b5122b6a7b
This change * moves `termination_by` and `decreasing_by` next to the function they apply to * simplify the syntax of `termination_by` * apply the `decreasing_by` goal to all goals at once, for better interactive use. See the section in `RELEASES.md` for more details and migration advise. This is a hard breaking change, requiring developers to touch every `termination_by` in their code base. We decided to still do it as a hard-breaking change, because supporting both old and new syntax at the same time would be non-trivial, and not save that much. Moreover, this requires changes to some metaprograms that developers might have written, and supporting both syntaxes at the same time would make _their_ migration harder.
31 lines
991 B
Text
31 lines
991 B
Text
def evenq (n: Nat) : Bool := Nat.mod n 2 = 0
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private theorem pack_loop_terminates : (n : Nat) → n / 2 < n.succ
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| 0 => by decide
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| 1 => by decide
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| n+2 => by
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rw [Nat.div_eq]
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split
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· rw [Nat.add_sub_self_right]
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have := pack_loop_terminates n
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calc n/2 + 1 < Nat.succ n + 1 := Nat.add_le_add_right this 1
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_ < Nat.succ (n + 2) := Nat.succ_lt_succ (Nat.succ_lt_succ (Nat.lt_succ_self _))
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· apply Nat.zero_lt_succ
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def pack (n: Nat) : List Nat :=
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let rec
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loop (n : Nat) (acc : Nat) (accs: List Nat) : List Nat :=
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let next (n: Nat) := n / 2;
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match n with
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| Nat.zero => List.cons acc accs
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| n+1 => match evenq n with
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| true => loop (next n) 0 (List.cons acc accs)
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| false => loop (next n) (acc+1) accs
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termination_by n
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decreasing_by all_goals
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simp [invImage, InvImage, Prod.lex, sizeOfWFRel, measure, Nat.lt_wfRel]
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apply pack_loop_terminates
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loop n 0 []
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#eval pack 27
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