2,773 research outputs found
Introducing a Calculus of Effects and Handlers for Natural Language Semantics
In compositional model-theoretic semantics, researchers assemble
truth-conditions or other kinds of denotations using the lambda calculus. It
was previously observed that the lambda terms and/or the denotations studied
tend to follow the same pattern: they are instances of a monad. In this paper,
we present an extension of the simply-typed lambda calculus that exploits this
uniformity using the recently discovered technique of effect handlers. We prove
that our calculus exhibits some of the key formal properties of the lambda
calculus and we use it to construct a modular semantics for a small fragment
that involves multiple distinct semantic phenomena
Meta-F*: Proof Automation with SMT, Tactics, and Metaprograms
We introduce Meta-F*, a tactics and metaprogramming framework for the F*
program verifier. The main novelty of Meta-F* is allowing the use of tactics
and metaprogramming to discharge assertions not solvable by SMT, or to just
simplify them into well-behaved SMT fragments. Plus, Meta-F* can be used to
generate verified code automatically.
Meta-F* is implemented as an F* effect, which, given the powerful effect
system of F*, heavily increases code reuse and even enables the lightweight
verification of metaprograms. Metaprograms can be either interpreted, or
compiled to efficient native code that can be dynamically loaded into the F*
type-checker and can interoperate with interpreted code. Evaluation on
realistic case studies shows that Meta-F* provides substantial gains in proof
development, efficiency, and robustness.Comment: Full version of ESOP'19 pape
Theory and Practice of Action Semantics
Action Semantics is a framework for the formal descriptionof programming languages. Its main advantage over other frameworksis pragmatic: action-semantic descriptions (ASDs) scale up smoothly torealistic programming languages. This is due to the inherent extensibilityand modifiability of ASDs, ensuring that extensions and changes tothe described language require only proportionate changes in its description.(In denotational or operational semantics, adding an unforeseenconstruct to a language may require a reformulation of the entire description.)After sketching the background for the development of action semantics,we summarize the main ideas of the framework, and provide a simpleillustrative example of an ASD. We identify which features of ASDsare crucial for good pragmatics. Then we explain the foundations ofaction semantics, and survey recent advances in its theory and practicalapplications. Finally, we assess the prospects for further developmentand use of action semantics.The action semantics framework was initially developed at the Universityof Aarhus by the present author, in collaboration with David Watt(University of Glasgow). Groups and individuals scattered around fivecontinents have since contributed to its theory and practice
Adventures in Formalisation: Financial Contracts, Modules, and Two-Level Type Theory
We present three projects concerned with applications of proof assistants in
the area of programming language theory and mathematics. The first project is
about a certified compilation technique for a domain-specific programming
language for financial contracts (the CL language). The code in CL is
translated into a simple expression language well-suited for integration with
software components implementing Monte Carlo simulation techniques (pricing
engines). The compilation procedure is accompanied with formal proofs of
correctness carried out in Coq. The second project presents techniques that
allow for formal reasoning with nested and mutually inductive structures built
up from finite maps and sets. The techniques, which build on the theory of
nominal sets combined with the ability to work with isomorphic representations
of finite maps, make it possible to give a formal treatment, in Coq, of a
higher-order module system, including the ability to eliminate at compile time
abstraction barriers introduced by the module system. The development is based
on earlier work on static interpretation of modules and provides the foundation
for a higher-order module language for Futhark, an optimising compiler
targeting data-parallel architectures. The third project presents an
implementation of two-level type theory, a version of Martin-Lof type theory
with two equality types: the first acts as the usual equality of homotopy type
theory, while the second allows us to reason about strict equality. In this
system, we can formalise results of partially meta-theoretic nature. We develop
and explore in details how two-level type theory can be implemented in a proof
assistant, providing a prototype implementation in the proof assistant Lean. We
demonstrate an application of two-level type theory by developing some results
on the theory of inverse diagrams using our Lean implementation.Comment: PhD thesis defended in January 2018 at University of Copenhagen,
Department of Computer Scienc
Trees from Functions as Processes
Levy-Longo Trees and Bohm Trees are the best known tree structures on the
{\lambda}-calculus. We give general conditions under which an encoding of the
{\lambda}-calculus into the {\pi}-calculus is sound and complete with respect
to such trees. We apply these conditions to various encodings of the
call-by-name {\lambda}-calculus, showing how the two kinds of tree can be
obtained by varying the behavioural equivalence adopted in the {\pi}-calculus
and/or the encoding
Action semantics in retrospect
This paper is a themed account of the action semantics project, which Peter Mosses has led since the 1980s. It explains his motivations for developing action semantics, the inspirations behind its design, and the foundations of action semantics based on unified algebras. It goes on to outline some applications of action semantics to describe real programming languages, and some efforts to implement programming languages using action semantics directed compiler generation. It concludes by outlining more recent developments and reflecting on the success of the action semantics project
Data re-engineering using formal transformations
This thesis presents and analyses a solution to the problem of formally re- engineering program data structures, allowing new representations of a program to be developed. The work is based around Ward's theory of program transformations which uses a Wide Spectrum Language, WSL, whose semantics were specially developed for use in proof of program transformations. The re-engineered code exhibits equivalent functionality to the original but differs in the degree of data abstraction and representation. Previous transformational re-engineering work has concentrated upon control flow restructuring, which has highlighted a lack of support for data restructuring in the maintainer's tool-set. Problems have been encountered during program transformation due to the lack of support for data re-engineering. A lack of strict data semantics and manipulation capabilities has left the maintainer unable to produce optimally re-engineered solutions. It has also hindered the migration of programs into other languages because it has not been possible to convert data structures into an appropriate form in the target language. The main contribution of the thesis is the Data Re-Engineering and Abstraction Mechanism (DREAM) which allows theories about type equivalence to be represented and used in a re-engineering environment. DREAM is based around the technique of "ghosting", a way of introducing different representations of data, which provides the theoretical underpinning of the changes applied to the program. A second major contribution is the introduction of data typing into the WSL language. This allows DREAM to be integrated into the existing transformation theories within WSL. These theoretical extensions of the original work have been shown to be practically viable by implementation within a prototype transformation tool, the Maintainer's Assistant. The extended tool has been used to re-engineer heavily modified, commercial legacy code. The results of this have shown that useful re-engineering work can be performed and that DREAM integrates well with existing control flow transformations
Type Checking Semantic Functions in ASDF
When writing semantic descriptions of programming languages, it is convenient to have tools for checking the descriptions. With frameworks that use inductively defined semantic functions to map programs to their denotations, we would like to check that the semantic functions result in denotations with certain properties. In this paper we present a type system for a modular style of the action semantic framework that, given signatures of all the semantic functions used in a semantic equation defining a semantic function, performs a soft type check on the action in the semantic equation. We introduce types for actions that describe different properties of the actions, like the type of data they expect and produce, whether they can fail or have side effects, etc. A type system for actions which uses these new action types is presented. Using the new action types in the signatures of semantic functions, the language describer can assert properties of semantic functions and have the assertions checked by an implementation of the type system. The type system has been implemented for use in connection with the recently developed formalism ASDF. The formalism supports writing language definitions by combining modules that describe single language constructs. This is possible due to the inherent modularity in ASDF. We show how we manage to preserve the modularity and still perform specialised type checks for each module
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