1,207,160 research outputs found
Applied Type System: An Approach to Practical Programming with Theorem-Proving
The framework Pure Type System (PTS) offers a simple and general approach to
designing and formalizing type systems. However, in the presence of dependent
types, there often exist certain acute problems that make it difficult for PTS
to directly accommodate many common realistic programming features such as
general recursion, recursive types, effects (e.g., exceptions, references,
input/output), etc. In this paper, Applied Type System (ATS) is presented as a
framework for designing and formalizing type systems in support of practical
programming with advanced types (including dependent types). In particular, it
is demonstrated that ATS can readily accommodate a paradigm referred to as
programming with theorem-proving (PwTP) in which programs and proofs are
constructed in a syntactically intertwined manner, yielding a practical
approach to internalizing constraint-solving needed during type-checking. The
key salient feature of ATS lies in a complete separation between statics, where
types are formed and reasoned about, and dynamics, where programs are
constructed and evaluated. With this separation, it is no longer possible for a
program to occur in a type as is otherwise allowed in PTS. The paper contains
not only a formal development of ATS but also some examples taken from
ats-lang.org, a programming language with a type system rooted in ATS, in
support of employing ATS as a framework to formulate advanced type systems for
practical programming
Formal verification in Coq of program properties involving the global state effect
The syntax of an imperative language does not mention explicitly the state,
while its denotational semantics has to mention it. In this paper we present a
framework for the verification in Coq of properties of programs manipulating
the global state effect. These properties are expressed in a proof system which
is close to the syntax, as in effect systems, in the sense that the state does
not appear explicitly in the type of expressions which manipulate it. Rather,
the state appears via decorations added to terms and to equations. In this
system, proofs of programs thus present two aspects: properties can be verified
{\em up to effects} or the effects can be taken into account. The design of our
Coq library consequently reflects these two aspects: our framework is centered
around the construction of two inductive and dependent types, one for terms up
to effects and one for the manipulation of decorations
Recommended from our members
Robust permanence for ecological equations with internal and external feedbacks.
Species experience both internal feedbacks with endogenous factors such as trait evolution and external feedbacks with exogenous factors such as weather. These feedbacks can play an important role in determining whether populations persist or communities of species coexist. To provide a general mathematical framework for studying these effects, we develop a theorem for coexistence for ecological models accounting for internal and external feedbacks. Specifically, we use average Lyapunov functions and Morse decompositions to develop sufficient and necessary conditions for robust permanence, a form of coexistence robust to large perturbations of the population densities and small structural perturbations of the models. We illustrate how our results can be applied to verify permanence in non-autonomous models, structured population models, including those with frequency-dependent feedbacks, and models of eco-evolutionary dynamics. In these applications, we discuss how our results relate to previous results for models with particular types of feedbacks
Mathematical modeling of tumor therapy with oncolytic viruses: Effects of parametric heterogeneity on cell dynamics
One of the mechanisms that ensure cancer robustness is tumor heterogeneity,
and its effects on tumor cells dynamics have to be taken into account when
studying cancer progression. There is no unifying theoretical framework in
mathematical modeling of carcinogenesis that would account for parametric
heterogeneity. Here we formulate a modeling approach that naturally takes stock
of inherent cancer cell heterogeneity and illustrate it with a model of
interaction between a tumor and an oncolytic virus. We show that several
phenomena that are absent in homogeneous models, such as cancer recurrence,
tumor dormancy, an others, appear in heterogeneous setting. We also demonstrate
that, within the applied modeling framework, to overcome the adverse effect of
tumor cell heterogeneity on cancer progression, a heterogeneous population of
an oncolytic virus must be used. Heterogeneity in parameters of the model, such
as tumor cell susceptibility to virus infection and virus replication rate, can
lead to complex, time-dependent behaviors of the tumor. Thus, irregular,
quasi-chaotic behavior of the tumor-virus system can be caused not only by
random perturbations but also by the heterogeneity of the tumor and the virus.
The modeling approach described here reveals the importance of tumor cell and
virus heterogeneity for the outcome of cancer therapy. It should be
straightforward to apply these techniques to mathematical modeling of other
types of anticancer therapy.Comment: 45 pages, 6 figures; submitted to Biology Direc
A Framework for Resource Dependent EDSLs in a Dependently Typed Language (Artifact)
Idris' Effects library demonstrates how to embed resource dependent algebraic effect handlers into a dependently typed host language, providing run-time and compile-time based reasoning on type-level resources. Building upon this work, Resources is a framework for realising Embedded Domain Specific Languages (EDSLs) with type systems that contain domain specific substructural properties. Differing from Effects, Resources allows a language’s substructural properties to be encoded within type-level resources that are associated with language variables. Such an association allows for multiple effect instances to be reasoned about autonomically and without explicit type-level declaration. Type-level predicates are used as proof that the language’s substructural properties hold. Several exemplar EDSLs are presented that illustrates our framework’s operation and how dependent types provide correctness-by-construction guarantees that substructural properties of written programs hold
A Framework for Resource Dependent EDSLs in a Dependently Typed Language (Pearl)
Idris' Effects library demonstrates how to embed resource dependent algebraic effect handlers into a dependently typed host language, providing run-time and compile-time based reasoning on type-level resources. Building upon this work, Resources is a framework for realising Embedded Domain Specific Languages (EDSLs) with type systems that contain domain specific substructural properties. Differing from Effects, Resources allows a language’s substructural properties to be encoded within type-level resources that are associated with language variables. Such an association allows for multiple effect instances to be reasoned about autonomically and without explicit type-level declaration. Type-level predicates are used as proof that the language’s substructural properties hold. Several exemplar EDSLs are presented that illustrates our framework’s operation and how dependent types provide correctness-by-construction guarantees that substructural properties of written programs hold
ICT Strategies of Democratic Intermediaries
A conceptual framework is proposed for discussing the ICT strategies of intermediaries and their effects on democratic intermediation. The main line of reasoning is that both ‘disintermediation’ and ‘re-intermediation’ have to be related to specific models of democracy and styles of citizenship. The linkage strategies of preference intermediaries, the supportive strategies of information intermediaries and the facilitative strategies of interaction intermediaries are discussed. The quality of democracy would be dependent on the interplay between different democratic practices, types of citizenship and intermediaries
- …