haskell compiler as theorem prover
play

Haskell: Compiler as Theorem-Prover Greg Price ( price ) 2007 Nov 19 - PowerPoint PPT Presentation

Mar 02, 2023 •377 likes •869 views

Haskell: Compiler as Theorem-Prover Greg Price ( price ) 2007 Nov 19 code samples: http://cluedumps.mit.edu/wiki/2007/11-19 Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 1 / 26 Software Transactional Memory 1

  1. Haskell: Compiler as Theorem-Prover Greg Price ( price ) 2007 Nov 19 code samples: http://cluedumps.mit.edu/wiki/2007/11-19 Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 1 / 26

  2. Software Transactional Memory 1 Protocol Types 2 More theorems 3 The Big Picture 4 References 5 Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 2 / 26

  3. Software Transactional Memory Concurrency: locking Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 4 / 26

  4. Software Transactional Memory Concurrency: locking costly, deadlocks, bugs. Optimistic transactions, restarting Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 4 / 26

  5. Software Transactional Memory Concurrency: locking costly, deadlocks, bugs. Optimistic transactions, restarting Worse bugs: void f() { void g() { begin_transaction(); begin_transaction(); if (x != y) x++; launch_missiles(); y++; end_transaction(); end_transaction(); } } Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 4 / 26

  6. Software Transactional Memory Concurrency: locking costly, deadlocks, bugs. Optimistic transactions, restarting Worse bugs: void f() { void g() { begin_transaction(); begin_transaction(); if (x != y) x++; launch_missiles(); y++; end_transaction(); end_transaction(); } } Restart side effects? Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 4 / 26

  7. Software Transactional Memory Concurrency: locking costly, deadlocks, bugs. Optimistic transactions, restarting Worse bugs: void f() { void g() { begin_transaction(); begin_transaction(); if (x != y) x++; launch_missiles(); y++; end_transaction(); end_transaction(); } } Restart side effects? & all the old bugs too Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 4 / 26

  8. Software Transactional Memory Solution: f = atomically $ do xv <- readTVar x yv <- readTVar y if xv /= yv then launch_missiles_soon else return () g = atomically $ do xv <- readTVar x; writeTVar x (xv+1) yv <- readTVar y; writeTVar y (yv+1) (see example STMExample ) Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 6 / 26

  9. Software Transactional Memory Solution: f = atomically $ do xv <- readTVar x yv <- readTVar y if xv /= yv then launch_missiles_soon else return () g = atomically $ do xv <- readTVar x; writeTVar x (xv+1) yv <- readTVar y; writeTVar y (yv+1) (see example STMExample ) can’t have (non-transactional) side effects Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 6 / 26

  10. Software Transactional Memory Solution: f = atomically $ do xv <- readTVar x yv <- readTVar y if xv /= yv then launch_missiles_soon else return () g = atomically $ do xv <- readTVar x; writeTVar x (xv+1) yv <- readTVar y; writeTVar y (yv+1) (see example STMExample ) can’t have (non-transactional) side effects no special compiler support (except runtime) Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 6 / 26

  11. Software Transactional Memory Solution: f = atomically $ do xv <- readTVar x yv <- readTVar y if xv /= yv then launch_missiles_soon else return () g = atomically $ do xv <- readTVar x; writeTVar x (xv+1) yv <- readTVar y; writeTVar y (yv+1) (see example STMExample ) can’t have (non-transactional) side effects no special compiler support (except runtime) other bugs ruled out too Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 6 / 26

  12. STM: Guaranteeing No Side Effects pure Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 8 / 26

  13. STM: Guaranteeing No Side Effects pure putStr "hello" :: IO () Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 8 / 26

  14. STM: Guaranteeing No Side Effects pure an IO action putStr "hello" :: IO () Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 8 / 26

  15. STM: Guaranteeing No Side Effects pure an IO action putStr "hello" :: IO () sequenced: do { ...; f :: IO a; ... } Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 8 / 26

  16. STM: Guaranteeing No Side Effects pure an IO action putStr "hello" :: IO () sequenced: do { ...; f :: IO a; ... } executed only through main : main :: IO () main = do putStr "Hello world!\n" launch_missiles Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 8 / 26

  17. STM: Guaranteeing No Side Effects pure an IO action putStr "hello" :: IO () sequenced: do { ...; f :: IO a; ... } executed only through main : main :: IO () main = do putStr "Hello world!\n" launch_missiles ⇒ side effects only through type IO a Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 8 / 26

  18. STM: Guaranteeing No Side Effects side effects only through type IO a Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 10 / 26

  19. STM: Guaranteeing No Side Effects side effects only through type IO a atomically :: STM a -> IO a Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 10 / 26

  20. STM: Guaranteeing No Side Effects side effects only through type IO a atomically :: STM a -> IO a newTVar :: a -> STM (TVar a) readTVar :: TVar a -> STM a writeTVar :: TVar a -> a -> STM () Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 10 / 26

  21. STM: Guaranteeing No Side Effects side effects only through type IO a atomically :: STM a -> IO a newTVar :: a -> STM (TVar a) readTVar :: TVar a -> STM a writeTVar :: TVar a -> a -> STM () do { ...; f :: STM a; ... } (same) Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 10 / 26

  22. Software Transactional Memory 1 Protocol Types 2 More theorems 3 The Big Picture 4 References 5 Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 11 / 26

  23. Protocol Types spec :: Spec ((Snd Int :+: Snd String) :->: End) IOChan a protocol spec Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 13 / 26

  24. Protocol Types spec :: Spec ((Snd Int :+: Snd String) :->: End) IOChan � �� � s a protocol spec Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 13 / 26

  25. Protocol Types spec :: Spec ((Snd Int :+: Snd String) :->: End) IOChan � �� � s a protocol spec accept spec request spec Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 13 / 26

  26. Protocol Types spec :: Spec ((Snd Int :+: Snd String) :->: End) IOChan � �� � s a protocol spec accept spec :: (Extend M (ChanCap c s) e e’ n) => LinearT IO e e’ (LVar n) request spec :: (Dual s s’, Extend M (ChanCap c s’) e e’ n) => LinearT IO e e’ (LVar n) Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 13 / 26

  27. Protocol Types spec :: Spec ((Snd Int :+: Snd String) :->: End) IOChan � �� � s a protocol spec accept spec :: (Extend M (ChanCap c s) e e’ n) => LinearT IO e e’ (LVar n) request spec :: (Dual s s’, Extend M (ChanCap c s’) e e’ n) => LinearT IO e e’ (LVar n) runLinearT (accept spec >>>= ...) :: IO a executes protocol exactly Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 13 / 26

  28. Protocol Types: Means of Proof runLinearT :: LinearT IO Empty Empty a -> IO a Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 15 / 26

  29. Protocol Types: Means of Proof runLinearT :: LinearT IO Empty Empty a -> IO a environments of capabilities Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 15 / 26

  30. Protocol Types: Means of Proof runLinearT :: LinearT IO Empty Empty a -> IO a environments of capabilities send :: (Evolve n c (Snd a :->: x) e x e’) => LVar n -> a -> LinearT IO e e’ () recv :: (Evolve n c (Rcv a :->: x) e x e’) => LVar n -> LinearT IO e e’ a Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 15 / 26

  31. Protocol Types: Means of Proof runLinearT :: LinearT IO Empty Empty a -> IO a environments of capabilities send :: (Evolve n c (Snd a :->: x) e x e’) => LVar n -> a -> LinearT IO e e’ () recv :: (Evolve n c (Rcv a :->: x) e x e’) => LVar n -> LinearT IO e e’ a sel1 :: (Evolve n c ((x1:+:x2):->:y) e (x1:->:y) e’) => LVar n -> LinearT IO e e’ () Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 15 / 26

  32. Protocol Types: Generic Building Blocks data T class Prop a data F instance Prop T instance Prop F Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 17 / 26

  33. Protocol Types: Generic Building Blocks data T class Prop a data F instance Prop T instance Prop F class Prop b => Equal x y b | x y -> b Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 17 / 26

Recommend

1 What is a Theorem Prover? What is a Theorem? Theorem: A formalizable statement which is

1 What is a Theorem Prover? What is a Theorem? Theorem: A formalizable statement which is

Prerequisites Course 2D1453, 2006-07 Undergraduate logic and discrete maths CS literacy Advanced Formal Methods Some functional programming experience useful The theorem prover Isabelle is programming in SML Some SML

644 views • 4 slides
Meditation for a Theorem Prover Reasoning and Consciousness Teaching a Theorem Prover to let

Meditation for a Theorem Prover Reasoning and Consciousness Teaching a Theorem Prover to let

Meditation for a Theorem Prover Reasoning and Consciousness Teaching a Theorem Prover to let its Mind Wander Ulrich Furbach Claudia Schon Univ. Koblenz - DFG Project Cognitive Reasoning Reasoning and Consciousness Teaching a

715 views • 55 slides
A realtime GraphQL backend as a compiler in Haskell http://bit.ly/graphql-haskell Heippa!

A realtime GraphQL backend as a compiler in Haskell http://bit.ly/graphql-haskell Heippa!

A realtime GraphQL backend as a compiler in Haskell http://bit.ly/graphql-haskell Heippa! Tanmai Gopal @tanmaigo http://bit.ly/graphql-haskell Contents 1. The compiler approach 2. Compiler pipeline a. Parse b. GraphQL AST c.

467 views • 21 slides
A Self-Verifying Theorem Prover Jared Davis (advertisement by J Strother Moore)

A Self-Verifying Theorem Prover Jared Davis (advertisement by J Strother Moore)

A Self-Verifying Theorem Prover Jared Davis (advertisement by J Strother Moore) Department of Computer Sciences University of Texas at Austin September 18, 2009 1 Theorem Prover ? Yes Proof Checker Yes No 2 Rules of

693 views • 40 slides
CML Theorem Prover Simon Foster 2nd Review Brussels, 21 November, 2013 Deliverable: D33.2 (m24)

CML Theorem Prover Simon Foster 2nd Review Brussels, 21 November, 2013 Deliverable: D33.2 (m24)

CML Theorem Prover Simon Foster 2nd Review Brussels, 21 November, 2013 Deliverable: D33.2 (m24) www.compass-research.eu Theorem Prover Usage CML specifications to be verified by the COMPASS tool type-checking alone is insufficient to

311 views • 8 slides
A Parallelized Theorem Prover for Interactive Theorem Proving David L. Rager, Warren A. Hunt Jr.,

A Parallelized Theorem Prover for Interactive Theorem Proving David L. Rager, Warren A. Hunt Jr.,

Introduction Parallelism Primitives Parallelizing ACL2 Evaluate Approach Conclusion A Parallelized Theorem Prover for Interactive Theorem Proving David L. Rager, Warren A. Hunt Jr., and Matt Kaufmann ragerdl@defthm.com, hunt@cs.utexas.edu,

835 views • 59 slides
CSE 110A: Winter 2020 Fundamentals of Compiler Design I Intro to Haskell Owen Arden

CSE 110A: Winter 2020 Fundamentals of Compiler Design I Intro to Haskell Owen Arden

CSE 110A: Winter 2020 Fundamentals of Compiler Design I Intro to Haskell Owen Arden UC Santa Cruz Based on course materials developed by Nadia Polikarpova and Ranjit Jhala Why Haskell? Haskell programs tend to be simple and

190 views • 17 slides
Intel Labs Haskell Research Compiler Hai (Paul) Liu with Neal Glew, Leaf Peterson, Todd A.

Intel Labs Haskell Research Compiler Hai (Paul) Liu with Neal Glew, Leaf Peterson, Todd A.

Intel Labs Haskell Research Compiler Hai (Paul) Liu with Neal Glew, Leaf Peterson, Todd A. Anderson Intel Labs. September 28, 2016 Intel Labs Haskell Research Compiler An alternative Haskell compiler that: uses GHC as frontend; does

605 views • 48 slides
SMAC and XGBoost your Theorem Prover Edvard K. Holden Konstantin Korovin The University of

SMAC and XGBoost your Theorem Prover Edvard K. Holden Konstantin Korovin The University of

SMAC and XGBoost your Theorem Prover Edvard K. Holden Konstantin Korovin The University of Manchester 1 Theorem Proving in First-Order Logic Proof Axioms + Conjecture iProver | Counter model | Timeout 2 Heuristics - The Key to Success

1.03k views • 26 slides
The Helium Haskell compiler and its new LLVM backend Ivo Gabe de Wolff - ivogabe@ivogabe.nl [

The Helium Haskell compiler and its new LLVM backend Ivo Gabe de Wolff - ivogabe@ivogabe.nl [

The Helium Haskell compiler and its new LLVM backend Ivo Gabe de Wolff - ivogabe@ivogabe.nl [ Faculty of Science Information and Computing Sciences] 1 Haskell Functional Pure Lambda (function expression) Pattern matching

398 views • 29 slides
Lean Theorem Prover Tom van Bussel June 14, 2017 Goals It aims to bridge the gap between

Lean Theorem Prover Tom van Bussel June 14, 2017 Goals It aims to bridge the gap between

Lean Theorem Prover Tom van Bussel June 14, 2017 Goals It aims to bridge the gap between interactive and automated theorem proving, by situating automated tools and methods in a framework that supports user interaction and the construction

324 views • 21 slides
Hygienic Macros for the ACL2 Theorem Prover Carl Eastlund Matthias Felleisen cce@ccs.neu.edu

Hygienic Macros for the ACL2 Theorem Prover Carl Eastlund Matthias Felleisen cce@ccs.neu.edu

Hygienic Macros for the ACL2 Theorem Prover Carl Eastlund Matthias Felleisen cce@ccs.neu.edu matthias@ccs.neu.edu Northeastern University Boston, MA, USA 1 The ACL2 Theorem Prover 2 (defun double (x) (+ x x)) (defun map-double (lst) (if

898 views • 52 slides
Clause Features for Theorem Prover Guidance uv 1 Josef Urban 1 Jan Jakub AITP19, Obergurgl,

Clause Features for Theorem Prover Guidance uv 1 Josef Urban 1 Jan Jakub AITP19, Obergurgl,

Clause Features for Theorem Prover Guidance uv 1 Josef Urban 1 Jan Jakub AITP19, Obergurgl, Austria, April 2019 1 Czech Technical University in Prague, Czech Republic Jan Jakub uv, Josef Urban Clause Features for Theorem Prover Guidance

589 views • 35 slides
PROGR OGRAMMING NG IN N HA HASKE KELL LL Chapter 2 - First Steps 0 Glasgow Haskell

PROGR OGRAMMING NG IN N HA HASKE KELL LL Chapter 2 - First Steps 0 Glasgow Haskell

PROGR OGRAMMING NG IN N HA HASKE KELL LL Chapter 2 - First Steps 0 Glasgow Haskell Compiler GHC is the leading implementation of Haskell, and comprises a compiler and interpreter; The interactive nature of the interpreter makes it

403 views • 23 slides
The Abella Interactive Theorem Prover (System Description) Andrew Gacek Department of Computer

The Abella Interactive Theorem Prover (System Description) Andrew Gacek Department of Computer

The Abella Interactive Theorem Prover (System Description) Andrew Gacek Department of Computer Science and Engineering University of Minnesota IJCAR 08 August 12, 2008 Characteristics of the Abella System Abella is a theorem proving

794 views • 40 slides
Tableau Theorem Prover for Intuitionistic Propositional Logic Larry Diehl Portland State

Tableau Theorem Prover for Intuitionistic Propositional Logic Larry Diehl Portland State

Tableau Theorem Prover for Intuitionistic Propositional Logic Larry Diehl Portland State University CS 510 - Mathematical Logic and Programming Languages Larry Diehl Tableau Theorem Prover for Intuitionistic Propositional Logic Motivation

357 views • 22 slides
Tableau Theorem Prover for Intuitionistic Propositional Logic Larry Diehl Portland State

Tableau Theorem Prover for Intuitionistic Propositional Logic Larry Diehl Portland State

Tableau Theorem Prover for Intuitionistic Propositional Logic Larry Diehl Portland State University CS 510 - Mathematical Logic and Programming Languages Larry Diehl Tableau Theorem Prover for Intuitionistic Propositional Logic Motivation

289 views • 17 slides
yet another nice and accurate interactive theorem prover (sufficiently similar, sufficiently

yet another nice and accurate interactive theorem prover (sufficiently similar, sufficiently

yet another nice and accurate interactive theorem prover (sufficiently similar, sufficiently different) Freek Wiedijk Radboud University Nijmegen 2018 06 25 0 nice combining the nicest aspects of state-of-the-art provers:

288 views • 25 slides
The Lean Theorem Prover Jeremy Avigad Department of Philosophy and Department of Mathematical

The Lean Theorem Prover Jeremy Avigad Department of Philosophy and Department of Mathematical

The Lean Theorem Prover Jeremy Avigad Department of Philosophy and Department of Mathematical Sciences Carnegie Mellon University (Leans principal developer is Leonardo de Moura, Microsoft Research, Redmond) September 2014 . Automated

965 views • 14 slides
Deriving a Relationship from a Single Example Neil Mitchell community.haskell.org/~ndm/derive

Deriving a Relationship from a Single Example Neil Mitchell community.haskell.org/~ndm/derive

Deriving a Relationship from a Single Example Neil Mitchell community.haskell.org/~ndm/derive Haskell data type Haskell lets us define data types: data Language = Haskell [Extension] Compiler | Javascript | Cpp Version Eq instance

1.46k views • 56 slides
Reachability Analysis in the KeYmaera X Theorem Prover SNR 2017 | Uppsala, Sweden | April 22,

Reachability Analysis in the KeYmaera X Theorem Prover SNR 2017 | Uppsala, Sweden | April 22,

Reachability Analysis in the KeYmaera X Theorem Prover SNR 2017 | Uppsala, Sweden | April 22, 2017 Nathan Fulton Other System Contributors: Stefan Mitsch, Andr Platzer, Brandon Bohrer, Yong Kiam Tan, Jan-David Quesel, ... Trustworthy

932 views • 57 slides
Automation and Computation in the Lean Theorem Prover Robert Y. Lewis 1 Leonardo de Moura 2 1

Automation and Computation in the Lean Theorem Prover Robert Y. Lewis 1 Leonardo de Moura 2 1

Automation and Computation in the Lean Theorem Prover Robert Y. Lewis 1 Leonardo de Moura 2 1 Carnegie Mellon University 2 Microsoft Research, Redmond April 6, 2016 Goals for this talk Introduce Lean: a new proof assistant based on dependent

673 views • 39 slides
The Lean Theorem Prover Jeremy Avigad Department of Philosophy and Department of Mathematical

The Lean Theorem Prover Jeremy Avigad Department of Philosophy and Department of Mathematical

The Lean Theorem Prover Jeremy Avigad Department of Philosophy and Department of Mathematical Sciences Carnegie Mellon University June 29, 2017 Formal and Symbolic Methods Computers open up new opportunities for mathematical reasoning.

1.24k views • 57 slides
Formalising Filesystems in the ACL2 Theorem Prover An Application To FAT32 Mihir Mehta

Formalising Filesystems in the ACL2 Theorem Prover An Application To FAT32 Mihir Mehta

Formalising Filesystems in the ACL2 Theorem Prover An Application To FAT32 Mihir Mehta Department of Computer Science University of Texas at Austin mihir@cs.utexas.edu 05 November, 2018 1/25 Why filesystem verification matters

486 views • 25 slides

More recommend