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Haskell, as implemented in the Glasgow Haskell Compiler (GHC), has been adding new type-level programming features for some time. Many of these features---chiefly: generalized algebraic datatypes (GADTs), type families, kind polymorphism, and promoted datatypes---have brought Haskell to the doorstep of dependent types. Many dependently typed programs can even currently be encoded, but often the constructions are painful. In this dissertation, I describe Dependent Haskell, which supports full<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1610.07978v2">arXiv:1610.07978v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a4emu7gcqfddznq4wbjf4mvhym">fatcat:a4emu7gcqfddznq4wbjf4mvhym</a> </span>
more »... endent types via a backward-compatible extension to today's Haskell. An important contribution of this work is an implementation, in GHC, of a portion of Dependent Haskell, with the rest to follow. The features I have implemented are already released, in GHC 8.0. This dissertation contains several practical examples of Dependent Haskell code, a full description of the differences between Dependent Haskell and today's Haskell, a novel type-safe dependently typed lambda-calculus (called Pico) suitable for use as an intermediate language for compiling Dependent Haskell, and a type inference and elaboration algorithm, Bake, that translates Dependent Haskell to type-correct Pico.
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