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ef730c7eb1
Refactor the DIY equational reasoning library to be a bit more like the generic pre-order reasoning library: Change the `...` notation into a constructor for a new `Step` datatype. This seems to help idris disambiguate between the two kinds of reasoning when they're used in the same file (e.g., frex). Co-authored-by: Ohad Kammar <ohad.kammar@ed.ac.uk>
38 lines
1018 B
Idris
38 lines
1018 B
Idris
||| Until Idris2 starts supporting the 'syntax' keyword, here's a
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||| poor-man's equational reasoning
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module Syntax.PreorderReasoning
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infixl 0 ~~
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prefix 1 |~
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infix 1 ...
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|||Slightly nicer syntax for justifying equations:
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|||```
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||| |~ a
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||| ~~ b ...( justification )
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|||```
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|||and we can think of the `...( justification )` as ASCII art for a thought bubble.
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public export
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data Step : a -> b -> Type where
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(...) : (0 y : a) -> (0 step : x ~=~ y) -> Step x y
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public export
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data FastDerivation : (x : a) -> (y : b) -> Type where
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(|~) : (0 x : a) -> FastDerivation x x
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(~~) : FastDerivation x y -> {0 z : a} -> (step : Step y z) -> FastDerivation x z
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public export
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Calc : {x : a} -> {y : b} -> FastDerivation x y -> x ~=~ y
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Calc (|~ x) = Refl
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Calc ((~~) {y=_} der (_ ... Refl)) = Calc der
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{- -- requires import Data.Nat
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0
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example : (x : Nat) -> (x + 1) + 0 = 1 + x
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example x =
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Calc $
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|~ (x + 1) + 0
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~~ x+1 ...( plusZeroRightNeutral $ x + 1 )
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~~ 1+x ...( plusCommutative x 1 )
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-}
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