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New draft: Proofs, upside down
There is a new draft on my web page, that should be of interest to those who enjoyed my posts about reversing data structures and the relation between natural deduction and sequent calculus. It is an...
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New draft on Normalization by Evaluation using GADTs
There is a new draft on my web page! It is called Tagless and Typeful Normalization by Evaluation using Generalized Algebraic Data Types, which is a mouthful, but only describes accurately the cool new...
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Quick, dirty and shallow definitions
Here is a quick hack. A few months ago, I advocated for pointer equality in OCaml (==) as a way to deal with fresh symbols in a toy compiler. Today, I’ll show another application of pointer equality:...
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1 ≠ 0
Learning Coq is usually an enlightening experience. I know it first-hand, it can also be a quite frustrating one, because it seems at first to involve remembering quite a lot of arbitrarily-named...
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Update on Typeful Normalization by Evaluation
In October, I publicized here a new draft on normalization by evaluation, which provoked some very helpful comments and constructive criticisms. Together with Chantal and Olivier, we thus revised the...
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Representing pattern-matching with GADTs
Here is a little programming pearl. I’ve been wanting to work on pattern-matching for a while now, and it seems like I will finally have this opportunity here at my new (academic) home, McGill....
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Big-step disjunctive normal forms
This is probably a second-semester functional programming exercise, but I found it surprisingly hard, and could not find a solution online. So at the risk of depriving a TA from a problem for its...
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Typeful disjunctive normal form
This is the answer to last post’s puzzle. I gave an algorithm to put a formula in disjunctive normal form, and suggested to prove it correct in OCaml, thanks to GADTs. My solution happens to include a...
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Escaping continuations
Beta had a funny joke at POPL last year; he said: “you exit a monad like you exit a building on fire: by running”. I recently got myself in the stressful situation of being trapped in a monad—the...
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Parametric HOAS with first-class modules
One of the first choice to make when starting the development of a compiler, or any program manipulating syntax with binders (e.g. programs with functions and variables), is how to represent these...
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