92 lines
1.6 KiB
Text
92 lines
1.6 KiB
Text
import Lean
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def f : Nat → Bool
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| 0 => true
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| n + 1 => (match n with
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| 0 => true
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| _ + 1 => true) && f n
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def g (i j : Nat) : Nat :=
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if i < 5 then 0 else
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match j with
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| Nat.zero => 1
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| Nat.succ j => g i j
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def h (i j : Nat) : Nat :=
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i +
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match j with
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| Nat.zero => 1
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| Nat.succ j => h i j
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def r (i j : Nat) : Nat :=
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i +
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match j with
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| Nat.zero => 1
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| Nat.succ j =>
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i * match j with
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| Nat.zero => 2
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| Nat.succ j => r i j
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def s (i j : Nat) : Nat :=
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let z :=
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match j with
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| Nat.zero => i
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| Nat.succ j => s i j
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z + z
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example : f 0 = true :=
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rfl
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example : f (i+1) = ((match i with | 0 => true | _ + 1 => true) && f i) :=
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rfl
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example : g i (j + 1) = if i < 5 then 0 else g i j :=
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rfl
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example : g i 0 = if i < 5 then 0 else 1 :=
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rfl
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example : h i 0 = i + 1 :=
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rfl
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example : h i (j + 1) = i + h i j :=
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rfl
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example : r i 0 = i + 1 :=
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rfl
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example : r i 1 = i + i * 2 :=
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rfl
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example : r i (j + 2) = i + i * r i j :=
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rfl
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example : s i (j + 1) = let z := s i j; z + z :=
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rfl
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open Lean
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open Lean.Meta
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open Lean.Elab
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open Lean.Elab.Command
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elab "unfold " e:term : command =>
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runTermElabM none fun xs => do
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let e ← instantiateMVars (← Term.withSynthesize <| Term.elabTerm e none)
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match (← unfoldDefinition? e) with
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| some e => logInfo m!"{e}"
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| none => throwError ""
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section end
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variable (i j : Nat)
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unfold f 0
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unfold f (i+1)
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unfold g i 0
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unfold g i (j+1)
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unfold h i 0
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unfold h i (j + 1)
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unfold r i 0
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unfold r i 1
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unfold r i (j + 2)
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unfold r i j.succ.succ
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unfold s i (j + 1)
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