mirror of
https://github.com/Kindelia/Kind2.git
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157 lines
2.1 KiB
Plaintext
157 lines
2.1 KiB
Plaintext
Bool : Type
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True : Bool
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False : Bool
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CBool : Type
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CBool = (t: Type) t -> t -> t
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CBool.to_bool (x : CBool) : Bool
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CBool.to_bool x = (x Bool True False)
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CTrue : CBool
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CTrue = @p @t @f t
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CFalse : CBool
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CFalse = @p @t @f f
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And (a: CBool) (b: CBool) : CBool
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And a b = @p @t @f (a p (b p t f) f)
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CNat : Type
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CNat = (n: Type) (n -> n) -> n -> n
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Add (a: CNat) (b: CNat) : CNat
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Add a b = @n @s @z (a n s (b n s z))
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CMul (a: CNat) (b: CNat) : CNat
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CMul a b = @n @s (a n (b n s))
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Suc (a: CNat) : CNat
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Suc a = @n @s @z (s (a n s z))
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CEqual (t: Type) (a: t) (b: t) : Type
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CEqual t a b = (p: t -> Type) (p a) -> (p b)
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CRefl (t: Type) (x: t) : (CEqual t x x)
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CRefl t x = @p @px px
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N0 : CNat
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N0 = @n @s @z z
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N2 : CNat
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N2 = @n @s @z (s (s z))
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N3 : CNat
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N3 = @n @s @z (s (s (s z)))
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N4 : CNat
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N4 = @n @s @z (s (s (s (s z))))
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N5 : CNat
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N5 = @n @s @z (s (s (s (s (s z)))))
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N10 : CNat
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N10 = (CMul N2 N5)
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N10b : CNat
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N10b = (CMul N5 N2)
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N15 : CNat
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N15 = (Add N10 N5)
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N15b : CNat
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N15b = (Add N10b N5)
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N18 : CNat
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N18 = (Add N15 N3)
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N18b : CNat
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N18b = (Add N15b N3)
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N19 : CNat
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N19 = (Add N15 N4)
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N19b : CNat
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N19b = (Add N15b N4)
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N20 : CNat
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N20 = (CMul N2 N10)
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N20b : CNat
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N20b = (CMul N2 N10b)
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N21 : CNat
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N21 = (Suc N20)
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N21b : CNat
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N21b = (Suc N20b)
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N22 : CNat
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N22 = (Suc N21)
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N22b : CNat
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N22b = (Suc N21b)
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N23 : CNat
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N23 = (Suc N22)
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N23b : CNat
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N23b = (Suc N22b)
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N100 : CNat
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N100 = (CMul N10 N10)
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N100b : CNat
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N100b = (CMul N10b N10b)
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N10k : CNat
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N10k = (CMul N100 N100)
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N10kb : CNat
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N10kb = (CMul N100b N100b)
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N100k : CNat
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N100k = (CMul N10k N10)
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N100kb : CNat
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N100kb = (CMul N10kb N10b)
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N1M : CNat
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N1M = (CMul N10k N100)
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N1Mb : CNat
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N1Mb = (CMul N10kb N100b)
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N5M : CNat
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N5M = (CMul N1M N5)
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N5Mb : CNat
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N5Mb = (CMul N1Mb N5)
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N10M : CNat
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N10M = (CMul N5M N2)
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N10Mb : CNat
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N10Mb = (CMul N5Mb N2)
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CTree : Type
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CTree = (t: Type) (t -> t -> t) -> t -> t
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CLeaf : CTree
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CLeaf = @t @n @l l
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CNode (t1: CTree) (t2: CTree) : CTree
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CNode t1 t2 = @t @n @l (n (t1 t n l) (t2 t n l))
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FullCTree (n: CNat) : CTree
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FullCTree n = (n CTree @t(CNode t t) CLeaf)
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Num : CNat
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Num = N2
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Force (n: CNat) : Bool
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Force n = (n Bool @x(x) True)
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Main : (CEqual CNat N1M N1Mb)
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Main = (CRefl CNat N1M)
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