419 lines
15 KiB
C++
419 lines
15 KiB
C++
/*
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Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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*/
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#include "util/sstream.h"
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#include "kernel/abstract.h"
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#include "library/annotation.h"
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#include "library/placeholder.h"
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#include "library/explicit.h"
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#include "library/tactic/tactic.h"
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#include "library/tactic/expr_to_tactic.h"
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#include "library/typed_expr.h"
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#include "library/choice.h"
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#include "library/let.h"
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#include "frontends/lean/builtin_exprs.h"
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#include "frontends/lean/token_table.h"
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#include "frontends/lean/calc.h"
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#include "frontends/lean/begin_end_ext.h"
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#include "frontends/lean/parser.h"
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#include "frontends/lean/extra_info.h"
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#include "frontends/lean/util.h"
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namespace lean {
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namespace notation {
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static name g_llevel_curly(".{"), g_rcurly("}"), g_in("in"), g_colon(":"), g_assign(":=");
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static name g_comma(","), g_visible("[visible]"), g_from("from"), g_using("using");
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static name g_then("then"), g_have("have"), g_by("by"), g_qed("qed"), g_end("end");
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static name g_take("take"), g_assume("assume"), g_show("show"), g_fun("fun");
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static expr parse_Type(parser & p, unsigned, expr const *, pos_info const & pos) {
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if (p.curr_is_token(g_llevel_curly)) {
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p.next();
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level l = p.parse_level();
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p.check_token_next(g_rcurly, "invalid Type expression, '}' expected");
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return p.save_pos(mk_sort(l), pos);
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} else {
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return p.save_pos(mk_sort(mk_level_placeholder()), pos);
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}
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}
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static expr parse_Type_prime(parser & p, unsigned, expr const *, pos_info const & pos) {
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return p.save_pos(mk_sort(mk_succ(mk_level_placeholder())), pos);
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}
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static expr parse_let(parser & p, pos_info const & pos);
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static expr parse_let_body(parser & p, pos_info const & pos) {
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if (p.curr_is_token(g_comma)) {
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p.next();
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return parse_let(p, pos);
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} else if (p.curr_is_token(g_in)) {
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p.next();
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return p.parse_expr();
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} else {
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throw parser_error("invalid let declaration, 'in' or ',' expected", p.pos());
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}
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}
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static void parse_let_modifiers(parser & p, bool & is_visible) {
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while (true) {
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if (p.curr_is_token(g_visible)) {
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is_visible = true;
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p.next();
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} else {
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break;
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}
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}
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}
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static expr parse_let(parser & p, pos_info const & pos) {
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parser::local_scope scope1(p);
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if (p.parse_local_notation_decl()) {
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return parse_let_body(p, pos);
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} else {
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auto id_pos = p.pos();
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name id = p.check_atomic_id_next("invalid let declaration, identifier expected");
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bool is_visible = false;
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optional<expr> type;
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expr value;
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parse_let_modifiers(p, is_visible);
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if (p.curr_is_token(g_assign)) {
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p.next();
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value = p.parse_expr();
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} else if (p.curr_is_token(g_colon)) {
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p.next();
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type = p.parse_expr();
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p.check_token_next(g_assign, "invalid declaration, ':=' expected");
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value = p.parse_expr();
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} else {
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parser::local_scope scope2(p);
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buffer<expr> ps;
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auto lenv = p.parse_binders(ps);
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if (p.curr_is_token(g_colon)) {
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p.next();
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type = p.parse_scoped_expr(ps, lenv);
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type = Pi(ps, *type, p);
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}
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p.check_token_next(g_assign, "invalid let declaration, ':=' expected");
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value = p.parse_scoped_expr(ps, lenv);
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value = Fun(ps, value, p);
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}
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expr v;
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if (type)
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v = p.save_pos(mk_typed_expr(*type, value), p.pos_of(value));
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else
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v = value;
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v = p.save_pos(mk_let_value(v), id_pos);
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p.add_local_expr(id, v);
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expr b = parse_let_body(p, pos);
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return p.save_pos(mk_let(id, v, b), pos);
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}
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}
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static expr parse_let_expr(parser & p, unsigned, expr const *, pos_info const & pos) {
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return parse_let(p, pos);
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}
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static expr parse_placeholder(parser & p, unsigned, expr const *, pos_info const & pos) {
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return p.save_pos(mk_explicit_expr_placeholder(), pos);
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}
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static expr parse_by(parser & p, unsigned, expr const *, pos_info const & pos) {
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expr t = p.parse_expr();
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return p.mk_by(t, pos);
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}
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static expr parse_begin_end(parser & p, unsigned, expr const *, pos_info const & pos) {
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if (!p.has_tactic_decls())
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throw parser_error("invalid 'begin-end' expression, tactic module has not been imported", pos);
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optional<expr> pre_tac = get_begin_end_pre_tactic(p.env());
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optional<expr> r;
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while (true) {
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bool use_exact = (p.curr_is_token(g_have) || p.curr_is_token(g_show) || p.curr_is_token(g_assume) ||
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p.curr_is_token(g_take) || p.curr_is_token(g_fun));
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auto pos = p.pos();
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expr tac = p.parse_expr();
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if (use_exact)
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tac = p.mk_app(get_exact_tac_fn(), tac, pos);
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if (pre_tac)
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tac = p.mk_app({get_and_then_tac_fn(), *pre_tac, tac}, pos);
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tac = p.mk_app(get_determ_tac_fn(), tac, pos);
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r = r ? p.mk_app({get_and_then_tac_fn(), *r, tac}, pos) : tac;
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if (p.curr_is_token(g_end)) {
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auto pos = p.pos();
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p.next();
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return p.mk_by(*r, pos);
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} else if (p.curr_is_token(g_comma)) {
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p.next();
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} else {
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throw parser_error("invalid begin-end, ',' or 'end' expected", p.pos());
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}
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}
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}
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static expr parse_proof(parser & p, expr const & prop) {
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if (p.curr_is_token(g_from)) {
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// parse: 'from' expr
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p.next();
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return p.parse_expr();
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} else if (p.curr_is_token(g_by)) {
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// parse: 'by' tactic
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auto pos = p.pos();
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p.next();
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expr t = p.parse_expr();
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return p.mk_by(t, pos);
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} else if (p.curr_is_token(g_using)) {
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// parse: 'using' locals* ',' proof
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auto using_pos = p.pos();
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p.next();
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parser::local_scope scope(p);
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buffer<expr> locals;
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while (!p.curr_is_token(g_comma)) {
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auto id_pos = p.pos();
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expr l = p.parse_expr();
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if (!is_local(l))
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throw parser_error("invalid 'using' declaration for 'have', local expected", id_pos);
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p.add_local(l);
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locals.push_back(l);
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}
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p.next(); // consume ','
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expr pr = parse_proof(p, prop);
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unsigned i = locals.size();
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while (i > 0) {
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--i;
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expr l = locals[i];
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pr = p.save_pos(Fun(l, pr), using_pos);
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pr = p.save_pos(pr(l), using_pos);
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}
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return pr;
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} else {
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throw parser_error("invalid expression, 'by', 'using' or 'from' expected", p.pos());
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}
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}
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static expr parse_have_core(parser & p, pos_info const & pos, optional<expr> const & prev_local) {
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auto id_pos = p.pos();
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bool is_visible = false;
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name id;
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expr prop;
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if (p.curr_is_token(g_visible)) {
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p.next();
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is_visible = true;
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id = p.mk_fresh_name();
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prop = p.parse_expr();
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} else if (p.curr_is_identifier()) {
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id = p.get_name_val();
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p.next();
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if (p.curr_is_token(g_visible)) {
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p.next();
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p.check_token_next(g_colon, "invalid 'have' declaration, ':' expected");
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is_visible = true;
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prop = p.parse_expr();
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} else if (p.curr_is_token(g_colon)) {
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p.next();
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prop = p.parse_expr();
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} else {
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expr left = p.id_to_expr(id, id_pos);
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id = p.mk_fresh_name();
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prop = p.parse_led(left);
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}
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} else {
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id = p.mk_fresh_name();
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prop = p.parse_expr();
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}
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p.check_token_next(g_comma, "invalid 'have' declaration, ',' expected");
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expr proof;
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if (prev_local) {
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parser::local_scope scope(p);
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p.add_local(*prev_local);
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auto proof_pos = p.pos();
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proof = parse_proof(p, prop);
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proof = p.save_pos(Fun(*prev_local, proof), proof_pos);
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proof = p.save_pos(proof(*prev_local), proof_pos);
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} else {
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proof = parse_proof(p, prop);
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}
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p.check_token_next(g_comma, "invalid 'have' declaration, ',' expected");
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parser::local_scope scope(p);
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binder_info bi = mk_contextual_info(is_visible);
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expr l = p.save_pos(mk_local(id, prop, bi), pos);
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p.add_local(l);
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expr body;
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if (p.curr_is_token(g_then)) {
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auto then_pos = p.pos();
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p.next();
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p.check_token_next(g_have, "invalid 'then have' declaration, 'have' expected");
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body = parse_have_core(p, then_pos, some_expr(l));
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} else {
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body = p.parse_expr();
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}
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// remark: mk_contextual_info(false) informs the elaborator that prop should not occur inside metavariables.
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body = abstract(body, l);
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expr r = p.save_pos(mk_have_annotation(p.save_pos(mk_lambda(id, prop, body, bi), pos)), pos);
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return p.mk_app(r, proof, pos);
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}
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static expr parse_have(parser & p, unsigned, expr const *, pos_info const & pos) {
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return parse_have_core(p, pos, none_expr());
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}
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static name H_show("H_show");
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static expr parse_show(parser & p, unsigned, expr const *, pos_info const & pos) {
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expr prop = p.parse_expr();
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p.check_token_next(g_comma, "invalid 'show' declaration, ',' expected");
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expr proof = parse_proof(p, prop);
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expr b = p.save_pos(mk_lambda(H_show, prop, Var(0)), pos);
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expr r = p.mk_app(b, proof, pos);
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return p.save_pos(mk_show_annotation(r), pos);
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}
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static name g_exists_elim("exists_elim");
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static expr parse_obtain(parser & p, unsigned, expr const *, pos_info const & pos) {
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if (!p.env().find(g_exists_elim))
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throw parser_error("invalid use of 'obtain' expression, environment does not contain 'exists_elim' theorem", pos);
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// exists_elim {A : Type} {P : A → Prop} {B : Prop} (H1 : ∃ x : A, P x) (H2 : ∀ (a : A) (H : P a), B)
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buffer<expr> ps;
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auto b_pos = p.pos();
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environment env = p.parse_binders(ps);
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unsigned num_ps = ps.size();
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if (num_ps < 2)
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throw parser_error("invalid 'obtain' expression, at least 2 binders expected", b_pos);
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bool is_visible = false;
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if (p.curr_is_token(g_visible)) {
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p.next();
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is_visible = true;
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}
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if (!is_visible) {
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expr H = ps[num_ps-1];
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ps[num_ps-1] = update_local(H, mlocal_type(H), local_info(H).update_contextual(false));
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}
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p.check_token_next(g_comma, "invalid 'obtain' expression, ',' expected");
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p.check_token_next(g_from, "invalid 'obtain' expression, 'from' expected");
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expr H1 = p.parse_expr();
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p.check_token_next(g_comma, "invalid 'obtain' expression, ',' expected");
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expr b = p.parse_scoped_expr(ps, env);
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expr H = ps[num_ps-1];
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name H_name = local_pp_name(H);
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unsigned i = num_ps-1;
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while (i > 1) {
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--i;
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expr a = ps[i];
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expr H_aux = mk_local(p.mk_fresh_name(), H_name.append_after(i), mk_expr_placeholder(), mk_contextual_info(false));
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expr H2 = Fun({a, H}, b);
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b = mk_constant(g_exists_elim)(H_aux, H2);
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H = H_aux;
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}
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expr a = ps[0];
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expr H2 = Fun({a, H}, b);
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expr r = mk_constant(g_exists_elim)(H1, H2);
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return p.rec_save_pos(r, pos);
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}
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static expr parse_calc_expr(parser & p, unsigned, expr const *, pos_info const &) {
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return parse_calc(p);
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}
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static expr parse_overwrite_notation(parser & p, unsigned, expr const *, pos_info const &) {
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name n = p.check_id_next("invalid '#' local notation, identifier expected");
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environment env = overwrite_notation(p.env(), n);
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return p.parse_scoped_expr(0, nullptr, env);
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}
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static expr parse_explicit_expr(parser & p, unsigned, expr const *, pos_info const & pos) {
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expr e = p.parse_expr(get_max_prec());
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if (is_choice(e)) {
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buffer<expr> new_choices;
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for (unsigned i = 0; i < get_num_choices(e); i++)
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new_choices.push_back(p.save_pos(mk_explicit(get_choice(e, i)), pos));
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return p.save_pos(mk_choice(new_choices.size(), new_choices.data()), pos);
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} else {
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return p.save_pos(mk_explicit(e), pos);
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}
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}
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static expr parse_including_expr(parser & p, unsigned, expr const *, pos_info const & pos) {
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buffer<expr> locals;
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while (!p.curr_is_token(g_comma)) {
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auto pos = p.pos();
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name id = p.check_id_next("invalid 'including', identifier expected");
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if (auto it = p.get_local(id)) {
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locals.push_back(*it);
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} else {
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throw parser_error(sstream() << "invalid 'including', '" << id << "' is not a local declaraton", pos);
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}
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}
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p.next();
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parser::local_scope scope(p);
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buffer<expr> new_locals;
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for (auto old_l : locals) {
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binder_info bi = mk_contextual_info(true);
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expr new_l = p.save_pos(mk_local(local_pp_name(old_l), mk_as_is(mlocal_type(old_l)), bi), pos);
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p.add_local(new_l);
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new_locals.push_back(new_l);
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}
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expr r = Fun(new_locals, p.parse_expr(), p);
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r = p.rec_save_pos(mk_app(r, locals), pos);
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return r;
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}
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static expr parse_sorry(parser & p, unsigned, expr const *, pos_info const & pos) {
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return p.mk_sorry(pos);
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}
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static expr parse_rparen(parser & p, unsigned, expr const * args, pos_info const & pos) {
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if (p.collecting_info())
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return p.save_pos(mk_extra_info(args[0]), pos);
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else
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return args[0];
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}
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parse_table init_nud_table() {
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action Expr(mk_expr_action());
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action Skip(mk_skip_action());
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action Binders(mk_binders_action());
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expr x0 = mk_var(0);
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parse_table r;
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r = r.add({transition("_", mk_ext_action(parse_placeholder))}, x0);
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r = r.add({transition("by", mk_ext_action(parse_by))}, x0);
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r = r.add({transition("have", mk_ext_action(parse_have))}, x0);
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r = r.add({transition("show", mk_ext_action(parse_show))}, x0);
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r = r.add({transition("obtain", mk_ext_action(parse_obtain))}, x0);
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r = r.add({transition("(", Expr), transition(")", mk_ext_action(parse_rparen))}, x0);
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r = r.add({transition("fun", Binders), transition(",", mk_scoped_expr_action(x0))}, x0);
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r = r.add({transition("Pi", Binders), transition(",", mk_scoped_expr_action(x0, 0, false))}, x0);
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r = r.add({transition("Type", mk_ext_action(parse_Type))}, x0);
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r = r.add({transition("Type'", mk_ext_action(parse_Type_prime))}, x0);
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r = r.add({transition("let", mk_ext_action(parse_let_expr))}, x0);
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r = r.add({transition("calc", mk_ext_action(parse_calc_expr))}, x0);
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r = r.add({transition("#", mk_ext_action(parse_overwrite_notation))}, x0);
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r = r.add({transition("@", mk_ext_action(parse_explicit_expr))}, x0);
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r = r.add({transition("begin", mk_ext_action(parse_begin_end))}, x0);
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r = r.add({transition("sorry", mk_ext_action(parse_sorry))}, x0);
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r = r.add({transition("including", mk_ext_action(parse_including_expr))}, x0);
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return r;
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}
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parse_table init_led_table() {
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parse_table r(false);
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r = r.add({transition("->", mk_expr_action(get_arrow_prec()-1))}, mk_arrow(Var(1), Var(1)));
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return r;
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}
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}
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bool is_show_aux_name(name const & n) { return n == notation::H_show; }
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parse_table get_builtin_nud_table() {
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static optional<parse_table> r;
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if (!r)
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r = notation::init_nud_table();
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return *r;
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}
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parse_table get_builtin_led_table() {
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static optional<parse_table> r;
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if (!r)
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r = notation::init_led_table();
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return *r;
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}
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}
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