Linear Types Can Change the Blockchain

We present an interpretation of classical linear logic in terms of operations on the blockchain. Anyone who understands the current economic, sociological , and technological situation is likely to be very excited by what the blockchain technology promises. Anyone who has actually had to work with the blockchain in real situations with mission-critical exchanges on the line is very likely to be motivated to find a more scalable and reliable architecture for the blockchain. This paper takes a few key steps towards finding a way to explain and test a hypothesis that linear proofs provide the basis for a much more scalable architecture for the blockchain. For background on what is meant here by linear proofs, [5] interprets them in terms of games, while [3] interprets them in terms of traditional computational calculi like the lambda calculus. A linear proof is a formal structure representing a proof of a formula in linear logic [6]. The Curry-Howard isomorphism [13] tells us that formulae are types (as in data types in a programming language), and that proofs are programs. This is a very broad and deep idea. In the 90's, for example, Abramsky extended it to proofs as processes [4], which Wadler was only very recently able to realize as a correspondence between linear proofs and π-calculus processes [14]. In this context it means that linear proofs provide a representation of both data (blocks) and program (ex-ecutable transactions) that gives several advantages over the current choices made by the blockchain. The blockchain is a great example of data that is also program; it's a giant ledger spread out over the In-ternet, that's made of a bunch of distributed, but interacting servers [11]. To become more scalable, and reliable, both ledger and servers will need certain characteristics of data/program that have to do with a property called compositionality. Scalability is always all about being able to build composite systems from components. For example, if we can prove that sections of the blockchain can be safely isolated from other sections, for example, if all blocks necessary to prove that Alice has sufficient funds to send M btc to Betty, can be isolated from the blocks necessary to prove that Alfred has sufficient funds to send N btc to Bob, then Alice and Betty, and Alfred and Bob can safely work with projections of the blockchain, and thus complete their transactions, not only in isolation …