Churchill, M., Laird, J. and McCusker, G., 2011. Imperative programs as proofs via game semantics. IEEE, pp. 65-74. (Annual Symposium on Logic in Computer Science)
Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this paper we describe a logical counterpart to this extension, in which proofs denote such strategies. We can embed intuitionistic first-order linear logic into this system, as well as an imperative total programming language. The logic makes explicit use of the fact that in the game semantics the exponential can be expressed as a final co algebra. We establish a full completeness theorem for our logic, showing that every bounded strategy is the denotation of a proof.
|Item Type ||Conference or Workshop Items (UNSPECIFIED)|
|Creators||Churchill, M., Laird, J. and McCusker, G.|
|Departments||Faculty of Science > Computer Science|
|Publisher Statement||CLM11.pdf: © 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.|
|Additional Information||26th Annual IEEE Symposium on Logic in Computer Science. Toronto, Ontario, Canada. 21–24 June 2011|
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