scholarly journals A Quantum Interpretation of Bunched Logic & Quantum Separation Logic

Author(s):  
Li Zhou ◽  
Gilles Barthe ◽  
Justin Hsu ◽  
Mingsheng Ying ◽  
Nengkun Yu
2022 ◽  
Vol 6 (POPL) ◽  
pp. 1-27
Author(s):  
Xuan-Bach Le ◽  
Shang-Wei Lin ◽  
Jun Sun ◽  
David Sanan

It is well-known that quantum programs are not only complicated to design but also challenging to verify because the quantum states can have exponential size and require sophisticated mathematics to encode and manipulate. To tackle the state-space explosion problem for quantum reasoning, we propose a Hoare-style inference framework that supports local reasoning for quantum programs. By providing a quantum interpretation of the separating conjunction, we are able to infuse separation logic into our framework and apply local reasoning using a quantum frame rule that is similar to the classical frame rule. For evaluation, we apply our framework to verify various quantum programs including Deutsch–Jozsa’s algorithm and Grover's algorithm.


2021 ◽  
Vol 31 ◽  
Author(s):  
THOMAS VAN STRYDONCK ◽  
FRANK PIESSENS ◽  
DOMINIQUE DEVRIESE

Abstract Separation logic is a powerful program logic for the static modular verification of imperative programs. However, dynamic checking of separation logic contracts on the boundaries between verified and untrusted modules is hard because it requires one to enforce (among other things) that outcalls from a verified to an untrusted module do not access memory resources currently owned by the verified module. This paper proposes an approach to dynamic contract checking by relying on support for capabilities, a well-studied form of unforgeable memory pointers that enables fine-grained, efficient memory access control. More specifically, we rely on a form of capabilities called linear capabilities for which the hardware enforces that they cannot be copied. We formalize our approach as a fully abstract compiler from a statically verified source language to an unverified target language with support for linear capabilities. The key insight behind our compiler is that memory resources described by spatial separation logic predicates can be represented at run time by linear capabilities. The compiler is separation-logic-proof-directed: it uses the separation logic proof of the source program to determine how memory accesses in the source program should be compiled to linear capability accesses in the target program. The full abstraction property of the compiler essentially guarantees that compiled verified modules can interact with untrusted target language modules as if they were compiled from verified code as well. This article is an extended version of one that was presented at ICFP 2019 (Van Strydonck et al., 2019).


2020 ◽  
Vol 4 (ICFP) ◽  
pp. 1-29
Author(s):  
Glen Mével ◽  
Jacques-Henri Jourdan ◽  
François Pottier

2021 ◽  
Vol 5 (POPL) ◽  
pp. 1-29
Author(s):  
Léon Gondelman ◽  
Simon Oddershede Gregersen ◽  
Abel Nieto ◽  
Amin Timany ◽  
Lars Birkedal

2020 ◽  
Vol 4 (POPL) ◽  
pp. 1-32 ◽  
Author(s):  
Ralf Jung ◽  
Rodolphe Lepigre ◽  
Gaurav Parthasarathy ◽  
Marianna Rapoport ◽  
Amin Timany ◽  
...  
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