mirror of https://github.com/nmvdw/HITs-Examples
67 lines
1.3 KiB
Plaintext
67 lines
1.3 KiB
Plaintext
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{-# OPTIONS --without-K --rewriting #-}
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open import HoTT
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module Syntax where
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data Maybe (A : Set) : Set where
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Just : A -> Maybe A
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Nothing : Maybe A
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eqN : Nat -> Nat -> Bool
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eqN 0 0 = true
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eqN 0 _ = false
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eqN (S _) 0 = false
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eqN (S n) (S m) = eqN n m
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-- first coordinate represents the variable x_i, second the value
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State : Set
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State = List (Nat × Nat)
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_[_:==_] : State -> Nat -> Nat -> State
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nil [ x :== n ] = (x , n) :: nil
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((y , m) :: s) [ x :== n ] =
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if eqN x y
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then (x , n) :: s
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else ((y , m) :: (s [ x :== n ]))
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equals : State -> Nat -> Nat -> Set
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equals nil _ _ = Empty
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equals ((x , n) :: s) y m =
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if eqN x y
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then
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if eqN n m
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then Unit
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else Empty
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else equals s y m
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unequals : State -> Nat -> Nat -> Set
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unequals nil _ _ = Unit
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unequals ((x , n) :: s) y m =
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if eqN x y
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then
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if eqN n m
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then Empty
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else Unit
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else unequals s y m
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defined : State -> Nat -> Set
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defined nil y = Empty
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defined ((x , n) :: s) y =
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if eqN x y
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then Unit
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else defined s y
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undefined : State -> Nat -> Set
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undefined nil y = Unit
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undefined ((x , n) :: s) y =
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if eqN x y
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then Empty
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else undefined s y
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data Syntax : Set where
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skip : Syntax
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_:=_ : Nat -> Nat -> Syntax
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conc : Syntax -> Syntax -> Syntax
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while_==_do_ : Nat -> Nat -> Syntax -> Syntax
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