mirror of
https://github.com/idris-lang/Idris2.git
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57 lines
1.9 KiB
Idris
57 lines
1.9 KiB
Idris
import Data.List
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import Data.List.Elem
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%search_timeout 1000
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||| A Place has an ID and a number of tokens
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data Place : Type where
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MkPlace : (i : Nat) -> (nTokens : Nat) -> Place
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||| A transition has a name
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data Transition : Type where
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MkTransition : String -> Transition
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||| An Input links a Place and a Transition...
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data Input : Type where
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MkInput : (from : Place) -> (to : Transition) -> Input
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-- Accessor functions for proof
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0 inputFrom : Input -> Place
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inputFrom (MkInput p t) = p
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0 inputTo : Input -> Transition
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inputTo (MkInput p t) = t
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data SoundInputFrom : Input -> List Place -> Type where
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MkSoundInputFrom : (i : Input)
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-> (ps : List Place)
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-> (prf : Elem (inputFrom i) ps)
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-> SoundInputFrom i ps
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data SoundInputTo : Input -> List Transition -> Type where
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MkSoundInputTo : (i : Input)
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-> (ts : List Transition)
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-> (prf : Elem (inputTo i) ts)
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-> SoundInputTo i ts
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data SoundInput : Input -> List Place -> List Transition -> Type where
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MkSoundInput : (i : Input)
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-> (ps : List Place)
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-> (ts : List Transition)
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-> (fromOK : SoundInputFrom i ps)
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-> (toOK : SoundInputTo i ts)
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-> SoundInput i ps ts
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data AllInputsSound : List Input -> List Place -> List Transition -> Type where
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NilInputsIsSound : AllInputsSound [] _ _
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ConsIsSound : (headIsSound : SoundInput i ps ts)
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-> (tailIsSound : AllInputsSound is ps ts)
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-> AllInputsSound (i :: is) ps ts
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-- Searching here finds the right answer immediately, but then if we don't
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-- have a timeout, it takes ages to explore more non-solutions! So we cut off
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-- after a second
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tailIsNotSound : (contra : (AllInputsSound is ps ts -> Void))
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-> AllInputsSound (i :: is) ps ts
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-> Void
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