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Add homogeneous equality

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2013-08-30 14:26:12 -07:00
parent f886485056
commit 4ef4655183
6 changed files with 26 additions and 1 deletions
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9
examples/ex14.lean Normal file
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@ -0,0 +1,9 @@
Variable N : Type
Variable a : N
Variable b : N
Show a ≃ b
Check a ≃ b
Set lean::pp::implicit true
Show a ≃ b
Show (Type 1) ≃ (Type 1)
Show true ≃ false

2
src/frontends/lean/lean_frontend.cpp
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@ -283,8 +283,8 @@ struct frontend::imp {
};
frontend::frontend():m_imp(new imp(*this)) {
init_builtin_notation(*this);
init_toplevel(m_imp->m_env);
init_builtin_notation(*this);
m_imp->m_state.set_formatter(mk_pp_formatter(*this));
}
frontend::frontend(imp * new_ptr):m_imp(new_ptr) {

4
src/frontends/lean/lean_notation.cpp
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@ -12,6 +12,10 @@ namespace lean {
\brief Initialize builtin notation.
*/
void init_builtin_notation(frontend & f) {
f.mark_implicit_arguments("heq", {true, false, false});
f.add_infix("==", 50, mk_homo_eq_fn());
f.add_infix("≃", 50, mk_homo_eq_fn());
f.add_prefix("\u00ac", 40, mk_not_fn()); // "¬"
f.add_infixr("&&", 35, mk_and_fn()); // "&&"
f.add_infixr("/\\", 35, mk_and_fn()); // "/\"

4
src/kernel/builtin.cpp
View file

@ -183,6 +183,7 @@ MK_CONSTANT(or_fn, name("or"));
MK_CONSTANT(not_fn, name("not"));
MK_CONSTANT(forall_fn, name("forall"));
MK_CONSTANT(exists_fn, name("exists"));
MK_CONSTANT(homo_eq_fn, name("heq"));
// Axioms
MK_CONSTANT(mp_fn, name("MP"));
@ -238,6 +239,9 @@ void add_basic_theory(environment & env) {
// TODO: introduce epsilon
env.add_definition(exists_fn_name, q_type, Fun({{A,TypeU}, {P, A_pred}}, Not(Forall(A, Fun({x, A}, Not(P(x)))))));
// homogeneous equality
env.add_definition(homo_eq_fn_name, Pi({A,TypeU}, A >> (A >> Bool)), Fun({{A,TypeU}, {x,A}, {y,A}}, Eq(x, y)));
// MP : Pi (a b : Bool) (H1 : a => b) (H2 : a), b
env.add_axiom(mp_fn_name, Pi({{a, Bool}, {b, Bool}, {H1, Implies(a, b)}, {H2, a}}, b));

6
src/kernel/builtin.h
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@ -109,6 +109,12 @@ expr mk_exists_fn();
inline expr mk_exists(expr const & A, expr const & P) { return mk_app(mk_exists_fn(), A, P); }
inline expr Exists(expr const & A, expr const & P) { return mk_exists(A, P); }
/** \brief Homogeneous equality. It has type: <tt>Pi (A : Type), A -> A -> Bool */
expr mk_homo_eq_fn();
/** \brief Return the term (homo_eq A l r) */
inline expr mk_homo_eq(expr const & A, expr const & l, expr const & r) { return mk_app(mk_homo_eq_fn(), A, l, r); }
inline expr hEq(expr const & A, expr const & l, expr const & r) { return mk_homo_eq(A, l, r); }
/** \brief Modus Ponens axiom */
expr mk_mp_fn();
/** \brief (Axiom) {a : Bool}, {b : Bool}, H1 : a => b, H2 : a |- MP(a, b, H1, H2) : b */

2
src/shell/CMakeLists.txt
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@ -14,3 +14,5 @@ add_test(lean9 ${CMAKE_CURRENT_BINARY_DIR}/lean "${LEAN_SOURCE_DIR}/../examples/
add_test(lean10 ${CMAKE_CURRENT_BINARY_DIR}/lean "${LEAN_SOURCE_DIR}/../examples/ex10.lean")
add_test(lean11 ${CMAKE_CURRENT_BINARY_DIR}/lean "${LEAN_SOURCE_DIR}/../examples/ex11.lean")
add_test(lean12 ${CMAKE_CURRENT_BINARY_DIR}/lean "${LEAN_SOURCE_DIR}/../examples/ex12.lean")
add_test(lean13 ${CMAKE_CURRENT_BINARY_DIR}/lean "${LEAN_SOURCE_DIR}/../examples/ex13.lean")
add_test(lean14 ${CMAKE_CURRENT_BINARY_DIR}/lean "${LEAN_SOURCE_DIR}/../examples/ex14.lean")