66 lines
2.8 KiB
Lua
66 lines
2.8 KiB
Lua
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local env = environment()
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local N = Const("N")
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local p = Const("p")
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local q = Const("q")
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local a = Const("a")
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local b = Const("b")
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local f = Const("f")
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local H1 = Const("H1")
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local H2 = Const("H2")
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local And = Const("and")
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local and_intro = Const("and_intro")
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local A = Local("A", Bool)
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local B = Local("B", Bool)
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env = add_decl(env, mk_var_decl("N", Type))
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env = add_decl(env, mk_var_decl("p", mk_arrow(N, N, Bool)))
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env = add_decl(env, mk_var_decl("q", mk_arrow(N, Bool)))
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env = add_decl(env, mk_var_decl("f", mk_arrow(N, N)))
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env = add_decl(env, mk_var_decl("a", N))
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env = add_decl(env, mk_var_decl("b", N))
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env = add_decl(env, mk_var_decl("and", mk_arrow(Bool, Bool, Bool)))
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env = add_decl(env, mk_var_decl("and_intro", Pi({A, B}, mk_arrow(A, B, And(A, B)))))
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env = add_decl(env, mk_var_decl("foo_intro", Pi({A, B}, mk_arrow(B, B))))
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env = add_decl(env, mk_var_decl("foo_intro2", Pi({A, B}, mk_arrow(B, B))))
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env = add_decl(env, mk_axiom("Ax1", q(a)))
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env = add_decl(env, mk_axiom("Ax2", q(a)))
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env = add_decl(env, mk_axiom("Ax3", q(b)))
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local Ax1 = Const("Ax1")
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local Ax2 = Const("Ax2")
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local Ax3 = Const("Ax3")
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local foo_intro = Const("foo_intro")
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local foo_intro2 = Const("foo_intro2")
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local cs = {}
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local ng = name_generator("foo")
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local tc = type_checker(env, ng, function (c) print(c); cs[#cs+1] = c end)
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local m1 = mk_metavar("m1", Bool)
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print("before is_def_eq")
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assert(tc:is_def_eq(and_intro(m1, q(a)), and_intro(q(a), q(b))))
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-- The constraint and_intro(m1, q(a)) == and_intro(q(a), q(b)) is added.
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-- Reason: a unification hint may be able to solve it
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assert(#cs == 1)
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assert(cs[1]:lhs() == and_intro(m1, q(a)))
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assert(cs[1]:rhs() == and_intro(q(a), q(b)))
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local cs = {}
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local tc = type_checker(env, ng, function (c) print(c); cs[#cs+1] = c end)
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assert(tc:is_def_eq(foo_intro(m1, q(a), Ax1), foo_intro(q(a), q(a), Ax2)))
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assert(#cs == 1) -- constraint is used, but there is an alternative that does not use it
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assert(cs[1]:lhs() == m1)
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assert(cs[1]:rhs() == q(a))
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cs = {}
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local tc = type_checker(env, ng, function (c) print(c); cs[#cs+1] = c end)
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assert(tc:is_def_eq(foo_intro(m1, q(a), Ax1), foo_intro2(q(a), q(a), Ax2)))
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assert(#cs == 0) -- constraint should be ignored since we have shown definitional equality using proof irrelevance
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cs = {}
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local tc = type_checker(env, ng, function (c) print(c); cs[#cs+1] = c end)
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print("before failure")
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assert(not pcall(function() print(tc:check(and_intro(m1, q(a), Ax1, Ax3))) end))
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assert(#cs == 0) -- the check failed, so the constraints should be preserved
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cs = {}
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print("before success")
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print(tc:check(and_intro(m1, q(a), Ax1, Ax2)))
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assert(#cs == 1) -- the check succeeded, and we must get one constraint
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-- Demo: infer method may generate constraints
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-- local m2 = mk_metavar("m2", mk_metavar("ty_m2", mk_sort(mk_meta_univ("s_m2"))))
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-- print(tc:infer(mk_pi("x", m2, Var(0))))
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