Determine type for interleaved columns

This determines the least type which includes all the columns being
interleaved as the type of the target column.

pkg/binfile/computation.go

@@ -94,8 +94,16 @@ func addInterleavedComputation(c *jsonInterleavedComputation, index uint,
 	target_id := asColumn(c.Target)
 	dst_col := columns[target_id]
 	dst_hnd := asHandle(dst_col.Handle)
+	// Initially assume bottom type
+	var dst_type sc.Type = sc.NewUintType(0)
+	// Ensure each column's types included
+	for i := range sources {
+		src_col := schema.Columns().Nth(sources[i])
+		// Update the column type
+		dst_type = sc.Join(dst_type, src_col.Type())
+	}
 	// Finally, add the sorted permutation assignment
-	schema.AddAssignment(assignment.NewInterleaving(ctx, dst_hnd.column, sources))
+	schema.AddAssignment(assignment.NewInterleaving(ctx, dst_hnd.column, sources, dst_type))
 	// Update allocation information.
 	colmap[target_id] = index
 	//

pkg/hir/parser.go

@@ -404,7 +404,7 @@ func (p *hirParser) parseInterleavingDeclaration(l *sexp.List) error {
 		sources[i] = cid
 	}
 	// Add assignment
-	p.env.AddAssignment(assignment.NewInterleaving(ctx, sexpTarget.Value, sources))
+	p.env.AddAssignment(assignment.NewInterleaving(ctx, sexpTarget.Value, sources, &sc.FieldType{}))
 	// Done
 	return nil
 }

pkg/schema/assignment/interleave.go

@@ -19,11 +19,11 @@ type Interleaving struct {
 }
 
 // NewInterleaving constructs a new interleaving assignment.
-func NewInterleaving(context tr.Context, name string, sources []uint) *Interleaving {
+func NewInterleaving(context tr.Context, name string, sources []uint, datatype sc.Type) *Interleaving {
 	// Update multiplier
 	context = context.Multiply(uint(len(sources)))
 	// Fixme: determine interleaving type
-	target := sc.NewColumn(context, name, &sc.FieldType{})
+	target := sc.NewColumn(context, name, datatype)
 
 	return &Interleaving{target, sources}
 }

pkg/schema/type.go

@@ -139,3 +139,20 @@ func (p *FieldType) Accept(val fr.Element) bool {
 func (p *FieldType) String() string {
 	return "𝔽"
 }
+
+// Join compute the Least Upper Bound of two types.  For example, the lub of u16
+// and u128 is u128, etc.
+func Join(lhs Type, rhs Type) Type {
+	if lhs.AsField() != nil || rhs.AsField() != nil {
+		return &FieldType{}
+	}
+	//
+	uLhs := lhs.AsUint()
+	uRhs := rhs.AsUint()
+	//
+	if uLhs.nbits >= uRhs.nbits {
+		return uLhs
+	}
+	//
+	return uRhs
+}