Abstract This paper presents a fully verified interactive theorem prover for higher-order logic, more specifically: a fully verified clone of HOL Light. Our verification proof of this new system results in an end-to-end correctness theorem that guarantees the soundness of the entire system down to the machine code that executes at runtime. Our theorem states that every exported fact produced by this machine-code program is valid in higher-order logic. Our implementation consists of a read-eval-print loop (REPL) that executes the CakeML compiler internally. Throughout this work, we have strived to make the REPL of the new system provide a user experience as close to HOL Light’s as possible. To this end, we have, e.g., made the new system parse the same variant of OCaml syntax as HOL Light. All of the work described in this paper has been carried out in the HOL4 theorem prover.

Causal models of agents have been used to analyse the safety aspects of machine learning systems. But identifying agents is non-trivial – often the causal model is just assumed by the modeller without much justification – and modelling failures can lead to mistakes in the safety analysis. This paper proposes the first formal causal definition of agents – roughly that agents are systems that would adapt their policy if their actions influenced the world in a different way. From this we derive the first causal discovery algorithm for discovering the presence of agents from empirical data, given a set of variables and under certain assumptions. We also provide algorithms for translating between causal models and game-theoretic influence diagrams. We demonstrate our approach by resolving some previous confusions caused by incorrect causal modelling of agents.

Causal models of agents have been used to analyse the safety aspects of machine learning systems. But identifying agents is non-trivial – often the causal model is just assumed by the modeller without much justification – and modelling failures can lead to mistakes in the safety analysis. This paper proposes the first formal causal definition of agents – roughly that agents are systems that would adapt their policy if their actions influenced the world in a different way. From this we derive the first causal discovery algorithm for discovering the presence of agents from empirical data, given a set of variables and under certain assumptions. We also provide algorithms for translating between causal models and game-theoretic influence diagrams. We demonstrate our approach by resolving some previous confusions caused by incorrect causal modelling of agents.

We have extended the verified CakeML compiler with a new language primitive, Eval, which permits evaluation of new CakeML syntax at runtime. This new implementation supports an ambitious form of compilation at runtime and dynamic execution, where the original and dynamically added code can share (higher-order) values and recursively call each other. This is, to our knowledge, the first verified run-time environment capable of supporting a standard LCF-style theorem prover design. Modifying the modern CakeML compiler pipeline and proofs to support a dynamic computation semantics was an extensive project. We review the design decisions, proof techniques, and proof engineering lessons from the project, and highlight some unexpected complications.

This paper presents a fully verified interactive theorem prover for higher-order logic, more specifically: a fully verified clone of HOL Light. Our verification proof of this new system results in an end-to-end correctness theorem that guarantees the soundness of the entire system down to the machine code that executes at runtime. Our theorem states that every exported fact produced by this machine-code program is valid in higher-order logic. Our implementation consists of a read-eval-print loop (REPL) that executes the CakeML compiler internally. Throughout this work, we have strived to make the REPL of the new system provide a user experience as close to HOL Light’s as possible. To this end, we have, e.g., made the new system parse the same variant of OCaml syntax as HOL Light. All of the work described in this paper has been carried out in the HOL4 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.

Developing technology for building verified stacks, i.e., computer systems with comprehensive proofs of correctness, is one way the science of programming languages furthers the computing discipline. While there have been successful projects verifying complex, realistic system components, including compilers (software) and processors (hardware), to date these verification efforts have not been compatible to the point of enabling a single end-to-end correctness theorem about running a verified compiler on a verified processor.

Abstract The CakeML compiler is, to the best of our knowledge, the most realistic verified compiler for a functional programming language to date. The architecture of the compiler, a sequence of intermediate languages through which high-level features are compiled away incrementally, enables verification of each compilation pass at an appropriate level of semantic detail. Parts of the compiler’s implementation resemble mainstream (unverified) compilers for strict functional languages, and it supports several important features and optimisations. These include efficient curried multi-argument functions, configurable data representations, efficient exceptions, register allocation, and more. The compiler produces machine code for five architectures: x86-64, ARMv6, ARMv8, MIPS-64, and RISC-V. The generated machine code contains the verified runtime system which includes a verified generational copying garbage collector and a verified arbitrary precision arithmetic (bignum) library. In this paper, we present the overall design of the compiler backend, including its 12 intermediate languages. We explain how the semantics and proofs fit together and provide detail on how the compiler has been bootstrapped inside the logic of a theorem prover. The entire development has been carried out within the HOL4 theorem prover.

This paper describes how the latest CakeML compiler supports verified compilation down to multiple realistically modelled target architectures. In particular, we describe how the compiler definition, the various language semantics, and the correctness proofs were organised to minimize target-specific overhead. With our setup we have incorporated compilation to four 64-bit architectures, ARMv8, x86-64, MIPS-64, RISC-V, and one 32-bit architecture, ARMv6. Our correctness theorem allows interference from the environment: the top-level correctness statement takes into account execution of foreign code and per-instruction interference from external processes, such as interrupt handlers in operating systems. The entire CakeML development is formalised in the HOL4 theorem prover.

We have designed an intermediate language (IL) for the CakeML compiler that supports the verified, efficient compilation of functions and calls. Verified compilation steps include batching of multiple curried arguments, detecting calls to statically known functions, and specialising calls to known functions with no free variables. Finally, we verify the translation to a lower-level IL that only supports closed, first-order functions. These compilation steps resemble those found in other compilers (especially OCaml). Our contribution here is the design of the semantics of the IL, and the demonstration that our verification techniques over this semantics work well in practice at this scale. The entire development was carried out in the HOL4 theorem prover.

We have developed and mechanically verified a new compiler backend for CakeML. Our new compiler features a sequence of intermediate languages that allows it to incrementally compile away high-level features and enables verification at the right levels of semantic detail. In this way, it resembles mainstream (unverified) compilers for strict functional languages. The compiler supports efficient curried multi-argument functions, configurable data representations, exceptions that unwind the call stack, register allocation, and more. The compiler targets several architectures: x86-64, ARMv6, ARMv8, MIPS-64, and RISC-V.

We present a mechanised semantics for higher-order logic (HOL), and a proof of soundness for the inference system, including the rules for making definitions, implemented by the kernel of the HOL Light theorem prover. Our work extends Harrison’s verification of the inference system without definitions. Soundness of the logic extends to soundness of a theorem prover, because we also show that a synthesised implementation of the kernel in CakeML refines the inference system. Apart from adding support for definitions and synthesising an implementation, we improve on Harrison’s work by making our model of HOL parametric on the universe of sets, and we prove soundness for an improved principle of constant specification in the hope of encouraging its adoption. Our semantics supports defined constants directly via a context, and we find this approach cleaner than our previous work formalising Wiedijk’s Stateless HOL.

We have developed and mechanically verified an ML system called CakeML, which supports a substantial subset of Standard ML. CakeML is implemented as an interactive read-eval-print loop (REPL) in x86-64 machine code. Our correctness theorem ensures that this REPL implementation prints only those results permitted by the semantics of CakeML. Our verification effort touches on a breadth of topics including lexing, parsing, type checking, incremental and dynamic compilation, garbage collection, arbitrary-precision arithmetic, and compiler bootstrapping.