Final answer:
The substance with high hardness, lack of electrical conductivity, and a melting point of 3440°C is a Covalent Network Solid, characterized by a 3D network of strong covalent bonds.
Step-by-step explanation:
The substance described as very hard, does not conduct electricity, and has a melting point of 3440°C can be classified as a Covalent Network Solid. Covalent network solids, such as diamond, silicon, and silicon carbide, are characterized by a three-dimensional network of strong covalent bonds.
These properties provide covalent network solids with exceptional hardness, high melting points, and the absence of conductivity in their solid state. Diamond is a notable example of this type with a melting point above 3500°C, making it one of the hardest known substances.