// If restricted is true, we don't use (e <-> true) rewrite
list<expr_pair> apply(expr const & e, expr const & H, bool restrited) {
expr c, Hdec, A, arg1, arg2;
if (is_relation(e)) {
return mk_singleton(e, H);
} else if (is_standard(m_env) && is_not(m_env, e, arg1)) {
expr new_e = mk_iff(arg1, mk_false());
expr new_H = mk_app(mk_constant(get_iff_false_intro_name()), arg1, H);
return mk_singleton(new_e, new_H);
} else if (is_standard(m_env) && is_and(e, arg1, arg2)) {
// TODO(Leo): we can extend this trick to any type that has only one constructor
expr H1 = mk_app(mk_constant(get_and_elim_left_name()), arg1, arg2, H);
expr H2 = mk_app(mk_constant(get_and_elim_right_name()), arg1, arg2, H);
auto r1 = apply(arg1, H1, restrited);
auto r2 = apply(arg2, H2, restrited);
return append(r1, r2);
} else if (is_pi(e)) {
// TODO(dhs): keep name?
expr local = m_tctx.mk_tmp_local(binding_domain(e), binding_info(e));
expr new_e = instantiate(binding_body(e), local);
expr new_H = mk_app(H, local);
auto r = apply(new_e, new_H, restrited);
unsigned len = length(r);
if (len == 0) {
return r;
} else if (len == 1 && head(r).first == new_e && head(r).second == new_H) {
return mk_singleton(e, H);
} else {
return lift(local, r);
}
} else if (is_standard(m_env) && is_ite(e, c, Hdec, A, arg1, arg2) && is_prop(e)) {
// TODO(Leo): support HoTT mode if users request
expr not_c = mk_app(mk_constant(get_not_name()), c);
expr Hc = m_tctx.mk_tmp_local(c);
expr Hnc = m_tctx.mk_tmp_local(not_c);
expr H1 = mk_app({mk_constant(get_implies_of_if_pos_name()),
c, arg1, arg2, Hdec, e, Hc});
expr H2 = mk_app({mk_constant(get_implies_of_if_neg_name()),
c, arg1, arg2, Hdec, e, Hnc});
auto r1 = lift(Hc, apply(arg1, H1, restrited));
auto r2 = lift(Hnc, apply(arg2, H2, restrited));
return append(r1, r2);
} else if (!restrited) {
expr new_e = m_tctx.whnf(e);
if (new_e != e) {
if (auto r = apply(new_e, H, true))
return r;
}
if (is_standard(m_env) && is_prop(e)) {
expr new_e = mk_iff(e, mk_true());
expr new_H = mk_app(mk_constant(get_iff_true_intro_name()), e, H);
return mk_singleton(new_e, new_H);
} else {
return list<expr_pair>();
}
} else {
return list<expr_pair>();
}
}
/*
** Function that gets the lexical type
** of a requested element (always symbolized
** by two chars in order to fit to || or && etc.
*/
t_lextype get_lextype(char a, char b, char c)
{
t_lextype lextype;
lextype = WORD;
if (is_delim(b, c))
lextype = DELIM;
else if (is_redirection(b, c))
lextype = REDIR;
else if (is_and(b, c))
lextype = AND;
else if (IS_PAR(b))
lextype = PAR;
else if (IS_QUOTE(b) && a != '\\')
lextype = QUOTE;
else if (IS_DQUOTE(b) && a != '\\')
lextype = DQUOTE;
else if (IS_BQUOTE(b))
lextype = BACKQUOTE;
return (lextype);
}
object *eval(object *exp, object *env) {
object *procedure;
object *arguments;
object *result;
bool tailcall = false;
do {
if (is_self_evaluating(exp))
return exp;
if (is_variable(exp))
return lookup_variable_value(exp, env);
if (is_quoted(exp))
return text_of_quotation(exp);
if (is_assignment(exp))
return eval_assignment(exp, env);
if (is_definition(exp))
return eval_definition(exp, env);
if (is_if(exp)) {
exp = is_true(eval(if_predicate(exp), env)) ? if_consequent(exp) : if_alternative(exp);
tailcall = true;
continue;
}
if (is_lambda(exp))
return make_compound_proc(lambda_parameters(exp), lambda_body(exp), env);
if (is_begin(exp)) {
exp = begin_actions(exp);
while (!is_last_exp(exp)) {
eval(first_exp(exp), env);
exp = rest_exps(exp);
}
exp = first_exp(exp);
tailcall = true;
continue;
}
if (is_cond(exp)) {
exp = cond_to_if(exp);
tailcall = true;
continue;
}
if (is_let(exp)) {
exp = let_to_application(exp);
tailcall = true;
continue;
}
if (is_and(exp)) {
exp = and_tests(exp);
if (is_empty(exp))
return make_boolean(true);
while (!is_last_exp(exp)) {
result = eval(first_exp(exp), env);
if (is_false(result))
return result;
exp = rest_exps(exp);
}
exp = first_exp(exp);
tailcall = true;
continue;
}
if (is_or(exp)) {
exp = or_tests(exp);
if (is_empty(exp)) {
return make_boolean(false);
}
while (!is_last_exp(exp)) {
result = eval(first_exp(exp), env);
if (is_true(result))
return result;
exp = rest_exps(exp);
}
exp = first_exp(exp);
tailcall = true;
continue;
}
if (is_application(exp)) {
procedure = eval(operator(exp), env);
arguments = list_of_values(operands(exp), env);
if (is_primitive_proc(procedure) && procedure->data.primitive_proc.fn == eval_proc) {
exp = eval_expression(arguments);
env = eval_environment(arguments);
tailcall = true;
continue;
}
if (is_primitive_proc(procedure) && procedure->data.primitive_proc.fn == apply_proc) {
procedure = apply_operator(arguments);
arguments = apply_operands(arguments);
}
if (is_primitive_proc(procedure))
return (procedure->data.primitive_proc.fn)(arguments);
if (is_compound_proc(procedure)) {
env = extend_environment(procedure->data.compound_proc.parameters, arguments, procedure->data.compound_proc.env);
exp = make_begin(procedure->data.compound_proc.body);
tailcall = true;
continue;
}
return make_error(342, "unknown procedure type");
} // is_application()
} while (tailcall);
fprintf(stderr, "cannot eval unknown expression type\n");
exit(EXIT_FAILURE);
}
object *bs_eval(object *exp, object *env)
{
tailcall:
if (is_empty_list(exp)) {
error("unable to evaluate empty list");
} else if (is_self_evaluating(exp)) {
return exp;
} else if (is_variable(exp)) {
return lookup_variable_value(exp, env);
} else if (is_quoted(exp)) {
return quoted_expression(exp);
} else if (is_assignment(exp)) {
return eval_assignment(exp, env);
} else if (is_definition(exp)) {
return eval_definition(exp, env);
} else if (is_if(exp)) {
if (is_true(bs_eval(if_predicate(exp), env))) {
exp = if_consequent(exp);
} else {
exp = if_alternate(exp);
}
goto tailcall;
} else if (is_lambda(exp)) {
return make_compound_proc(lambda_parameters(exp),
lambda_body(exp),
env);
} else if (is_begin(exp)) {
exp = begin_actions(exp);
if (is_empty_list(exp)) {
error("empty begin block");
}
while (!is_empty_list(cdr(exp))) {
bs_eval(car(exp), env);
exp = cdr(exp);
}
exp = car(exp);
goto tailcall;
} else if (is_cond(exp)) {
exp = cond_to_if(exp);
goto tailcall;
} else if (is_let(exp)) {
exp = let_to_application(exp);
goto tailcall;
} else if (is_and(exp)) {
exp = and_tests(exp);
if (is_empty_list(exp)) {
return get_boolean(1);
}
object *result;
while (!is_empty_list(cdr(exp))) {
result = bs_eval(car(exp), env);
if (is_false(result)) {
return result;
}
exp = cdr(exp);
}
exp = car(exp);
goto tailcall;
} else if (is_or(exp)) {
exp = or_tests(exp);
if (is_empty_list(exp)) {
return get_boolean(0);
}
object *result;
while (!is_empty_list(cdr(exp))) {
result = bs_eval(car(exp), env);
if (is_true(result)) {
return result;
}
exp = cdr(exp);
}
exp = car(exp);
goto tailcall;
} else if (is_application(exp)) {
object *procedure = bs_eval(application_operator(exp), env);
object *parameters = eval_parameters(application_operands(exp), env);
// handle eval specially for tailcall requirement.
if (is_primitive_proc(procedure) &&
procedure->value.primitive_proc == eval_proc) {
exp = eval_expression(parameters);
env = eval_environment(parameters);
goto tailcall;
}
// handle apply specially for tailcall requirement.
if (is_primitive_proc(procedure) &&
procedure->value.primitive_proc == apply_proc) {
procedure = apply_operator(parameters);
parameters = apply_operands(parameters);
}
if (is_primitive_proc(procedure)) {
return (procedure->value.primitive_proc)(parameters);
} else if (is_compound_proc(procedure)) {
env = extend_environment(
procedure->value.compound_proc.parameters,
parameters,
procedure->value.compound_proc.env);
exp = make_begin(procedure->value.compound_proc.body);
goto tailcall;
} else {
error("unable to apply unknown procedure type");
}
} else {
error("unable to evaluate expression");
}
}
///////////////////////////////////////////////////////////////////
//eval
//requires two arguments:exp & tail_context
///////////////////////////////////////////////////////////////////
cellpoint eval(void)
{
if (is_true(is_self_evaluating(args_ref(1)))){
reg = args_ref(1);
}else if (is_true(is_variable(args_ref(1)))){
reg = args_ref(1);
args_push(current_env);
args_push(reg);
reg = lookup_var_val();
}else if (is_true(is_quoted(args_ref(1)))){
args_push(args_ref(1));
reg = quotation_text();
}else if (is_true(is_assignment(args_ref(1)))){
args_push(args_ref(1));
reg = eval_assignment();
}else if (is_true(is_definition(args_ref(1)))){
args_push(args_ref(1));
reg = eval_definition();
}else if (is_true(is_if(args_ref(1)))){
//eval if expression with the second argument (tail_context)
reg = args_ref(1);
args_push(args_ref(2));
args_push(reg);
reg = eval_if();
}else if (is_true(is_lambda(args_ref(1)))){
args_push(args_ref(1));
reg = eval_lambda();
}else if (is_true(is_begin(args_ref(1)))){
args_push(args_ref(1));
reg = begin_actions();
//eval the actions of begin exp with the second argument (tail_context)
args_push(args_ref(2));
args_push(reg);
reg = eval_sequence();
}else if (is_true(is_cond(args_ref(1)))){
args_push(args_ref(1));
reg = cond_2_if();
//eval the exp with the second argument (tail_context)
args_push(args_ref(2));
args_push(reg);
reg = eval();
}else if (is_true(is_and(args_ref(1)))){
reg = args_ref(1);
args_push(args_ref(2));
args_push(reg);
reg = eval_and();
}else if (is_true(is_or(args_ref(1)))){
reg = args_ref(1);
args_push(args_ref(2));
args_push(reg);
reg = eval_or();
}else if (is_true(is_let(args_ref(1)))){
//convert let to combination
args_push(args_ref(1));
reg = let_2_combination();
//evals the combination
args_push(args_ref(2));
args_push(reg);
reg = eval();
}else if (is_true(is_letstar(args_ref(1)))){
//convert let* to nested lets
args_push(args_ref(1));
reg = letstar_2_nested_lets();
//evals the nested lets
args_push(args_ref(2));
args_push(reg);
reg = eval();
}else if (is_true(is_application(args_ref(1)))){
//computes operator
args_push(args_ref(1));
reg = operator();
args_push(a_false);
args_push(reg);
reg = eval();
stack_push(&vars_stack, reg);
//computes operands
args_push(args_ref(1));
reg = operands();
args_push(reg);
reg = list_of_values();
//calls apply with the second argument (tail_context)
args_push(args_ref(2));
args_push(reg);
args_push(stack_pop(&vars_stack));
reg = apply();
}else {
printf("Unknown expression type -- EVAL\n");
error_handler();
}
args_pop(2);
return reg;
}
