In this paper we present Declassification Core Calculus (DeCC), a graded modal type theory for relaxed semantic declassification, a declassification criterion inspired from Delimited Release and Relaxed Noninterference. We build upon Dependency Core Calculus (DCC) that already has a graded monad for classification of information. DeCC inherits DCC's graded monad, but adds a new modality for the purpose of declassification. We build a logical relation model describing both the unary and relational semantics of the types including the two graded modalities, and use this model to prove the soundness of DeCC. We describe how our new modality interacts with DCC's graded monad via distributive laws, and also describe the conditions under which our new modality forms a comonad. This work has been mechanised in the HOL4 theorem prover.

Abstract We add an efficient function for computation to the kernels of higher-order logic interactive theorem provers. First, we develop and prove sound our approach for Candle. Candle is a port of HOL Light which has been proved sound with respect to the inference rules of its higher-order logic; we extend its implementation and soundness proof. Second, we replicate our now-verified implementation for HOL4 with only minor changes, and build additional automation for ease of use. The automation exists outside of the HOL4 kernel, and requires no additional trust. We exercise our new computation function and associated automation on the evaluation of the CakeML compiler backend within HOL4’s logic, demonstrating an order of magnitude speedup. This is an extended version of our previous conference paper [2], which described implementation and soundness proofs for Candle. Our HOL4 implementation and automation are new, as are the CakeML benchmarks.

Abstract Inlining is a crucial optimisation when compiling functional programming languages. This paper describes how we have implemented and verified function inlining and loop specialisation for PureCake, a verified compiler for a Haskell-like (purely functional, lazy) programming language. A novel aspect of our formalisation is that we justify inlining by pushing and pulling "Image missing"-bindings. All of our work has been mechanised in the HOL4 interactive theorem prover.

We present PureCake, a mechanically-verified compiler for PureLang, a lazy, purely functional programming language with monadic effects. PureLang syntax is Haskell-like and indentation-sensitive, and its constraint-based Hindley-Milner type system guarantees safe execution. We derive sound equational reasoning principles over its operational semantics, dramatically simplifying some proofs. We prove end-to-end correctness for the compilation of PureLang down to machine code---the first such result for any lazy language---by targeting CakeML and composing with its verified compiler. Multiple optimisation passes are necessary to handle realistic lazy idioms effectively. We develop PureCake entirely within the HOL4 interactive theorem prover.

Abstract We introduce an automatic method for producing stateful ML programs together with proofs of correctness from monadic functions in HOL. Our mechanism supports references, exceptions, and I/O operations, and can generate functions manipulating local state, which can then be encapsulated for use in a pure context. We apply this approach to several non-trivial examples, including the instruction encoder and register allocator of the otherwise pure CakeML compiler, which now benefits from better runtime performance. This development has been carried out in the HOL4 theorem prover.