lean2/src/frontends/lean/notation.cpp

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/*
Copyright (c) 2013 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include "kernel/builtin.h"
#include "library/basic_thms.h"
#include "library/arith/arith.h"
#include "frontends/lean/frontend.h"
namespace lean {
void add_alias(environment const & env, name const & n, name const & m) {
object const & obj = env->get_object(n);
env->add_definition(m, obj.get_type(), mk_constant(n));
}
/**
\brief Initialize builtin notation.
*/
void init_builtin_notation(environment const & env, io_state & ios) {
if (!env->mark_builtin_imported("lean_notation"))
return;
add_infix(env, ios, "=", 50, mk_homo_eq_fn());
mark_implicit_arguments(env, mk_homo_eq_fn(), 1);
mark_implicit_arguments(env, mk_if_fn(), 1);
add_prefix(env, ios, "\u00ac", 40, mk_not_fn()); // "¬"
add_infixr(env, ios, "&&", 35, mk_and_fn()); // "&&"
add_infixr(env, ios, "/\\", 35, mk_and_fn()); // "/\"
add_infixr(env, ios, "\u2227", 35, mk_and_fn()); // "∧"
add_infixr(env, ios, "||", 30, mk_or_fn()); // "||"
add_infixr(env, ios, "\\/", 30, mk_or_fn()); // "\/"
add_infixr(env, ios, "\u2228", 30, mk_or_fn()); // ""
add_infixr(env, ios, "=>", 25, mk_implies_fn()); // "=>"
add_infixr(env, ios, "\u21D2", 25, mk_implies_fn()); // "⇒"
add_infixr(env, ios, "<=>", 25, mk_iff_fn()); // "<=>"
add_infixr(env, ios, "\u21D4", 25, mk_iff_fn()); // "⇔"
add_infixl(env, ios, "+", 65, mk_nat_add_fn());
add_infixl(env, ios, "-", 65, mk_nat_sub_fn());
add_prefix(env, ios, "-", 75, mk_nat_neg_fn());
add_infixl(env, ios, "*", 70, mk_nat_mul_fn());
add_infix(env, ios, "<=", 50, mk_nat_le_fn());
add_infix(env, ios, "\u2264", 50, mk_nat_le_fn()); // ≤
add_infix(env, ios, ">=", 50, mk_nat_ge_fn());
add_infix(env, ios, "\u2265", 50, mk_nat_ge_fn()); // ≥
add_infix(env, ios, "<", 50, mk_nat_lt_fn());
add_infix(env, ios, ">", 50, mk_nat_gt_fn());
add_mixfixc(env, ios, {"|", "|"}, 55, mk_nat_id_fn()); // absolute value for naturals is the identity function
add_infixl(env, ios, "+", 65, mk_int_add_fn());
add_infixl(env, ios, "-", 65, mk_int_sub_fn());
add_prefix(env, ios, "-", 75, mk_int_neg_fn());
add_infixl(env, ios, "*", 70, mk_int_mul_fn());
add_infixl(env, ios, "div", 70, mk_int_div_fn());
add_infixl(env, ios, "mod", 70, mk_int_mod_fn());
add_infix(env, ios, "|", 50, mk_int_divides_fn());
add_mixfixc(env, ios, {"|", "|"}, 55, mk_int_abs_fn());
add_infix(env, ios, "<=", 50, mk_int_le_fn());
add_infix(env, ios, "\u2264", 50, mk_int_le_fn()); // ≤
add_infix(env, ios, ">=", 50, mk_int_ge_fn());
add_infix(env, ios, "\u2265", 50, mk_int_ge_fn()); // ≥
add_infix(env, ios, "<", 50, mk_int_lt_fn());
add_infix(env, ios, ">", 50, mk_int_gt_fn());
add_infixl(env, ios, "+", 65, mk_real_add_fn());
add_infixl(env, ios, "-", 65, mk_real_sub_fn());
add_prefix(env, ios, "-", 75, mk_real_neg_fn());
add_infixl(env, ios, "*", 70, mk_real_mul_fn());
add_infixl(env, ios, "/", 70, mk_real_div_fn());
add_mixfixc(env, ios, {"|", "|"}, 55, mk_real_abs_fn());
add_infix(env, ios, "<=", 50, mk_real_le_fn());
add_infix(env, ios, "\u2264", 50, mk_real_le_fn()); // ≤
add_infix(env, ios, ">=", 50, mk_real_ge_fn());
add_infix(env, ios, "\u2265", 50, mk_real_ge_fn()); // ≥
add_infix(env, ios, "<", 50, mk_real_lt_fn());
add_infix(env, ios, ">", 50, mk_real_gt_fn());
add_coercion(env, mk_nat_to_int_fn());
add_coercion(env, mk_int_to_real_fn());
add_coercion(env, mk_nat_to_real_fn());
// implicit arguments for builtin axioms
mark_implicit_arguments(env, mk_mp_fn(), 2);
mark_implicit_arguments(env, mk_discharge_fn(), 2);
mark_implicit_arguments(env, mk_refl_fn(), 1);
mark_implicit_arguments(env, mk_subst_fn(), 4);
add_alias(env, "Subst", "SubstP");
mark_implicit_arguments(env, "SubstP", 3);
mark_implicit_arguments(env, mk_eta_fn(), 2);
mark_implicit_arguments(env, mk_abst_fn(), 4);
mark_implicit_arguments(env, mk_imp_antisym_fn(), 2);
mark_implicit_arguments(env, mk_hsymm_fn(), 4);
mark_implicit_arguments(env, mk_htrans_fn(), 6);
// implicit arguments for basic theorems
mark_implicit_arguments(env, mk_absurd_fn(), 1);
mark_implicit_arguments(env, mk_double_neg_elim_fn(), 1);
mark_implicit_arguments(env, mk_mt_fn(), 2);
mark_implicit_arguments(env, mk_contrapos_fn(), 2);
mark_implicit_arguments(env, mk_eq_mp_fn(), 2);
mark_implicit_arguments(env, mk_not_imp1_fn(), 2);
mark_implicit_arguments(env, mk_not_imp2_fn(), 2);
mark_implicit_arguments(env, mk_conj_fn(), 2);
mark_implicit_arguments(env, mk_conjunct1_fn(), 2);
mark_implicit_arguments(env, mk_conjunct2_fn(), 2);
mark_implicit_arguments(env, mk_disj1_fn(), 1);
mark_implicit_arguments(env, mk_disj2_fn(), 1);
mark_implicit_arguments(env, mk_disj_cases_fn(), 3);
mark_implicit_arguments(env, mk_refute_fn(), 1);
mark_implicit_arguments(env, mk_symm_fn(), 3);
mark_implicit_arguments(env, mk_trans_fn(), 4);
mark_implicit_arguments(env, mk_eqt_elim_fn(), 1);
mark_implicit_arguments(env, mk_eqt_intro_fn(), 1);
mark_implicit_arguments(env, mk_congr1_fn(), 4);
mark_implicit_arguments(env, mk_congr2_fn(), 4);
mark_implicit_arguments(env, mk_congr_fn(), 6);
mark_implicit_arguments(env, mk_forall_elim_fn(), 2);
mark_implicit_arguments(env, mk_forall_intro_fn(), 2);
mark_implicit_arguments(env, mk_exists_elim_fn(), 3);
mark_implicit_arguments(env, mk_exists_intro_fn(), 2);
}
}