Composing Transformations with Strategy Combinators

Composing Transformations with Strategy Combinators

CS4200 | Compiler Construction | November 12, 2020

Eelco Visser

Rewriting = Matching & Building

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Parameterized Rewrite Rules

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f(x,y|a,b): lhs -> rhs- strategy or rule parameters x,y- term parameters a,b- no matching

f(|a,b): lhs -> rhs- optional strategy parameters

f(x,y): lhs -> rhs- optional term parameters

f: lhs -> rhs

Parameterized Rewrite Rules

Parameterized Rewrite Rules: Map

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[ 1, 2, 3]

[ 2, 3, 4]

map(inc)

inc

1

2

3

2

3

4inc

inc

map(s): [] -> []map(s): [x|xs] -> [<s> x | <map(s)> xs]

Parameterized Rewrite Rules: Zip

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[ 1, 2, 3]

[ (1,4), (2,5), (3,6)]

[ 4, 5, 6]

zip

[ 1, 2, 3]

[ 5, 7, 9]

[ 4, 5, 6]

zip(add)

map(add)

zip(s): ([],[]) -> []zip(s): ([x|xs],[y|ys]) -> [<s> (x,y) | <zip(s)> (xs,ys)]

zip = zip(id)

Parameterized Rewrite Rules: Fold

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[1,2,3] foldr(!0,add) 6

[]

0

[3]

3

[2,3]

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[1,2,3]

foldr(s1,s2): [] -> <s1>foldr(s1,s2): [x|xs] -> <s2> (x,<foldr(s1,s2)> xs)

Parameterized Rewrite Rules: Inverse

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[1,2,3] inverse(|[]) [3,2,1]

[2,3]

[1][]

[1,2,3] [3]

[2,1] [3,2,1]

[]

inverse(|is): [] -> isinverse(|is): [x|xs] -> <inverse(|[x|is])> xs

Traversal Combinators

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Traversal: Topdown

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Const

Mul

Const

3 4 5

Const

Add1

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

topdown(s) = s ; all(topdown(s))

topdown(switch)

Traversal: Topdown

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Mul

Const

3

Const

4 5

Const

Add1

2

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

topdown(s) = s ; all(topdown(s))

topdown(switch)

Traversal: Topdown

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Mul

Const

3

Const

5 4

Const

Add1

2

3

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

topdown(s) = s ; all(topdown(s))

topdown(switch)

Traversal: Topdown/Try

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Const

Mul

Const

3 4 5

Const

Add1

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

topdown(s) = s ; all(topdown(s))

topdown(try(switch))

Traversal: Topdown/Try

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Mul

Const

3

Const

4 5

Const

Add1

2

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

topdown(s) = s ; all(topdown(s))

topdown(try(switch))

Traversal: Topdown/Try

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Mul

Const

3

Const

5 4

Const

Add1

2

3

4

5

6

7

8

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

topdown(s) = s ; all(topdown(s))

topdown(try(switch))

Traversal: Alltd

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Const

Mul

Const

3 4 5

Const

Add1

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

alltd(s) = s <+ all(alltd(s))

alltd(switch)

Traversal: Alltd

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Mul

Const

3

Const

4 5

Const

Add1

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

alltd(s) = s <+ all(alltd(s))

alltd(switch)

Traversal: bottomup

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Const

Mul

Const

3 4 5

Const

Add1

2

3

4

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

bottomup(s) = all(bottomup(s)) ; s

bottomup(switch)

Traversal: Bottomup

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Const

Mul

Const

3 4 5

Const

Add1

2

3

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

bottomup(s) = all(bottomup(s)) ; s

bottomup(try(switch))

Traversal: Bottomup

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Const

Mul

Const

3 4 5

Const

Add1

2

3

4

5

6

7

8

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

bottomup(s) = all(bottomup(s)) ; s

bottomup(try(switch))

Traversal: Bottomup

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Const

Mul

Const

3 4 5

Const

Add1

2

3

4

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

bottomup(s) = all(bottomup(s)) ; s

bottomup(try(switch))

Traversal: Bottomup

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Const

Mul

Const

3 5 4

Const

Add1

2

3

4

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

bottomup(s) = all(bottomup(s)) ; s

bottomup(try(switch))

Traversal: Bottomup

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Const

Mul

Const

3 5 4

Const

Add1

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

bottomup(s) = all(bottomup(s)) ; s

bottomup(try(switch))

Traversal: Bottomup

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Mul

Const

3

Const

5 4

Const

Add1

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

bottomup(s) = all(bottomup(s)) ; s

bottomup(try(switch))

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Traversal: Innermost

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Const

Mul

Const

3 4 5

Const

Add1

2

3

4

5

6

7

8

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

innermost(s) = bottomup(try(s ; innermost(s)))

innermost(switch)

Traversal: Innermost

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Const

Mul

Const

3 4 5

Const

Add1

2

3

4

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

innermost(s) = bottomup(try(s ; innermost(s)))

innermost(switch)

Traversal: Innermost

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Const

Mul

Const

3 5 4

Const

Add1

2

3

4

9

10

11

12

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

innermost(s) = bottomup(try(s ; innermost(s)))

innermost(switch)

Traversal: Innermost

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Const

Mul

Const

3 5 4

Const

Add1

2

3

4

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

innermost(s) = bottomup(try(s ; innermost(s)))

innermost(switch)

Traversal: Innermost

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Const

Mul

Const

3 4 5

Const

Add1

2

3

4

switch: Add(e1, e2) -> Add(e2, e1)switch: Mul(e1, e2) -> Mul(e2, e1)

innermost(s) = bottomup(try(s ; innermost(s)))

innermost(switch)

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Type-Unifying Transformations

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