.AllOutputs(mix), fhe.Input(mix, 3)),
             fhe.Wire(fhe.AllOutputs(mix), fhe.Input(mix, 4)),
+            fhe.Wire(fhe.AllOutputs(constant), fhe.Input(mix, 1)),
+            fhe.Wire(fhe.AllOutputs(constant), fhe.Input(mix, 2)),
+            fhe.Wire(fhe.AllOutputs(constant), fhe.Input(mix, 3)),
+            fhe.Wire(fhe.AllOutputs(constant), fhe.Input(mix, 4)),
         ]
     )
 
@@ -116,9 +124,9 @@ def levenshtein_simulate(my_module, x, y):
 def levenshtein_fhe(my_module, x, y):
     """Compute the distance in FHE."""
     if len(x) == 0:
-        return my_module.mix.encrypt(None, len(y), None, None, None)[1]
+        return my_module.constant.run(my_module.constant.encrypt(len(y)))
     if len(y) == 0:
-        return my_module.mix.encrypt(None, len(x), None, None, None)[1]
+        return my_module.constant.run(my_module.constant.encrypt(len(x)))
 
     if_equal = levenshtein_fhe(my_module, x[1:], y[1:])
     case_1 = levenshtein_fhe(my_module, x[1:], y)
@@ -208,7 +216,7 @@ def compile_module(mapping_to_int, args):
     ]
 
     my_module = LevenshsteinModule.compile(
-        {"equal": inputset_equal, "mix": inputset_mix},
+        {"equal": inputset_equal, "mix": inputset_mix, "constant": [i for i in range(len(mapping_to_int))]},
         show_mlir=args.show_mlir,
         p_error=10**-20,
         show_optimizer=args.show_optimizer,