Deriving competing predictions from grammatical approaches and reductionist approaches to Island effects

What is the relationship between grammatical theories and parsing theories? Marr (1982) famously proposed that our theories of information-processing devices can be usefully stated at multiple levels: the computational level, the representational-algorithmic level, and the implementational level. Marr described the computational level as an answer to the question “What problem must this device solve?” He argued that the computational level would specify the properties of the problem that must be solved by the device and the computations that the device must perform in service of that goal, in a way that abstracts away from the exigencies of actually solving the problem in practice. Marr used a cash register as an example: the computational-level description of a cash register comprises the theory of addition, including properties such as commutativity and associativity. However, at the computational level there is no statement of the procedure the device follows or the series of states it occupies to carry out addition. A theory at that level of description is a representational-algorithmic theory. For a cash register this could be the addition algorithm that we all learn in school, implemented in base 10: start from the right, and “carry over the ones”; or it could be implemented in base 2, which a digital device would use. Finally, Marr described the implementational level as a theory of how the operations of the algorithmic level are implemented in the hardware of the device. For a cash register, there are several hardware options that can implement this level, from the spinning drums in mechanical cash registers to the electronic processors in computers.