Typed holes are a powerful feature in GHC inspired by Agda. But what are typed holes, and how do they help us write code?
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.
Co-Creator of Haskell: Functional Programming, Thinking in Types, Useless Languages | Simon Jones
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.
inanna-malick/jev-dsl
Agent-first Haskell DSL for TypeSafe's Jev judgment model: typed packets, inferred types, answers under the same labels
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
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Mathematics in type theory.
An explanation of how to set up mathematics using universes, types, and terms
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 ...
