AndrasKovacs

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

AndrasKovacs

{-# 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

AndrasKovacs

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

AndrasKovacs

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

AndrasKovacs

{-# 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

AndrasKovacs

{-# 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.

AndrasKovacs

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.

AndrasKovacs

-- Examples

data Foo = A | B | C

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

foo :: Foo -> Int

AndrasKovacs

{-
At ICFP 2022 I attended a talk given by Tomasz Drab, about this paper:

    "A simple and efficient implementation of strong call by need by an abstract machine"
    https://dl.acm.org/doi/10.1145/3549822

This is right up my alley since I've implemented strong call-by-need evaluation
quite a few times (without ever doing more formal analysis of it) and I'm also
interested in performance improvements. Such evaluation is required in
conversion checking in dependently typed languages.

AndrasKovacs

{-# OPTIONS --type-in-type #-}

open import Relation.Binary.PropositionalEquality
  renaming (cong to ap; sym to infixl 6 _⁻¹; subst to tr; trans to infixr 4 _◾_)
open import Data.Product
  renaming (proj₁ to ₁; proj₂ to ₂)

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NatAlg : Set