Duplicate Binarity Constraints

[DavePearce]

(see #183)

This is an inefficiency, but I have labelled it as a bug here as it really should be fixed. Consider:

(module test)
(defcolumns (P :binary@prove))
(defperspective p1 P ((A :binary@prove)))
(defperspective p2 P ((B :binary)))

Here, a single binary constraint is given for the underlying column:

test.B-binarity :=
col#3 * (1 - col#3)

Now consider this:

(module test)
(defcolumns (P :binary@prove))
(defperspective p1 P ((A :binary@prove)))
(defperspective p2 P ((B :binary@prove)))

In this case, we get two binarity constraints:

test.A-binarity :=
col#2 * (1 - col#2)

test.B-binarity :=
col#3 * (1 - col#3)

Which we can see in the final define.go are really generated:

test__A_xor_B := build.RegisterCommit("test.A_xor_B", build.Settings.Traces.Test)
test__A_xor_B := build.RegisterCommit("test.A_xor_B", build.Settings.Traces.Test)
test__P1 := build.RegisterCommit("test.P1", build.Settings.Traces.Test)
test__P2 := build.RegisterCommit("test.P2", build.Settings.Traces.Test)

//
// Constraints
//
build.GlobalConstraint("test.A-binarity", test__A_xor_B.AsVariable().Mul(symbolic.NewConstant("1").Sub(test__A_xor_B.AsVariable())))
build.GlobalConstraint("test.B-binarity", test__A_xor_B.AsVariable().Mul(symbolic.NewConstant("1").Sub(test__A_xor_B.AsVariable())))
build.GlobalConstraint("test.P1-binarity", test__P1.AsVariable().Mul(symbolic.NewConstant("1").Sub(test__P1.AsVariable())))
build.GlobalConstraint("test.P2-binarity", test__P2.AsVariable().Mul(symbolic.NewConstant("1").Sub(test__P2.AsVariable())))
build.GlobalConstraint("test.c1", test__P1.AsVariable().Mul(test__A_xor_B.AsVariable().Sub(symbolic.NewConstant("10"))))

[delehef]

Probably the same as #186

[DavePearce]

Hmmm, this is actually quite tricky to implement correctly.