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Generalized Arrows


Multi-level languages and arrows both facilitate metaprogramming, the act of writing a program which generates a program. The arr function required of all arrows turns arbitrary metalanguage expressions into object language expressions; because of this, arrows may be used for metaprogramming only when the object language is a superset of the metalanguage.

This thesis introduces generalized arrows, which are less restrictive than arrows in that they impose no containment relationship between the object language and metalanguage; this allows generalized arrows to be used for heterogeneous metaprogramming. This thesis also establishes a correspondence between two-level programs and one-level programs which take a generalized arrow instance as a distinguished parameter. A translation across this correspondence is possible, and is called a flattening transformation.

The flattening translation is not specific to any particular object language; this means that it needs to be implemented only once for a given metalanguage compiler. Support for various object languages can then be added by implementing instances of the generalized arrow type class; this does not require knowledge of compiler internals. Because of the flattening transformation the users of these object languages are able to program using convenient multi-level types and syntax; the conversion to one-level terms manipulating generalized arrow instances is handled by the flattening transformation.

A modified version of the Glasgow Haskell Compiler (GHC) with multi-level types and expressions has been produced as a proof of concept. The Haskell extraction of the Coq formalization in this thesis have been compiled into this modified GHC as a new flattening pass.

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