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You could use the GHC codegen and RTS via the external STG IR. https://github.com/grin-compiler/ghc-whole-program-compiler-project
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There is a WIP Idris2 to Ext-STG compiler: https://github.com/andorp/IdrisExtSTGCodegen
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When writing a typechecker plugin, you can eliminate constraints from the user's program by providing an implementation of the corresponding dictionary. The way you provide that dictionary to ghc is by providing a core expression; for example, this evCast futureDict co expression has type EvTerm, whose first constructor takes an EvExpr, which is a synonym for CoreExpr.
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Therefore, one convoluted way to integrate your language into the ghc pipeline would be as follows. Define a magic typeclass: