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Introduction Interpreters and Compilers
Partial Evaluation
- Dr. Mattox Beckman
Introduction Interpreters and Compilers
Partial Evaluation Dr. Mattox Beckman University of Illinois at - - PowerPoint PPT Presentation
Partial Evaluation Dr. Mattox Beckman University of Illinois at - - PowerPoint PPT Presentation
Introduction Interpreters and Compilers Partial Evaluation Dr. Mattox Beckman University of Illinois at Urbana-Champaign Department of Computer Science Introduction Interpreters and Compilers Objectives You should be able to... Explain
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Introduction Interpreters and Compilers
An Interpreter
Notations
◮ Let S be a language. ◮ Let M be a program in language S. ◮ Let lower case letters be values in S. ◮ An S-interpreter is a program I such that
I(M, s, d) → x
◮ An S-partial evaluator is a program
P(M, s) → Ms such that Ms(d) = M(s, d)
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Introduction Interpreters and Compilers
Some examples
P(printf, "%s") → puts P(pow(n,x), 2) → λx . x * x P()
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Introduction Interpreters and Compilers
Basic Operation
Online
◮ Like eval, but distinguishes between “known” and
“unknown” values.
◮ Expressions that have all known sub-expressions are
specialized.
◮ Everything else is residualized. ◮ More aggressive, but can cause instability.
Offmine
◮ A preprocessor called a binding time analyser
annotates the source program.
◮ Everything that is known for sure is marked as
known.
◮ Everything else is marked as unknown.
◮ The partial evaluator then follows the annotations. ◮ Can lose opportunity to specializes, but more
stability.
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Introduction Interpreters and Compilers
BTA Example
◮ We underline the things that are known. ◮ We start with the input n. ◮ We annotate the “leaves” ◮ If all subexpressions are known, so is the expression. ◮ The parial evaluator will compute anything that’s underlined. ◮ It will unroll functions that the inputs are partially known.
1 pow n x = 2
if n > 0
3
then x * pow (n-1) x
4
else 1
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Introduction Interpreters and Compilers
BTA Example
◮ We underline the things that are known. ◮ We start with the input n. ◮ We annotate the “leaves” ◮ If all subexpressions are known, so is the expression. ◮ The parial evaluator will compute anything that’s underlined. ◮ It will unroll functions that the inputs are partially known.
1 pow n x = 2
if n > 0
3
then x * pow (n-1) x
4
else 1
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Introduction Interpreters and Compilers
BTA Example
◮ We underline the things that are known. ◮ We start with the input n. ◮ We annotate the “leaves” ◮ If all subexpressions are known, so is the expression. ◮ The parial evaluator will compute anything that’s underlined. ◮ It will unroll functions that the inputs are partially known.
1 pow n x = 2
if n >0
3
then x * pow (n-1) x
4
else 1
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Introduction Interpreters and Compilers
BTA Example
◮ We underline the things that are known. ◮ We start with the input n. ◮ We annotate the “leaves” ◮ If all subexpressions are known, so is the expression. ◮ The parial evaluator will compute anything that’s underlined. ◮ It will unroll functions that the inputs are partially known.
1 pow n x = 2
if n >0
3
then x * pow (n-1) x
4
else 1
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Introduction Interpreters and Compilers
Binding Time Analyzer
1 data AnnExp = AIntExp _ 2
| AVarExp String Bool
3
| AOpExp String AnnExp AnnExp
4
...
5 bta :: Exp -> BEnv -> AnnExp 6 bta (IntExp i) env = IntExp i 7 bta (VarExp s) env = AVarExp s bt 8
where bt = case H.lookup s env of
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Just b -> b
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Nothing -> False
11 bta (OpExp e1 e2) env = 12
let ae1 = bta e1 env
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ae2 = bta e2 env
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in AOpExp ae1 ae2 (isKnown ae1 && isKnown ae2)
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Introduction Interpreters and Compilers
The First Futamura Projection
P(I, S) → IS where IS(D) = I(S, D)
Compilation
◮ We have fed an interpreter to our parial evaluator. ◮ The result is IS... this is a compiled program! ◮ IS usually runs 4–10 times faster than I(S, P).
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Introduction Interpreters and Compilers
The Second Futamura Projection
P(P, I) → PI where PI(S) = P(I, S) and P(I, S)(D) = IS(D) = I(S, D)
Producing a Compiler
◮ Notice what PI actually does. ◮ We wrote an interpeter, and got a compiler... ◮ ... for free.
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Introduction Interpreters and Compilers