Analysis of Functional Transformation and Programs Neil Mitchell - - PDF document

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Analysis of Functional Transformation and Programs Neil Mitchell - - PDF document

Feb 14, 2023 28 likes •152 views

Analysis of Functional Transformation and Programs Neil Mitchell The Thesis Catch Uniplate Checking, safer Generic, shorter Supero Firstify Optimisation, faster Defunctionalisation Uniplate Generics library (similar to SYB1)

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SLIDE 1

Transformation and Analysis of Functional Programs

Neil Mitchell

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SLIDE 2

The Thesis Uniplate

Generic, shorter

Firstify

Defunctionalisation

Catch

Checking, safer

Supero

Optimisation, faster

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SLIDE 3

Uniplate

  • Generics library (similar to SYB1)
  • Write concise traversals over structures
  • Collect all variables in an expression:

[v | Var v <- universe x]

  • Make all variables title-case:

transform f where f (Var (x:xs)) = Var (toUpper x : xs) f x = x

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SLIDE 4

Uniplate advantages

  • No/few extensions
  • Simple types
  • Concise (~40% shorter than SYB)
  • Fast (at least 50% faster than SYB)
  • Makes use of compiler support
  • Does common stuff well
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SLIDE 5

Supero

  • A supercompiler

– Evaluate the program at compile time – Resituate so you terminate

  • Old ideas, but rarely implemented

– Supercompilation from Turchin – Homeomorphic embedding from Glück

  • First attempt for Haskell
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SLIDE 6

Supero improvements

  • New contributions

– A strategy for let bindings – A better generalisation

  • Competitive with C (microbenchmarks)
  • Faster than GHC (small benchmarks)
  • Still a prototype, lots of choices to make
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SLIDE 7

Firstify

  • Partial defunctionalisation +

First-order analysis method = Higher-order analysis method

  • Take several ingredients

– Arity raising, inlining, specialisation – Add termination bounds

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SLIDE 8

Firstify results

  • Very practically motivated

– Works well on the nofib suite

  • Stress test: print (0 :: Double)

– Makes use of Arrays, IO Monad, IO Function, Show Continuation, list comprehensions..

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SLIDE 9

Catch

  • Automatic safety proof

– If Catch says “Safe”, your program will not crash by calling error

  • First-order language (needs Firstify)
  • Division into two parts

– An algorithm (deals with Core) – A constraint language (the lossy bit)

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SLIDE 10

Catch constraints

  • Constraints must:

– Be finite (for a given type) – Provide three operations – The operations must be consistent

  • MP-constraints represent data type

patterns in a finite way

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SLIDE 11

Catch results

  • Tried on HsColour

– Real program, real users – Even a web service (hpaste.org) – Found 3 real bugs, now fixed – 1 false positive, but a nice refactoring

  • Very automatic, but still powerful
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SLIDE 12

Current status

  • Uniplate: already widely used
  • Supero: proof of concept
  • Firstify: works well enough for Catch
  • Catch: useful in some situations