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Add conv_eval
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/target
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/tmp
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239
bench/conv_eval.idr
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239
bench/conv_eval.idr
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CBool : Type
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CBool = (B : Type) -> B -> B -> B
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toBool : CBool -> Bool
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toBool = \b => b Bool True False
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ctrue : CBool
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ctrue = \b, t, f => t
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and : CBool -> CBool -> CBool
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and = \a, b, bb, t, f => a bb (b bb 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 : CNat -> CNat -> CNat
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add = \a, b, n, s, z => a n s (b n s z)
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cmul : CNat -> CNat -> CNat
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cmul = \a, b, n, s => a n (b n s)
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suc : CNat -> CNat
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suc = \a, n, s, z => s (a n s z)
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CEq : {A : Type} -> A -> A -> Type
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CEq = \x, y => (P : A -> Type) -> P x -> P y
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crefl : {A : Type} -> {x : A} -> CEq {A} x x
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crefl = \p, px => px
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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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Tree : Type
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Tree = (T : Type) -> (T -> T -> T) -> T -> T
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leaf : Tree
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leaf = \t, n, l => l
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node : Tree -> Tree -> Tree
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node = \t1, t2, t, n, l => n (t1 t n l) (t2 t n l)
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fullTree : CNat -> Tree
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fullTree = \n => n Tree (\t => node t t) leaf
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-- full tree with given trees at bottom level
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fullTreeWithLeaf : Tree -> CNat -> Tree
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fullTreeWithLeaf = \bottom, n => n Tree (\t => node t t) bottom
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forceTree : Tree -> CBool
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forceTree = \t => t CBool and ctrue
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t15 : Tree
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t15 = fullTree n15
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t15b : Tree
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t15b = fullTree n15b
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t18 : Tree
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t18 = fullTree n18
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t18b : Tree
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t18b = fullTree n18b
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t19 : Tree
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t19 = fullTree n19
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t19b : Tree
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t19b = fullTree n19b
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t20 : Tree
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t20 = fullTree n20
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t20b : Tree
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t20b = fullTree n20b
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t21 : Tree
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t21 = fullTree n21
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t21b : Tree
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t21b = fullTree n21b
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t22 : Tree
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t22 = fullTree n22
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t22b : Tree
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t22b = fullTree n22b
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t23 : Tree
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t23 = fullTree n23
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t23b : Tree
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t23b = fullTree n23b
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-- CNat conversion
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--------------------------------------------------------------------------------
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convn1M : CEq Main.n1M Main.n1Mb
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convn1M = crefl
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-- convn5M : CEq Main.n5M Main.n5Mb
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-- convn5M = crefl
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-- convn10M : CEq Main.n10M Main.n10Mb
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-- convn10M = crefl
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-- Full tree conversion
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--------------------------------------------------------------------------------
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-- convt15 : CEq Main.t15 Main.t15b
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-- convt15 = crefl
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-- convt18 : CEq Main.t18 Main.t18b
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-- convt18 = crefl
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-- convt19 : CEq Main.t19 Main.t19b
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-- convt19 = crefl
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-- convt20 : CEq Main.t20 Main.t20b
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-- convt20 = crefl
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-- convt21 : CEq Main.t21 Main.t21b
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-- convt21 = crefl
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-- convt22 : CEq Main.t22 Main.t22b
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-- convt22 = crefl
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-- convt23 : CEq Main.t23 Main.t23b
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-- convt23 = crefl
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-- Full meta-containing tree conversion
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--------------------------------------------------------------------------------
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-- convmt15 : CEq Main.t15b (fullTreeWithLeaf ? Main.n15 )
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-- convmt15 = crefl
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-- convmt18 : CEq Main.t18b (fullTreeWithLeaf ? Main.n18 )
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-- convmt18 = crefl
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-- convmt19 : CEq Main.t19b (fullTreeWithLeaf ? Main.n19 )
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-- convmt19 = crefl
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-- convmt20 : CEq Main.t20b (fullTreeWithLeaf ? Main.n20 )
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-- convmt20 = crefl
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-- convmt21 : CEq Main.t21b (fullTreeWithLeaf ? Main.n21 )
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-- convmt21 = crefl
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-- convmt22 : CEq Main.t22b (fullTreeWithLeaf ? Main.n22 )
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-- convmt22 = crefl
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-- convmt23 : CEq Main.t23b (fullTreeWithLeaf ? Main.n23 )
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-- convmt23 = crefl
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-- Full tree forcing
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--------------------------------------------------------------------------------
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-- forcet15 : CEq (toBool (forceTree Main.t15)) True
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-- forcet15 = crefl
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-- forcet18 : CEq (toBool (forceTree Main.t18)) True
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-- forcet18 = crefl
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-- forcet19 : CEq (toBool (forceTree Main.t19)) True
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-- forcet19 = crefl
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-- forcet20 : CEq (toBool (forceTree Main.t20)) True
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-- forcet20 = crefl
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-- forcet21 : CEq (toBool (forceTree Main.t21)) True
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-- forcet21 = crefl
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--forcet22 : CEq (toBool (forceTree Main.t22)) True
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--forcet22 = crefl
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-- forcet23 : CEq (toBool (forceTree Main.t23)) True
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-- forcet23 = crefl
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156
bench/conv_eval.kind2
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156
bench/conv_eval.kind2
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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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