相关论文: First-order natural deduction in Agda
The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual…
In this paper we describe how to leverage higher-order unification to type check a dependently typed language with meta-variables. The literature usually presents the unification algorithm as a standalone component, however the need to…
The gradual guarantee is an important litmus test for gradually typed languages, that is, languages that enable a mixture of static and dynamic typing. The gradual guarantee states that changing the precision of a type annotation does not…
We show how the basic Combinatory Homomorphic Automatic Differentiation (CHAD) algorithm can be optimised, using well-known methods, to yield a simple, composable, and generally applicable reverse-mode automatic differentiation (AD)…
We study a type checking algorithm that is able to type check a nontrivial subclass of functional programs that use features such as higher-rank, impredicative and second-order types. The only place the algorithm requires type annotation is…
We show how to apply forward and reverse mode Combinatory Homomorphic Automatic Differentiation (CHAD) to total functional programming languages with expressive type systems featuring the combination of - tuple types; - sum types; -…
We present Dependent Lambek Calculus, a domain-specific dependent type theory for verified parsing and formal grammar theory. In $\textrm{Lambek}^D$, linear types are used as a syntax for formal grammars,and parsers can be written as linear…
Andromeda is an LCF-style proof assistant where the user builds derivable judgments by writing code in a meta-level programming language AML. The only trusted component of Andromeda is a minimalist nucleus (an implementation of the…
Liquid Haskell is an extension to the Haskell programming language that adds support for refinement types: data types augmented with SMT-decidable logical predicates that refine the set of values that can inhabit a type. Furthermore, Liquid…
Dependent types help programmers write highly reliable code. However, this reliability comes at a cost: it can be challenging to write new prototypes in (or migrate old code to) dependently-typed programming languages. Gradual typing makes…
Graded Type Theory provides a mechanism to track and reason about resource usage in type systems. In this paper, we develop GraD, a novel version of such a graded dependent type system that includes functions, tensor products, additive…
In this paper we present the probabilistic typed natural deduction calculus TPTND, designed to reason about and derive trustworthiness properties of probabilistic computational processes, like those underlying current AI applications.…
Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…
We examine the connections between deterministic, complete, and general global optimisation of continuous functions and a general concept of regression from the perspective of constructive type theory via the concept of 'searchability'. We…
First-order logic is a natural way of expressing properties of computation. It is traditionally used in various program logics for expressing the correctness properties and certificates. Although such representations are expressive for some…
Native type systems are those in which type constructors are derived from term constructors, as well as the constructors of predicate logic and intuitionistic type theory. We present a method to construct native type systems for a broad…
Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful…
Gradually typed programming languages, which allow for soundly mixing static and dynamically typed programming styles, present a strong challenge for metatheorists. Even the simplest sound gradually typed languages feature at least…
We show that verification of object-oriented programs by means of the assertional method can be achieved in a simple way by exploiting a syntax-directed transformation from object-oriented programs to recursive programs. This transformation…
Within dependent type theory, we provide a topological counterpart of well-founded trees (for short, W-types) by using a proof-relevant version of the notion of inductively generated suplattices introduced in the context of formal topology…