Hardware Design with Generalized Arrows

41 Pages·2011·0.28 MB·English

Hardware Design with Generalized Arrows
Adam Megacz
[email protected]
03.Oct.2011
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This Project
(cid:73) First nontrivial application of generalized arrows.
(cid:73) Not (even close to) a complete circuit-design solution.
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Metaprogramming and the Milner Property
(cid:73) A metaprogram is a program which produces a program (called the
object program).
(cid:73) Metaprogramming is the act of writing metaprograms.
(cid:73) The Milner Property: “well-typed programs don’t go wrong.”
(cid:73) When one is metaprogramming, we want something stronger:
well-typed metaprograms should not be able to produce ill-typed
object programs (therefore the object programs can’t go wrong).
5/51
Metaprogramming and the Milner Property
(cid:73) A metaprogram is a program which produces a program (called the
object program).
(cid:73) Metaprogramming is the act of writing metaprograms.
(cid:73) The Milner Property: “well-typed programs don’t go wrong.”
(cid:73) When one is metaprogramming, we want something stronger:
well-typed metaprograms should not be able to produce ill-typed
object programs (therefore the object programs can’t go wrong).
5/51
Metaprogramming and the Milner Property
(cid:73) A metaprogram is a program which produces a program (called the
object program).
(cid:73) Metaprogramming is the act of writing metaprograms.
(cid:73) The Milner Property: “well-typed programs don’t go wrong.”
(cid:73) When one is metaprogramming, we want something stronger:
well-typed metaprograms should not be able to produce ill-typed
object programs (therefore the object programs can’t go wrong).
5/51
Metaprogramming and the Milner Property
(cid:73) A metaprogram is a program which produces a program (called the
object program).
(cid:73) Metaprogramming is the act of writing metaprograms.
(cid:73) The Milner Property: “well-typed programs don’t go wrong.”
(cid:73) When one is metaprogramming, we want something stronger:
well-typed metaprograms should not be able to produce ill-typed
object programs (therefore the object programs can’t go wrong).
5/51
What Problem Do Generalized Arrows Solve?
Generalized arrows are a representation for object programs which:
(cid:73) Has the “Milner property for metaprograms”
(cid:73) Does not assume that the object language’s expressions are a
superset of the metalanguage (like Monads and classic Arrows do).
(cid:73) A monad’s return lifts arbitrary Haskell functions into the monad
(cid:73) An arrow’s arr lifts arbitrary Haskell functions into the arrow
(cid:73) Does not assume that the object language’s typing judgments are a
superset of the metalanguage’s typing judgments (like Monads and
classic Arrows do).
(cid:73) Monadic metaprogramming cannot handle object languages with:
(cid:73) affinetypes,becauseof(return $ \ -> ())
(cid:73) lineartypes,becauseof(return $ \x -> (x,x))
(cid:73) orderedtypes,becauseof(return $ \(x,y) -> (y,x))
(cid:73) Likewise for arrows.
7/51
What Problem Do Generalized Arrows Solve?
Generalized arrows are a representation for object programs which:
(cid:73) Has the “Milner property for metaprograms”
(cid:73) Does not assume that the object language’s expressions are a
superset of the metalanguage (like Monads and classic Arrows do).
(cid:73) A monad’s return lifts arbitrary Haskell functions into the monad
(cid:73) An arrow’s arr lifts arbitrary Haskell functions into the arrow
(cid:73) Does not assume that the object language’s typing judgments are a
superset of the metalanguage’s typing judgments (like Monads and
classic Arrows do).
(cid:73) Monadic metaprogramming cannot handle object languages with:
(cid:73) affinetypes,becauseof(return $ \ -> ())
(cid:73) lineartypes,becauseof(return $ \x -> (x,x))
(cid:73) orderedtypes,becauseof(return $ \(x,y) -> (y,x))
(cid:73) Likewise for arrows.
7/51
What Problem Do Generalized Arrows Solve?
Generalized arrows are a representation for object programs which:
(cid:73) Has the “Milner property for metaprograms”
(cid:73) Does not assume that the object language’s expressions are a
superset of the metalanguage (like Monads and classic Arrows do).
(cid:73) A monad’s return lifts arbitrary Haskell functions into the monad
(cid:73) An arrow’s arr lifts arbitrary Haskell functions into the arrow
(cid:73) Does not assume that the object language’s typing judgments are a
superset of the metalanguage’s typing judgments (like Monads and
classic Arrows do).
(cid:73) Monadic metaprogramming cannot handle object languages with:
(cid:73) affinetypes,becauseof(return $ \ -> ())
(cid:73) lineartypes,becauseof(return $ \x -> (x,x))
(cid:73) orderedtypes,becauseof(return $ \(x,y) -> (y,x))
(cid:73) Likewise for arrows.
7/51
What Problem Do Generalized Arrows Solve?
Generalized arrows are a representation for object programs which:
(cid:73) Has the “Milner property for metaprograms”
(cid:73) Does not assume that the object language’s expressions are a
superset of the metalanguage (like Monads and classic Arrows do).
(cid:73) A monad’s return lifts arbitrary Haskell functions into the monad
(cid:73) An arrow’s arr lifts arbitrary Haskell functions into the arrow
(cid:73) Does not assume that the object language’s typing judgments are a
superset of the metalanguage’s typing judgments (like Monads and
classic Arrows do).
(cid:73) Monadic metaprogramming cannot handle object languages with:
(cid:73) affinetypes,becauseof(return $ \ -> ())
(cid:73) lineartypes,becauseof(return $ \x -> (x,x))
(cid:73) orderedtypes,becauseof(return $ \(x,y) -> (y,x))
(cid:73) Likewise for arrows.
7/51