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Degrees of parallelism and Boolean algebras
Guillaume Geoffroy I2M, Aix-Marseille Université 12 June 2019
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Degrees of parallelism and Boolean algebras Guillaume Geoffroy I2M, - - PowerPoint PPT Presentation
Degrees of parallelism and Boolean algebras Guillaume Geoffroy I2M, - - PowerPoint PPT Presentation
Degrees of parallelism and Boolean algebras Guillaume Geoffroy I2M, Aix-Marseille Universit 12 June 2019 1 / 9 Denotational models Programming Denotational language model Denotational models Programming Denotational language model
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Denotational models
Programming language Denotational model program t denotation t
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Denotational models
Programming language Denotational model program t denotation t (fun x → t) u = t[x := u]
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Denotational models
Programming language Denotational model program t denotation t (fun x → t) u = t[x := u] etc.
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Left-first or
fun x y → if (x) then true else y
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Left-first or
fun x y → if (x) then true else y true false true true true false true false x y
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Left-first or
fun x y → if (x) then true else y true false true true true false true false ? true x y
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Left-first or
fun x y → if (x) then true else y true false true true true false true false ? true ? x y
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Left-first or
fun x y → if (x) then true else y true false ? true true true ? false true false ? ? true ? ? x y
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Right-first or
fun x y → if (y) true else x true false ? true true true true false true false ? ? ? ? ? x y
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Parallel (symmetric) or
true false ? true true true true false true false ? ? true ? ? x y
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Parallel (symmetric) or
fun x y → ??? true false ? true true true true false true false ? ? true ? ? x y
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Voting function
true true ? true ? true true true true ? true true false false ? false ? false false false false ? false false
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Voting and parallel or can simulate each other
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Voting and parallel or can simulate each other
← →
- r = fun x y → vote
− →
- r x y
← −
- r x y
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Voting and parallel or can simulate each other
← →
- r = fun x y → vote
− →
- r x y
← −
- r x y
- true
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Voting and parallel or can simulate each other
← →
- r = fun x y → vote
− →
- r x y
← −
- r x y
- true
vote = fun x y z → ← →
- r
← →
- r
- (←
→ and x y) (← → and y z)
- (←
→ and z x)
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Degrees of parallelism
← →
- r
vote G vote4
3
Sequential
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Degrees of parallelism: the wild west
← →
- r
vote G vote4
3
Sequential
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Degrees of parallelism and Boolean algebras
Very particular denotational models Formulas in the language
- f Boolean algebras
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Degrees of parallelism and Boolean algebras
Very particular denotational models Formulas in the language
- f Boolean algebras
denotation d formula Fd
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Degrees of parallelism and Boolean algebras
Very particular denotational models Formulas in the language
- f Boolean algebras
denotation d formula Fd d simulates e iff
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Degrees of parallelism and Boolean algebras
Very particular denotational models Formulas in the language
- f Boolean algebras
denotation d formula Fd d simulates e iff Fd entails Fe
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