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test(lua): add constraint generation test when type checking with metavars

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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Leonardo de Moura 2014-05-14 11:06:48 -07:00
parent cf55a1bcc2
commit e57b943adf
1 changed files with 79 additions and 0 deletions
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tests/lua/tc2.lua Normal file
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local env = empty_environment()
local l = mk_param_univ("l")
local A = Const("A")
local a = Const("a")
local b = Const("b")
local P = Const("P")
env = add_decl(env, mk_definition("id", {l},
Pi(A, mk_sort(l), mk_arrow(A, mk_arrow(A, Bool))),
Fun({{A, mk_sort(l)}, {a, A}, {b, A}}, Pi(P, mk_arrow(A, Bool), mk_arrow(P(a), P(b))))))
local id_l = Const("id", {l})
local H = Const("H")
env = add_decl(env, mk_theorem("refl", {l},
Pi({{A, mk_sort(l)}, {a, A}}, id_l(A, a, a)),
Fun({{A, mk_sort(l)}, {a, A}, {P, mk_arrow(A, Bool)}, {H, P(a)}}, H)))
local H1 = Const("H1")
local H2 = Const("H2")
env = add_decl(env, mk_theorem("subst", {l},
Pi({{A, mk_sort(l)}, {P, mk_arrow(A, Bool)}, {a, A}, {b, A}, {H1, id_l(A, a, b)}, {H2, P(a)}}, P(b)),
Fun({{A, mk_sort(l)}, {P, mk_arrow(A, Bool)}, {a, A}, {b, A}, {H1, id_l(A, a, b)}, {H2, P(a)}},
H1(P, H2))))
local refl_l = Const("refl", {l})
local subst_l = Const("subst", {l})
local x = Const("x")
env = add_decl(env, mk_theorem("symm", {l},
Pi({{A, mk_sort(l)}, {a, A}, {b, A}, {H, id_l(A, a, b)}}, id_l(A, b, a)),
Fun({{A, mk_sort(l)}, {a, A}, {b, A}, {H, id_l(A, a, b)}},
subst_l(A, Fun(x, A, id_l(A, x, a)), a, b, H, refl_l(A, a)))))
local c = Const("c")
env = add_decl(env, mk_theorem("trans", {l},
Pi({{A, mk_sort(l)}, {a, A}, {b, A}, {c, A}, {H1, id_l(A, a, b)}, {H2, id_l(A, b, c)}}, id_l(A, a, c)),
Fun({{A, mk_sort(l)}, {a, A}, {b, A}, {c, A}, {H1, id_l(A, a, b)}, {H2, id_l(A, b, c)}},
subst_l(A, Fun(x, A, id_l(A, a, x)), b, c, H2, H1))))
local symm_l = Const("symm", {l})
local trans_l = Const("trans", {l})
print(env:get("trans"):value())
env = env:add_global_level("u")
local u = mk_global_univ("u")
local tc = type_checker(env)
print(tc:check(Const("trans", {u})))
local id_u = Const("id", {u})
local refl_u = Const("refl", {u})
local subst_u = Const("subst", {u})
local symm_u = Const("symm", {u})
local trans_u = Const("trans", {u})
local d = Const("d")
local H3 = Const("H3")
print(tc:check(Fun({{A, mk_sort(u)}, {a, A}, {b, A}, {c, A}, {d, A},
{H1, id_u(A, b, a)},
{H2, id_u(A, b, c)},
{H3, id_u(A, c, d)}},
trans_u(A, a, b, d,
symm_u(A, b, a, H1),
trans_u(A, b, c, d, H2, H3)))))
local cs = {}
local g = name_generator("tst")
local tc2 = type_checker(env, g, constraint_handler(function (c) print(c); cs[#cs+1] = c end))
print("=================")
local f = Const("f")
local mf_ty = mk_metavar("f_ty", Pi(A, mk_sort(u), mk_sort(mk_meta_univ("l_f"))))
local mA1 = mk_metavar("A1", Pi({{A, mk_sort(u)}, {f, mf_ty(A)}, {a, A}}, mk_sort(mk_meta_univ("l_A1"))))
print(tc2:check(Fun({{A, mk_sort(u)}, {f, mf_ty(A)}, {a, A}},
id_u(mA1(A, f, a), f(a), a))))
local cs = {}
local tc2 = type_checker(env, g, constraint_handler(function (c) print(c); cs[#cs+1] = c end))
local scope = {{A, mk_sort(u)}, {a, A}, {b, A}, {c, A}, {d, A}, {H1, id_u(A, b, a)},
{H2, id_u(A, b, c)}, {H3, id_u(A, c, d)}}
local mP = mk_metavar("P", Pi(scope, mk_metavar("P_ty", Pi(scope, mk_sort(mk_meta_univ("l_P"))))(A, a, b, c, d, H1, H2, H3)))(A, a, b, c, d, H1, H2, H3)
local ma = mk_metavar("a", Pi(scope, mk_metavar("a_ty", Pi(scope, mk_sort(mk_meta_univ("l_a"))))(A, a, b, c, d, H1, H2, H3)))(A, a, b, c, d, H1, H2, H3)
local mb = mk_metavar("b", Pi(scope, mk_metavar("b_ty", Pi(scope, mk_sort(mk_meta_univ("l_b"))))(A, a, b, c, d, H1, H2, H3)))(A, a, b, c, d, H1, H2, H3)
local mA1 = mk_metavar("A1", Pi(scope, mk_sort(mk_meta_univ("l_A1"))))(A, a, b, c, d, H1, H2, H3)
local mA2 = mk_metavar("A2", Pi(scope, mk_sort(mk_meta_univ("l_A2"))))(A, a, b, c, d, H1, H2, H3)
print("================")
print(tc2:check(Fun(scope,
subst_u(mA1, mP, mb, ma,
H1,
trans_u(mA2, b, c, d, H2, H3)))))