108 lines
2.5 KiB
Text
108 lines
2.5 KiB
Text
#check @Array.mk
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def v : Array Nat := Array.mk [1, 2, 3, 4]
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#guard v == #[1, 2, 3, 4, ]
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def w : Array Nat :=
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(Array.replicate 9 1).push 3
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#check @Array.casesOn
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def f : Fin w.size → Nat :=
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fun i => w[i]'(i.isLt)
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def arraySum (a : Array Nat) : Nat :=
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a.foldl Nat.add 0
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#guard Array.replicate 4 1 == #[1, 1, 1, 1]
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#guard Array.map (fun x => x+10) v == #[11, 12, 13, 14]
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#guard f ⟨1, sorry⟩ == 1
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#guard f ⟨9, sorry⟩ == 3
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#guard (((Array.replicate 1 1).push 2).push 3).foldl (fun x y => x + y) 0 == 6
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#guard arraySum (Array.replicate 10 1) == 10
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axiom axLt {a b : Nat} : a < b
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#guard #[1, 2, 3].insertIdx 0 10 == #[10, 1, 2, 3]
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#guard #[1, 2, 3].insertIdx 1 10 == #[1, 10, 2, 3]
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#guard #[1, 2, 3].insertIdx 2 10 == #[1, 2, 10, 3]
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#guard #[1, 2, 3].insertIdx 3 10 == #[1, 2, 3, 10]
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#guard #[].insertIdx 0 10 == #[10]
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def tst1 : IO Unit :=
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#[1, 2, 3, 4].forRevM IO.println
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/--
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info: 4
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3
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2
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1
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-/
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#guard_msgs in
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#eval tst1
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#guard #[1, 2].extract 0 1 == #[1]
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#guard #[1, 2].extract 0 0 == #[]
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#guard #[1, 2].extract 0 2 == #[1, 2]
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#guard #[1, 2, 3, 4].filterMap (fun x => if x % 2 == 0 then some (x + 10) else none) == #[12, 14]
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def tst : IO (List Nat) :=
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[1, 2, 3, 4].filterMapM fun x => do
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IO.println x;
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(if x % 2 == 0 then pure $ some (x + 10) else pure none)
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/--
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info: 1
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2
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3
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4
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---
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info: [12, 14]
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-/
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#guard_msgs in
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#eval tst
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#guard #[1, 3, 6, 2].getMax? (fun a b => a < b) == some 6
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#guard #[].getMax? (fun (a b : Nat) => a < b) == none
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#guard #[1, 8].getMax? (fun a b => a < b) == some 8
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#guard #[8, 1].getMax? (fun a b => a < b) == some 8
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#guard #[1, 6, 5, 3, 8, 2, 0].partition (fun x => x % 2 == 0) == (#[6, 8, 2, 0], #[1, 5, 3])
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def check (b : Bool) : IO Unit :=
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unless b do throw $ IO.userError "check failed"
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#guard #[].isPrefixOf #[2, 3]
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#guard (#[] : Array Nat).isPrefixOf #[]
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#guard #[2, 3].isPrefixOf #[2, 3]
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#guard #[2, 3].isPrefixOf #[2, 3, 4, 5]
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#guard ! #[2, 4].isPrefixOf #[2, 3]
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#guard ! #[2, 3, 4].isPrefixOf #[2, 3]
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#guard ! #[2].isPrefixOf #[]
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#guard ! #[4, 3].isPrefixOf #[2, 3, 4, 5]
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#guard #[1, 2, 3].allDiff
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#guard !#[1, 2, 1, 3].allDiff
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#guard #[1, 2, 4, 3].allDiff
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#guard (#[] : Array Nat).allDiff
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#guard !#[1, 1].allDiff
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#guard !#[1, 2, 3, 4, 5, 1].allDiff
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#guard #[1, 2, 3, 4, 5].allDiff
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#guard !#[1, 2, 3, 4, 5, 5].allDiff
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#guard !#[1, 3, 3, 4, 5].allDiff
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#guard !#[1, 2, 3, 4, 5, 3].allDiff
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#guard !#[1, 2, 3, 4, 5, 4].allDiff
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#guard #[1, 2, 3, 4, 5, 6].allDiff
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#guard Array.zip #[1, 2] #[3, 4, 6] == #[(1, 3), (2, 4)]
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theorem ex1 (a b c : Nat) : #[a, b].push c = #[a, 0, c].set! 1 b :=
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rfl
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