21 lines
929 B
Lua
21 lines
929 B
Lua
local env = empty_environment()
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env = add_decl(env, mk_var_decl("A", Bool))
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local A = Const("A")
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local x = Const("x")
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env = add_decl(env, mk_axiom("magic", Pi(x, Bool, x)))
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local saved_env = env
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env = add_decl(env, mk_axiom("Ax", A))
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env = add_decl(env, mk_definition("T1", A, Const("Ax")))
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-- The check mk_theorem("Ax", A, Const("T1")) failes because env
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-- contains the axiom named Ax.
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-- So, we cannot transform Ax into a theorem that depends on itself.
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-- (This is good)
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assert(not pcall(function() env:replace(check(env, mk_theorem("Ax", A, Const("T1")))) end))
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assert(env:find("Ax"):is_axiom())
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local magic = Const("magic")
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-- Replace axiom Ax with the theorem Ax that is checked in the old
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-- environment saved_env. Everything works because env is a descendant
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-- of saved_env
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env = env:replace(check(saved_env, mk_theorem("Ax", A, magic(A))))
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assert(not env:find("Ax"):is_axiom())
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assert(env:find("Ax"):is_theorem())
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