The dominant linguistic theory for specifying the syntax of software languages is Chomsky’s phrase-structure grammar. However, for graphical block languages (such as Scratch and other languages defined using Google’s Blockly library), we note that a different linguistic theory provides a better fitting model: the theory of dependency grammar. Indeed, as we make clear, there is a close, almost one-to-one correspondence between the specifications of graphical syntax required by Blockly and a classic capture of dependency grammar, which can be perfected by making only small extensions that remain entirely within the linguistic context. Taking the identified correspondence further suggests how Blockly languages can become context-sensitive, a requirement of many software languages that so far, Blockly addresses only in ad hoc ways.