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lean2/tests/lua/ceq1.lua

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feat(library/simplifier): add to_ceqs function that converts a theorem into a sequence of conditional equations Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 02:22:33 +00:00
local env = get_environment()
feat(library/simplifier): convert disequalities (a ≠ b) into equations '(a = b) = false' Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 23:30:16 +00:00
assert(env:find_object("neq_elim"))
feat(library/simplifier): add to_ceqs function that converts a theorem into a sequence of conditional equations Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 02:22:33 +00:00
function show_ceqs(ceqs)
for i = 1, #ceqs do
feat(library/simplifier): add is_permutation_ceq predicate Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-16 03:53:52 +00:00
print(ceqs[i][1], ceqs[i][2], is_permutation_ceq(ceqs[i][1]))
feat(library/simplifier): add to_ceqs function that converts a theorem into a sequence of conditional equations Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 02:22:33 +00:00
env:type_check(ceqs[i][2])
fix(library/simplifier): must use metavar_env in is_ceq, otherwise it may ceqs that contain metavariables Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-29 21:27:40 +00:00
assert(is_ceq(env, nil, ceqs[i][1]))
feat(library/simplifier): add to_ceqs function that converts a theorem into a sequence of conditional equations Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 02:22:33 +00:00
end
end
feat(library/simplifier): add is_permutation_ceq predicate Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-16 03:53:52 +00:00
function test_ceq(name, expected, is_perm)
feat(library/simplifier): add to_ceqs function that converts a theorem into a sequence of conditional equations Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 02:22:33 +00:00
local obj = env:find_object(name)
feat(library/simplifier): add support for metavariables in conditional rewrite rules Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-29 16:34:04 +00:00
local r = to_ceqs(env, nil, obj:get_type(), Const(name))
feat(library/simplifier): add to_ceqs function that converts a theorem into a sequence of conditional equations Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 02:22:33 +00:00
show_ceqs(r)
assert(#r == expected)
feat(library/simplifier): add is_permutation_ceq predicate Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-16 03:53:52 +00:00
if is_perm ~= nil then
for i = 1, #r do
assert(is_permutation_ceq(r[i][1]) == is_perm)
end
end
feat(library/simplifier): add to_ceqs function that converts a theorem into a sequence of conditional equations Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 02:22:33 +00:00
end
parse_lean_cmds([[
variable f : Nat -> Nat
axiom Ax1 : forall x : Nat, x > 0 -> f x < 0 /\ not (f x = 1)
axiom Ax2 : forall x : Nat, x < 0 -> f (f x) = x
variable g : Nat -> Nat -> Nat
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)
feat(library/simplifier): filter out propositions that cannot be used as conditional equations Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 20:05:14 +00:00
axiom Ax4 : forall x y : Nat, f x = x
axiom Ax5 : forall x y : Nat, f x = y /\ g x y = x
feat(library/simplifier): convert disequalities (a ≠ b) into equations '(a = b) = false' Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 23:30:16 +00:00
axiom Ax6 : forall x : Nat, f x ≠ 0
feat(library/simplifier): add to_ceqs function that converts a theorem into a sequence of conditional equations Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 02:22:33 +00:00
]])
test_ceq("Ax1", 2)
test_ceq("Ax2", 1)
test_ceq("Ax3", 4)
feat(library/simplifier): filter out propositions that cannot be used as conditional equations Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 20:05:14 +00:00
test_ceq("Ax4", 0)
test_ceq("Ax5", 1)
feat(library/simplifier): convert disequalities (a ≠ b) into equations '(a = b) = false' Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-15 23:30:16 +00:00
test_ceq("Ax6", 1)
refactor(library/simplifier): relax rule for conditional equalities The idea is to support conditional equations where the left-hand-side does not contain all theorem arguments, but the missing arguments can be inferred using type inference. For example, we will be able to have the eta theorem as rewrite rule: theorem eta {A : TypeU} {B : A → TypeU} (f : ∀ x : A, B x) : (λ x : A, f x) = f := funext (λ x : A, refl (f x)) Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-16 00:05:57 +00:00
test_ceq("eta", 1)
feat(library/simplifier): add is_permutation_ceq predicate Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-16 03:53:52 +00:00
test_ceq("not_not_eq", 1, false)
test_ceq("or_comm", 1, true)
test_ceq("or_assoc", 1, false)
test_ceq("or_id", 1, false)
test_ceq("or_falsel", 1, false)
test_ceq("or_falser", 1, false)
test_ceq("or_truel", 1, false)
test_ceq("or_truer", 1, false)
test_ceq("or_tauto", 1, false)
test_ceq("and_comm", 1, true)
test_ceq("and_assoc", 1, false)
test_ceq("and_id", 1, false)
test_ceq("and_falsel", 1, false)
test_ceq("and_falser", 1, false)
test_ceq("and_truel", 1, false)
test_ceq("and_truer", 1, false)
test_ceq("and_absurd", 1, false)
test_ceq("imp_truer", 1, false)
test_ceq("imp_truel", 1, false)
test_ceq("imp_falser", 1, false)
test_ceq("imp_falsel", 1, false)
test_ceq("not_and", 1, false)
test_ceq("not_or", 1, false)
test_ceq("not_iff", 1, false)
test_ceq("not_implies", 1, false)
test_ceq("or_left_comm", 1, true)
test_ceq("and_left_comm", 1, true)
test_ceq("forall_or_distributer", 1, false)
test_ceq("forall_or_distributel", 1, false)
test_ceq("forall_and_distribute", 1, false)
test_ceq("exists_and_distributer", 1, false)
test_ceq("exists_and_distributel", 1, false)
test_ceq("exists_or_distribute", 1, false)
test_ceq({"Nat", "add_zeror"}, 1, false)
test_ceq({"Nat", "add_zerol"}, 1, false)
test_ceq({"Nat", "add_comm"}, 1 , true)
test_ceq({"Nat", "add_assoc"}, 1, false)
test_ceq({"Nat", "mul_zerol"}, 1, false)
test_ceq({"Nat", "mul_zeror"}, 1, false)
test_ceq({"Nat", "mul_onel"}, 1, false)
test_ceq({"Nat", "mul_oner"}, 1, false)
test_ceq({"Nat", "mul_comm"}, 1, true)
test_ceq({"Nat", "mul_assoc"}, 1, false)
test_ceq({"Nat", "add_comm"}, 1, true)
test_ceq({"Nat", "add_assoc"}, 1, false)
test_ceq({"Nat", "distributer"}, 1, false)
test_ceq({"Nat", "distributel"}, 1, false)
test_ceq({"Nat", "le_refl"}, 1, false)
test_ceq({"Nat", "le_zero"}, 1, false)
test_ceq({"Nat", "not_lt_0"}, 1, false)
test_ceq({"Nat", "lt_nrefl"}, 1, false)
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