34 lines
907 B
Lua
34 lines
907 B
Lua
local env = get_environment()
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function show_ceqs(ceqs)
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for i = 1, #ceqs do
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print(ceqs[i][1], ceqs[i][2])
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env:type_check(ceqs[i][2])
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assert(is_ceq(env, ceqs[i][1]))
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end
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end
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function test_ceq(name, expected)
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local obj = env:find_object(name)
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local r = to_ceqs(env, obj:get_type(), Const(name))
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show_ceqs(r)
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assert(#r == expected)
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end
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parse_lean_cmds([[
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import if_then_else
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variable f : Nat -> Nat
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axiom Ax1 : forall x : Nat, x > 0 -> f x < 0 /\ not (f x = 1)
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axiom Ax2 : forall x : Nat, x < 0 -> f (f x) = x
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variable g : Nat -> Nat -> Nat
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axiom Ax3 : forall x : Nat, not (x = 1) -> if (x < 0) then (g x x = 0) else (g x x < 0 /\ g x 0 = 1 /\ g 0 x = 2)
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axiom Ax4 : forall x y : Nat, f x = x
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axiom Ax5 : forall x y : Nat, f x = y /\ g x y = x
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]])
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test_ceq("Ax1", 2)
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test_ceq("Ax2", 1)
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test_ceq("Ax3", 4)
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test_ceq("Ax4", 0)
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test_ceq("Ax5", 1)
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