Related papers: Type Theory With Erasure
We formalize a new type system for Elixir, a dynamically typed functional programming language of growing popularity that runs on the Erlang virtual machine. Our system combines gradual typing with semantic subtyping to enable precise,…
We present the type system $\mathtt{d}$, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. $\mathtt{d}$ extends existing lambda-typed systems by an existential…
Initial Semantics aims at interpreting the syntax associated to a signature as the initial object of some category of 'models', yielding induction and recursion principles for abstract syntax. Zsid\'o proves an initiality result for…
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…
A model of Martin-L\"of extensional type theory with universes is formalized in Agda, an interactive proof system based on Martin-L\"of intensional type theory. This may be understood, we claim, as a solution to the old problem of modelling…
Gradually typed languages are designed to support both dynamically typed and statically typed programming styles while preserving the benefits of each. While existing gradual type soundness theorems for these languages aim to show that…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
We present Tores, a core language for encoding metatheoretic proofs. The novel features we introduce are well-founded Mendler-style (co)recursion over indexed data types and a form of recursion over objects in the index language to build…
Generalised algebraic theories (GATs) allow multiple sorts indexed over each other. For example, the theories of categories or Martin-L{\"o}f type theories form GATs. Categories have two sorts, objects and morphisms, and the latter are…
The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage…
In various subjects including mathematics, one can hope to use mathematical thinking well when the right kinds of algebraic structure to consider can be discovered or spotted. Therefore, it would help to understand kinds of algebraic…
Tensor decomposition has recently been gaining attention in the machine learning community for the analysis of individual traces, such as Electronic Health Records (EHR). However, this task becomes significantly more difficult when the data…
We introduce layers to modal type theories, which subsequently enables type theories for pattern matching on code in meta-programming and clean and straightforward semantics.
Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program properties. There have been many such theories in recent years which equip a type theory with…
Mathematical morphology contributes many profitable tools to image processing area. Some of these methods considered to be basic but the most important fundamental of data processing in many various applications. In this paper, we modify…
Besides the text content, documents and their associated words usually come with rich sets of meta informa- tion, such as categories of documents and semantic/syntactic features of words, like those encoded in word embeddings. Incorporating…
We develop formal theories of conversion for Church-style lambda-terms with Pi-types in first-order syntax using one-sorted variables names and Stoughton's multiple substitutions. We then formalize the Pure Type Systems along some…
Algorithmic meta-theorems state that problems definable in a fixed logic can be solved efficiently on structures with certain properties. An example is Courcelle's Theorem, which states that all problems expressible in monadic second-order…
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of…
Session types have emerged as a powerful paradigm for structuring communication-based programs. They guarantee type soundness and session fidelity for concurrent programs with sophisticated communication protocols. As type soundness proofs…