49 lines
1.3 KiB
Text
49 lines
1.3 KiB
Text
import logic
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open tactic
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inductive list (A : Type) : Type :=
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nil {} : list A,
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cons : A → list A → list A
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namespace list end list open list
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open eq
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definition is_nil {A : Type} (l : list A) : Prop
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:= list.rec true (fun h t r, false) l
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theorem is_nil_nil (A : Type) : is_nil (@nil A)
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:= eq_true_elim (refl true)
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theorem cons_ne_nil {A : Type} (a : A) (l : list A) : ¬ cons a l = nil
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:= not_intro (assume H : cons a l = nil,
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absurd
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(calc true = is_nil (@nil A) : refl _
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... = is_nil (cons a l) : { symm H }
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... = false : refl _)
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true_ne_false)
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theorem T : is_nil (@nil Prop)
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:= by apply is_nil_nil
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(*
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local list = Const("list", {1})(Prop)
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local isNil = Const("is_nil", {1})(Prop)
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local Nil = Const({"list", "nil"}, {1})(Prop)
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local m = mk_metavar("m", list)
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print(isNil(Nil))
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print(isNil(m))
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function test_unify(env, m, lhs, rhs, num_s)
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print(tostring(lhs) .. " =?= " .. tostring(rhs) .. ", expected: " .. tostring(num_s))
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local ss = unify(env, lhs, rhs, name_generator(), substitution())
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local n = 0
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for s in ss do
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print("solution: " .. tostring(s:instantiate(m)))
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n = n + 1
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end
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if num_s ~= n then print("n: " .. n) end
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assert(num_s == n)
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end
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print("=====================")
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test_unify(get_env(), m, isNil(Nil), isNil(m), 2)
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*)
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