Does anyone know the distinction between normalization and evaluation in the context of lambda calculus? I thought they were effectively the same, but then there is thing called 'normalization by evaluation':
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What does 'evaluation' mean in the context of the 'traditional approach'?
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Yeah, I've been attempting to convert things to the restricted subset of expressions in my dependently typed language Pikelet. I was calling this normalization, but thought it was interchangeable with evaluation.
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I was attempting to hackily get around having to do full substitution by just adding defs to the the context and then renormalising, but I'm now running into an issue where I'm not keeping track of captured variables.
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Breaks down on more complicated expressions. I then tried doing an explicit substitution approach like in the PiSigma paper, but then my normal forms weren't fully reduced, so I needed to have a more interesting conversion rule.
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I then wondered, "how do I fully reduce my 'normalised terms' into 'normal forms' as opposed to 'weak head normal forms'". Seemed like I had a gap in understanding and things were breaking down.
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Note that I'm also trying to avoid HOAS as is commonly used in Haskell/ML implementations, because Rust isn't as good at that stuff. (not sure, but it might lead to Rc cycles that wouldn't be cleaned up)
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