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35 lines
1.4 KiB
Idris
35 lines
1.4 KiB
Idris
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||| N-ary simple (non-dependent) functions using telescopes
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||| Compare with `base/Data.Fun` and `contrib/Data.Fun.Extra` and with:
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||| Guillaume Allais. 2019. Generic level polymorphic n-ary functions. TyDe 2019.
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module Data.Telescope.SimpleFun
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import Data.Telescope.Telescope
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import Data.Telescope.Segment
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||| An n-ary function whose codomain does not depend on its
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||| arguments. The arguments may have dependencies.
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public export
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SimpleFun : (env : Left.Environment gamma) -> {n : Nat} -> (0 delta : Segment n gamma)
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-> (cod : Type) -> Type
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SimpleFun env {n = 0 } [] cod = cod
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SimpleFun env {n = S n} (ty :: delta) cod = (x : ty env) -> SimpleFun (env ** x) delta cod
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public export
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target : {0 env : Left.Environment gamma} -> {0 delta : Segment n gamma} -> {cod : Type}
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-> SimpleFun env delta cod -> Type
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target {cod} _ = cod
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public export
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uncurry : {n : Nat} -> {0 env : Left.Environment gamma} -> {0 delta : Segment n gamma}
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-> (f : SimpleFun env delta cod) -> Environment env delta -> cod
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uncurry {n = Z} {delta = []} f xs = f
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uncurry {n = S n} {delta = _ :: _} f (x .= xs) = uncurry (f x) xs
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public export
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curry : {n : Nat} -> {0 env : Left.Environment gamma} -> {0 delta : Segment n gamma}
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-> (f : Environment env delta -> cod)
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-> SimpleFun env delta cod
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curry {n = 0 } {delta = [] } f = f Empty
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curry {n = S n} {delta = ty :: delta} f = \x => curry (\xs => f (x .= xs))
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