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https://github.com/rybla/monadic-quicksort-verification
A Liquid Haskell verification of Mu and Chiang's "Deriving Monadic Quicksort."
https://github.com/rybla/monadic-quicksort-verification
Last synced: about 4 hours ago
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A Liquid Haskell verification of Mu and Chiang's "Deriving Monadic Quicksort."
- Host: GitHub
- URL: https://github.com/rybla/monadic-quicksort-verification
- Owner: rybla
- Created: 2021-01-05T21:35:51.000Z (almost 4 years ago)
- Default Branch: master
- Last Pushed: 2021-07-09T03:14:29.000Z (over 3 years ago)
- Last Synced: 2024-04-24T03:14:11.192Z (7 months ago)
- Language: SMT
- Homepage:
- Size: 26.2 MB
- Stars: 1
- Watchers: 2
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: ChangeLog.md
Awesome Lists containing this project
README
# Propositional Equality for Refinement Types
## How to run
```
# install the propositional equality library
cd propositional-equality
stack install
# run the tests/ examples in the paper
stack test
# run the case study
cd ..
stack install
```
# EDITS
old src: & new src & paper
PropositionalEquality & Relation.Equality.Prop & PEqProperties &
Relation.Equality.Prop &
EqRT & EqualProp & EqT & EqualityProp &
Reflexivity & Redefined as empty & refl & reflexivity &
Symmetry & Equality sym & symmetry Transitivity & Transitivity' & trans &
transitivity' & toSMT & concreteness & EqCtx & substitutability (+ flip args) &
eqRTCtx & same EqSMT & fromEqSMT EqFun & extensionality eqSMT & reflexivity
- all require importing refined unit :(
# TODO
Some restructuring could help. Maybe make them both top level dirsctories?
# Monadic Quicksort Verification in Liquid Haskell
A Liquid Haskell verification of Mu and Chiang's _[Deriving Monadic
Quicksort][mu s, chiang t - declarative pearl- deriving monadic quicksort]_.
## Tasks
- [ ] remove all top-level references to infixed notation, it seems to cause
problems that I cannot avoid. This will take a lot of effort, but its the
only thing I've found to work
- [ ] try `--fast` option
`Placeholder.M`:
- [ ] implement `interpretM`
- [x] prove `kleisli_associativity`
- [x] prove `bind_if`
- [x] prove `seq_bind_associativity`
- [x] prove `bind_associativity4`
- [x] prove `seq_associativity4`
- [x] prove `seq_pure_bind`
- [x] prove `seq_if_bind`
- [x] prove `pure_kleisli`
- [x] prove `refinesplus_equalprop`
- [x] prove `refinesplus_reflexivity`
- [x] prove `refinesplus_transitivity`
- [x] prove `refinesplus_substitutability`
- [x] prove `writeList_append`
- [x] prove `writeList_redundancy`
- [x] prove `writeList_commutativity`
`Sort.List`:
- [ ] prove termination `permute`
- [x] prove `pure_refines_permute`
- [x] prove `permute_preserves_length`
- [x] prove `bind_seq_associativity_with_permute_preserved_length`
- [x] prove `divide_and_conquer`
- [x] use auxes for `divide_and_conquer_aux`
- [x] prove `divide_and_conquer_lemma1`:
- [x] use auxes for `divide_and_conquer_lemma1_aux`
- [x] several `bind_associativity`
- [x] several `guard_and`
- [x] rearrange `guard`s
- [x] uses auxes to box `divide_and_conquer_lemma1_aux`
- [x] prove `divide_and_conquer_lemma2`
- [x] prove `Cons` case
- [x] progress with `guard` properties
- [x] prove `quicksort_refines_slowsort`
- [x] prove `Cons` case
`Sort.Array`:
- [x] prove `permute_kleisli_permute` in `Cons` case
- [x] prove `permute_kleisli_permute_lemma` in `Cons` case
- [x] prove `ipartl_spec`
- [x] prove `dispatch_preserves_length_append_ys_zs`
- [x] prove `dispatch_commutativity_seq_bind`
- [x] prove `ipartl_spec_lemma1`
- [x] prove `ipartl_spec_lemma1_step1`
- [x] prove `ipartl_spec_lemma1_step1`
- [x] prove `ipartl_spec_lemma1_step1`
- [x] prove `ipartl_spec_lemma2`
- [x] prove `ipartl_spec_lemma2_step1`
- [x] prove `ipartl_spec_lemma2_step2`
- [x] prove `ipartl_spec_lemma2_step3`
- [x] prove `ipartl_spec_lemma3`
- [x] prove `ipartl_spec_lemma3_aux1_Nil`
- [x] prove `ipartl_spec_lemma3_aux2_Nil`
- [x] case `Cons`
- [x] prove `ipartl_spec_lemma3_aux1_Cons`
- [x] prove `ipartl_spec_lemma3_aux2_Cons`
- [x] prove `ipartl_spec_steps1to3`
- [x] prove `ipartl_spec_steps1to3_lemma`
- [x] prove `ipartl_spec_steps3Ato4`
- [x] prove `ipartl_spec_steps4to7`
- [x] prove `ipartl_spec_steps4to7_lemma1`
- [x] prove `ipartl_spec_steps4to7_lemma2`
- [x] prove `ipartl_spec_steps4to5`
- [x] prove `ipartl_spec_steps4to5_lemma1`
- [x] prove `ipartl_spec_steps4to5_lemma2`
- [x] prove `ipartl_spec_steps5to6`
- [x] prove `ipartl_spec_steps6to7`
- [x] prove `ipartl_spec_steps7to8`
- [x] prove `ipartl_spec_steps7to8_lemma`
- [x] prove `ipartl_spec_steps8to9`
- [x] prove `ipartl_spec_steps`
- [ ] prove termination `iqsort`
- [x] prove `iqsort_spec`
- [x] prove `iqsort_step1`
- [x] prove `iqsort_step2`
- [x] prove `iqsort_step3`
- [x] prove `iqsort_step4`
[mu s, chiang t - declarative pearl- deriving monadic quicksort]:
https://scm.iis.sinica.edu.tw/pub/2020-monadic-sort.pdf