GHC/Typed holes - HaskellWiki

ghc-plugin-core-of-name/README.md at main · ocramz/ghc-plugin-core-of-name

Output the Core of a given Haskell expression with a GHC plugin - ocramz/ghc-plugin-core-of-name

Implementing a Hindley-Milner Type System (Part 1) | Blog

First part of a tutorial on implementing a Hindley-Milner type system for a simple, purely functional programming language in Haskell. We go over syntax representation, how the Hindley-Milner type system is defined, polymorphism vs. monomorphism, generalization, and instantiation.

Simply Typed Reverse-Mode Automatic Differentiation with Variants: Denotational Correctness via Idempotent Completion

Reverse-mode automatic differentiation can be derived denotationally as a structure-preserving interpretation of program syntax. In the usual simply typed model, each source type has one cotangent type. Variants break this representation because the valid cotangent space depends on the branch selected at run time; established correctness results therefore use primal-indexed families of cotangent spaces, whose direct internal language is dependent.

Theorems for free! | Proceedings of the fourth international conference on Functional programming languages and computer architecture

The polymorphic blame calculus integrates static typing, including universal types, with dynamic typing. The primary challenge with this integration is preserving parametricity: even dynamically-typed code should satisfy it once it has been cast to a ...

A theory of type polymorphism in programming

The aim of this work is largely a practical one. A widely employed style of programming, particularly in structure-processing languages which impose n…

Programming Language Foundations in Agda – Table of Contents

This book is an introduction to programming language theory using the proof assistant Agda.

Category Theory for Programmers: The Preface

Table of Contents Part One Category: The Essence of Composition Types and Functions Categories Great and Small Kleisli Categories Products and Coproducts Simple Algebraic Data Types Functors Functo…

Functional Query Languages with Categorical Types

We study three category-theoretic types in the context of functional query languages (typed lambda-calculi extended with additional operations for bulk data processing). The types we study are:

Principal type-schemes for functional programs | Proceedings of the 9th ACM SIGPLAN-SIGACT symposium on Principles of programming languages

As part of the Digital Library's transition to Open Access, new features for researchers are available in the Premium Edition. Click here to learn more.

Write You a Haskell ( Stephen Diehl )

Homotopy Type Theory: Univalent Foundations of Mathematics

Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type theory, which brings new ideas into the very foundation of mathematics. On the one hand, Voevodsky's subtle and beautiful "univalence axiom" implies that isomorphic structures can be identified. On the other hand, "higher inductive types" provide direct, logical descriptions of some of the basic spaces and constructions of homotopy theory. Both are impossible to capture directly in classical set-theoretic foundations, but when combined in homotopy type theory, they permit an entirely new kind of "logic of homotopy types". This suggests a new conception of foundations of mathematics, with intrinsic homotopical content, an "invariant" conception of the objects of mathematics -- and convenient machine implementations, which can serve as a practical aid to the working mathematician. This book is intended as a first systematic exposition of the basics of the resulting "Univalent Foundations" program, and a collection of examples of this new style of reasoning -- but without requiring the reader to know or learn any formal logic, or to use any computer proof assistant.

Generic deriving of generic traversals | Proceedings of the ACM on Programming Languages

Functional programmers have an established tradition of using traversals as a design pattern to work with recursive data structures. The technique is so prolific that a whole host of libraries have been designed to help in the task of automatically ...

Homotopical patch theory | ACM SIGPLAN Notices

Homotopy type theory is an extension of Martin-Löf type theory, based on a correspondence with homotopy theory and higher category theory. In homotopy type theory, the propositional equality type becomes proof-relevant, and corresponds to paths in a ...

generalized algebraic theory in nLab

A generalized algebraic theory (GAT, Cartmell 1978/86) is a dependent type theory in the syntactic sense: There are judgments declaring types and terms of types, where, critically, a type AA declared in context Γ\Gamma is allowed to depend on terms of Γ\Gamma. The only other judgments allowed are of equality (judgemental equality) of pairs of types or terms.

GATlab: Modeling and Programming with Generalized Algebraic Theories

Categories and categorical structures are increasingly recognized as useful abstractions for modeling in science and engineering. To uniformly implement category-theoretic mathematical models in software, we introduce GATlab, a domain-specific language for algebraic specification embedded in a technical programming language. GATlab is based on generalized algebraic theories (GATs), a logical system extending algebraic theories with dependent types so as to encompass category theory. Using GATlab, the programmer can specify generalized algebraic theories and their models, including both free models, based on symbolic expressions, and computational models, defined by arbitrary code in the host language. Moreover, the programmer can define maps between theories and use them to declaratively migrate models of one theory to models of another. In short, GATlab aims to provide a unified environment for both computer algebra and software interface design with generalized algebraic theories. In this paper, we describe the design, implementation, and applications of GATlab.