András Kovács AndrasKovacs

Lightweight region memory management in a two-stage language

Intro
Basics
- Stage inference
Regions
- Bit-stealing
- Using regions
Eager regions

Basic setup for formalizing elaboration

First attempts

Elaboration is, broadly speaking, taking user-written syntax and converting it to "core" syntax by filling in missing information and at the same time validating that the input is well-formed.

I haven't been fully happy with formalizations that I previously used, so I make a new attempt here. I focus on a minimal dependently typed case.

Garbage collection with zero cost at non-GC time

Every once in a while I investigate low-level backend options for PL-s, although so far I haven't actually written any such backend for my projects. Recently I've been looking at precise garbage collection in popular backends, and I've been (like on previous occasions) annoyed by limitations and compromises.

I was compelled to think about a system which accommodates precise relocating GC as much as possible. In one extreme configuration, described in this note, there

Inductive-Recursive Types, Generally

I write about inductive-recursive types here. "Generally" means "higher inductive-inductive-recursive" or "quotient inductive-inductive-recursive". This may sound quite gnarly, but fortunately the specification of signatures can be given with just a few type formers in an appropriate framework.

In particular, we'll have a theory of signatures which includes Mike Shulman's higher IR example.



	{-# language
	BlockArguments
	, CPP
	, LambdaCase
	, MagicHash
	, PatternSynonyms
	, Strict
	, TypeApplications

	{-# OPTIONS --without-K #-}

	-- version 1, conversion is indexed over conversion
	module IndexedConv where

	data Con : Set
	data Ty : Con → Set
	data Sub : Con → Con → Set
	data Tm : ∀ Γ → Ty Γ → Set
	data Con~ : Con → Con → Set

	{-# language
	BlockArguments
	, ConstraintKinds
	, ImplicitParams
	, LambdaCase
	, OverloadedStrings
	, PatternSynonyms
	, Strict
	, UnicodeSyntax
	#-}

	{-# language BlockArguments, LambdaCase, Strict, UnicodeSyntax #-}

	{-\|
	Minimal dependent lambda caluclus with:
	- HOAS-only representation
	- Lossless printing
	- Bidirectional checking
	- Efficient evaluation & conversion checking

	Inspired by https://gist.github.com/Hirrolot/27e6b02a051df333811a23b97c375196


	{-# OPTIONS --prop --without-K --show-irrelevant --safe #-}

	{-
	Challenge:
	- Define a deeply embedded faithfully represented syntax of a dependently typed
	TT in Agda.
	- Use an Agda fragment which has canonicity. This means that the combination of
	indexed inductive types & cubical equality is not allowed!
	- Prove consistency.

	-- Examples

	data Foo = A \| B \| C

	foo :: Foo -> Int
	foo A = 10
	foo B
	foo C = 20

	foo :: Foo -> Int