static struct term *_lambda_parse(struct lexer *lex, enum term_parse_res *res)
{
struct term *body = NULL;
struct term *ret = NULL;
if(lex->type != TOK_SYM) {
*res = PARSE_EXPECTED_SYM;
goto done;
} else {
char var[VAR_LEN];
strncpy(var, lex->sym, VAR_LEN);
lexer_advance(lex);
if(lex->type != TOK_DOT) {
*res = PARSE_EXPECTED_DOT;
goto done;
}
lexer_advance(lex);
body = _term_parse(lex, res);
if(! body) {
goto done;
}
ret = make_lambda(var, body);
}
done:
destroy_term(body);
return ret;
}
static inline object *let_to_application(object *exp)
{
return make_application(
make_lambda(let_variables(exp),
let_body(exp)),
let_values(exp));
}
//one arg: exp
static cellpoint definition_value(void)
{
if (is_true(is_null(cdr(cdr(args_ref(1)))))){
printf("define: bad syntax in: ");
write(args_ref(1));
newline();
error_handler();
}
reg = car(cdr(args_ref(1)));
if (is_true(is_symbol(reg))){
reg = car(cdr(cdr(args_ref(1))));
}else {
//get formal arguments list
reg = cdr(reg);
stack_push(&vars_stack, reg);
//get body
reg = cdr(cdr(args_ref(1)));
//make a lambda expression
args_push(reg);
args_push(stack_pop(&vars_stack));
reg = make_lambda();
}
args_pop(1);
return reg;
}
item definition_value(item exp){
if (car(cdr(exp)).type == t_symbol){
return car(cdr(cdr(exp)));
}
else
return make_lambda(cdr(car(cdr(exp))),
cdr(cdr(exp)));
}
static pSlipObject definition_value(pSlip gd, pSlipObject exp, pSlipEnvironment env)
{
if (sIsObject_Symbol(cadr(exp)) == S_TRUE)
{
return caddr(exp);
}
else
{
return make_lambda(gd, cdadr(exp), cddr(exp));
}
}
Value Value::definition_value(void) const{
const auto second=vlist.begin()+1;
if ( second->type == SYMBOL ) {
return *(second+1);
} else if ( second->type == LIST ) {
const auto second_second = second->vlist.begin()+1;
Vlist params = Vlist(second_second,second->vlist.end());
Vlist body = Vlist(second+1,vlist.end());
return make_lambda( params, body );
} else {
return *second;
}
}
term* normalize_fuel_lambda(context *Sigma, typing_context* Delta, term* t, int fuel) {
term* b = NULL;
term* A = normalize_fuel(Sigma, Delta, t->left, fuel-1);
context* extend = context_add(variable_dup(t->var), NULL, Sigma);
b = normalize_fuel(extend, Delta, t->right, fuel-1);
context_pop(extend);
if (!b) goto error;
return make_lambda(variable_dup(t->var), A, b);
error:
free_term(A);
free_term(b);
return NULL;
}
//one arg: exp
static cellpoint let_2_combination(void)
{
//get the binding vals of let expression
args_push(args_ref(1));
reg = let_vals();
stack_push(&vars_stack, reg);
//make a lambda expression
args_push(args_ref(1));
reg = let_vars();
stack_push(&vars_stack, reg);
args_push(args_ref(1));
reg = let_body();
args_push(reg);
args_push(stack_pop(&vars_stack));
reg = make_lambda();
//make a combination
reg = cons(reg, stack_pop(&vars_stack));
args_pop(1);
return reg;
}
lisp_obj *eval_expression(lisp_expr *expr, lisp_env *env, lisp_err *err)
{
lisp_obj *value = NULL;
assert(expr != NULL);
switch (expr->type){
case MKLAMBDA:
return make_lambda(expr, env);
case SELFEVAL:
value = expr->value.selfeval.value;
if (! value){
return NULL;
}
return retain(value);
case LOOKUP:
value = lookup(env, expr->value.lookup.name);
if (! value){
raise_error(err, UNKNOW_IDENTIFIER, "Unknow identifier \"%s\"", expr->value.lookup.name);
return NULL;
}
return retain(value);
case APPLICATION:
return apply(&(expr->value.application), env, err);
case CONDITION:
return eval_condition(&(expr->value.condition), env, err);
case DEFINE:
value = FORCE_VALUE(expr->value.define.expr, env, err);
if (! value){
return NULL;
}
release(set_env(env, expr->value.define.name, value));
default:
return NIL;
}
}
void graph_pylambda_evaluator::init(const std::string& lambda,
size_t num_partitions,
const std::vector<std::string>& vertex_fields,
const std::vector<std::string>& edge_fields,
size_t src_column_id,
size_t dst_column_id) {
clear();
// initialize members
size_t new_lambda_id = make_lambda(lambda);
// If it has changed, release the old one.
if(m_lambda_id != size_t(-1) && new_lambda_id != m_lambda_id) {
release_lambda(m_lambda_id);
}
m_lambda_id = new_lambda_id;
m_vertex_keys = vertex_fields;
m_edge_keys = edge_fields;
m_srcid_column = src_column_id;
m_dstid_column = dst_column_id;
m_graph_sync.init(num_partitions, vertex_fields);
}
/*
invariant: no sharing between returned term and *any* arguments.
the caller must free the result.
*/
term* substitute(variable* from, term* to, term* haystack) {
if (haystack == NULL) return NULL;
check(from != NULL && to != NULL, "substitute requires non-NULL arguments");
check(term_locally_well_formed(to), "substitute requires %W to be locally well-formed", to, print_term);
check(term_locally_well_formed(haystack),"substitute requires %W to be locally well-formed", haystack, print_term);
switch(haystack->tag) {
case VAR:
if (variable_equal(from, haystack->var)) {
return term_dup(to);
} else {
return term_dup(haystack);
}
case HOLE:
return term_dup(haystack);
case LAM:
if (variable_equal(from, haystack->var)) {
return make_lambda(variable_dup(haystack->var),
substitute(from, to, haystack->left),
term_dup(haystack->right));
} else {
if (is_free(haystack->var, to)) {
variable *g = gensym(haystack->var->name);
term *tg = make_var(g);
term* new_haystack = make_lambda(variable_dup(g), term_dup(haystack->left),
substitute(haystack->var, tg, haystack->right));
free_term(tg);
term* ans = substitute(from, to, new_haystack);
free_term(new_haystack);
return ans;
}
return make_lambda(variable_dup(haystack->var),
substitute(from, to, haystack->left),
substitute(from, to, haystack->right));
}
case PI:
if (variable_equal(from, haystack->var)) {
return make_pi(variable_dup(haystack->var),
substitute(from, to, haystack->left),
term_dup(haystack->right));
} else {
if (is_free(haystack->var, to)) {
variable *g = gensym(haystack->var->name);
term *tg = make_var(g);
term* new_haystack = make_pi(variable_dup(g), term_dup(haystack->left),
substitute(haystack->var, tg, haystack->right));
free_term(tg);
term* ans = substitute(from, to, new_haystack);
free_term(new_haystack);
return ans;
}
return make_pi(variable_dup(haystack->var),
substitute(from, to, haystack->left),
substitute(from, to, haystack->right));
}
case APP:
return make_app(substitute(from, to, haystack->left),
substitute(from, to, haystack->right));
case TYPE:
return term_dup(haystack);
case DATATYPE:
{
term* ans = make_datatype_term(variable_dup(haystack->var),
haystack->num_params, haystack->num_indices);
#define SUB_VEC(dst, src, n) do { \
int __i; \
for (__i = 0; __i < n; __i++) { \
dst[__i] = substitute(from, to, src[__i]); \
} \
} while(0)
SUB_VEC(ans->params, haystack->params, haystack->num_params);
SUB_VEC(ans->indices, haystack->indices, haystack->num_indices);
return ans;
}
case INTRO:
{
term* ans = make_intro(variable_dup(haystack->var),
substitute(from, to, haystack->left),
haystack->num_args,
haystack->num_params,
haystack->num_indices);
SUB_VEC(ans->args, haystack->args, haystack->num_args);
SUB_VEC(ans->params, haystack->params, haystack->num_params);
SUB_VEC(ans->indices, haystack->indices, haystack->num_indices);
return ans;
}
case ELIM:
{
term* ans = make_elim(variable_dup(haystack->var), haystack->num_args, haystack->num_params, haystack->num_indices);
SUB_VEC(ans->args, haystack->args, haystack->num_args);
SUB_VEC(ans->params, haystack->params, haystack->num_params);
SUB_VEC(ans->indices, haystack->indices, haystack->num_indices);
return ans;
}
case IMPLICIT:
return term_dup(haystack);
default:
sentinel("malformed term with tag %d", haystack->tag);
}
error:
return NULL;
}
int syntactically_identical(term* a, term* b) {
if (a == NULL || b == NULL) return a == b;
check(term_locally_well_formed(a) && term_locally_well_formed(b),
"alpha equiv requires well-formed arguments");
if (a->tag == HOLE) {
log_info("Hole should unify with %W", b, print_term);
return 1;
}
if (b->tag == HOLE) {
log_info("Hole should unify with %W", a, print_term);
return 1;
}
if (a->tag != b-> tag) return 0;
switch (a->tag) {
case VAR:
return variable_equal(a->var, b->var);
case LAM:
{
if (a->left != NULL && b->left != NULL && !syntactically_identical(a->left, b->left))
return 0;
if (variable_equal(a->var, b->var))
return syntactically_identical(a->right, b->right);
term* va = make_var(variable_dup(a->var));
term* bsubs = substitute(b->var, va, b->right);
free_term(va);
term* c = make_lambda(variable_dup(a->var), term_dup(b->left), bsubs);
int ans = syntactically_identical(a, c);
free_term(c);
return ans;
}
case PI:
{
if (!syntactically_identical(a->left, b->left))
return 0;
if (variable_equal(a->var, b->var))
return syntactically_identical(a->right, b->right);
term* va = make_var(variable_dup(a->var));
term* bsubs = substitute(b->var, va, b->right);
free_term(va);
term* c = make_pi(variable_dup(a->var), term_dup(b->left), bsubs);
int ans = syntactically_identical(a, c);
free_term(c);
return ans;
}
case APP:
return
syntactically_identical(a->left, b->left) &&
syntactically_identical(a->right, b->right);
case DATATYPE:
{
if (!variable_equal(a->var, b->var)) {
return 0;
}
#define EQ_VEC(a, an, b, bn) do { \
if (an != bn) return 0; \
int __i; \
for (__i = 0; __i < an; __i++) { \
if (!syntactically_identical(a[__i], b[__i])) return 0; \
} \
} while(0)
EQ_VEC(a->params, a->num_params, b->params, b->num_params);
EQ_VEC(a->indices, a->num_indices, b->indices, b->num_indices);
return 1;
}
case INTRO:
case ELIM:
{
if (!variable_equal(a->var, b->var)) {
return 0;
}
EQ_VEC(a->args, a->num_args, b->args, b->num_args);
EQ_VEC(a->params, a->num_params, b->params, b->num_params);
EQ_VEC(a->indices, a->num_indices, b->indices, b->num_indices);
return 1;
}
case TYPE:
return 1;
case IMPLICIT:
return syntactically_identical(a->right, b->right);
default:
sentinel("malformed term");
}
error:
return 0;
}
object *definition_value(object *exp) {
return is_symbol(cadr(exp)) ? caddr(exp) : make_lambda(cdadr(exp), cddr(exp));
}
object *let_to_application(object *exp) {
return make_application(make_lambda(let_parameters(exp), let_body(exp)), let_arguments(exp));
}
static data_t *get_definition_value(const data_t *exp) {
if(is_symbol(cadr(exp)))
return caddr(exp);
return make_lambda(cdadr(exp), cddr(exp));
}
static inline object *definition_value(object *exp)
{
return is_symbol(car(cdr(exp))) ? car(cdr(cdr(exp))) :
make_lambda(cdr(car(cdr(exp))), cdr(cdr(exp)));
}
static data_t *transform_let(const data_t *assignment, const data_t *body) {
return cons(make_lambda(get_let_var(assignment), body), get_let_exp(assignment));
}
int main(int argc, char *argv[])
{
if(argc == 1) {
printf("usage: %s <cmds> ...\n", argv[0]);
printf("<cmds> is one of:\n");
printf("<expr> -- push <expr> onto stack\n");
printf("<expr> <name> -alpha -- push alpha rename of <expr> using <name>\n");
printf("<expr> -beta -- push beta reduce of <expr>\n");
printf("<expr> -eta -- push eta convert of <expr>\n");
printf("<body> <var> -lambda -- push lambda binding free <var> in <body>\n");
printf("<fun> <arg> -apply -- push apply of <fun> and <arg>\n");
printf("<expr1> <expr2> -alpheq -- push \\x.\\y.x (true) or \\x.\\y.y (false) if <expr1> and <expr2> are alpha equivalent\n");
printf("-body -- move cursor into body of lambda\n");
printf("-fun -- move cursor into func of apply\n");
printf("-arg -- move cursor into arg of apply\n");
printf("-up -- move cursor up one level\n");
printf("-top -- move cursor to top level\n");
printf("<expr1> <expr2> -swap -- swap <expr1> and <expr2>\n");
printf("<expr> -dup -- duplicate <expr>\n");
printf("<expr1> <expr2> -repl -- replace <expr1> with <expr2> and remove <expr2>\n");
printf("-print -- print expression stack\n");
return 0;
}
struct termnode *term_top = NULL;
struct term *church_true, *church_false;
{
enum term_parse_res res;
char *expr = "\\a.\\b.a";
FILE *stream = fmemopen(expr, strlen(expr), "r");
church_true = term_parse(stream, &res);
fclose(stream);
expr = "\\a.\\b.b";
stream = fmemopen(expr, strlen(expr), "r");
church_false = term_parse(stream, &res);
fclose(stream);
}
for(int i = 1; i < argc; i++) {
if(strcmp(argv[i], "-alpha") == 0) {
if(! termstack_get(term_top, 1)) {
fprintf(stderr, "stack underflow\n");
break;
}
struct term *var = termstack_get(term_top, 0);
if(var->type != TYPE_VAR) {
fprintf(stderr, "alpha requires second arg VAR, got ");
term_print(stderr, var);
fputc('\n', stderr);
break;
}
struct term *expr = termstack_get(term_top, 1);
struct term *renamed = alpha_rename(expr, var->var);
if(renamed) {
termstack_push(&term_top, renamed);
} else {
fprintf(stderr, "alpha rename failed\n");
break;
}
} else if(strcmp(argv[i], "-beta") == 0) {
if(! termstack_get(term_top, 0)) {
fprintf(stderr, "stack underflow\n");
break;
}
struct term *term = termstack_get(term_top, 0);
struct term *reduced = beta_reduce(term);
if(reduced) {
termstack_push(&term_top, reduced);
} else {
fprintf(stderr, "beta reduction failed\n");
break;
}
} else if(strcmp(argv[i], "-eta") == 0) {
if(! termstack_get(term_top, 0)) {
fprintf(stderr, "stack underflow\n");
break;
}
struct term *converted = eta_convert(term_top->t);
if(converted) {
termstack_push(&term_top, converted);
} else {
fprintf(stderr, "eta conversion failed\n");
break;
}
} else if(strcmp(argv[i], "-lambda") == 0) {
if(! termstack_get(term_top, 1)) {
fprintf(stderr, "stack underflow\n");
break;
}
struct term *var = termstack_get(term_top, 0);
struct term *body = termstack_get(term_top, 1);
if(var->type != TYPE_VAR) {
fprintf(stderr, "lambda requires VAR, got ");
term_print(stderr, var);
fputc('\n', stderr);
break;
}
struct term *lambda = make_lambda(var->var, body);
if(lambda) {
termstack_push(&term_top, lambda);
} else {
fprintf(stderr, "create lambda failed\n");
break;
}
} else if(strcmp(argv[i], "-apply") == 0) {
if(! termstack_get(term_top, 1)) {
fprintf(stderr, "stack underflow\n");
break;
}
struct term *arg = termstack_get(term_top, 0);
struct term *fun = termstack_get(term_top, 1);
struct term *appl = make_appl(fun, arg);
if(appl) {
termstack_push(&term_top, appl);
} else {
fprintf(stderr, "create apply failed\n");
break;
}
} else if(strcmp(argv[i], "-alpheq") == 0) {
if(! termstack_get(term_top, 1)) {
fprintf(stderr, "stack underflow\n");
break;
}
struct term *t1_term = termstack_get(term_top, 0);
struct term *t2_term = termstack_get(term_top, 1);
if(alpha_eq(t1_term, t2_term)) {
termstack_push(&term_top, term_duplicate(church_true));
} else {
termstack_push(&term_top, term_duplicate(church_false));
}
} else if(strcmp(argv[i], "-print") == 0) {
for(struct termnode *n = term_top; n; n = n->next) {
term_print(stdout, termtrace_current(n->trace));
fprintf(stdout, "\n");
}
} else if(strcmp(argv[i], "-body") == 0) {
if(! termstack_get(term_top, 0)) {
fprintf(stderr, "stack underflow\n");
break;
}
if(termtrace_current(term_top->trace)->type != TYPE_LAMBDA) {
fprintf(stderr, "not a lambda\n");
break;
}
termtrace_go_body(&term_top->trace);
} else if(strcmp(argv[i], "-fun") == 0) {
if(! termstack_get(term_top, 0)) {
fprintf(stderr, "stack underflow\n");
break;
}
if(termtrace_current(term_top->trace)->type != TYPE_APPL) {
fprintf(stderr, "not an apply\n");
break;
}
termtrace_go_fun(&term_top->trace);
} else if(strcmp(argv[i], "-arg") == 0) {
if(! termstack_get(term_top, 0)) {
fprintf(stderr, "stack underflow\n");
break;
}
if(termtrace_current(term_top->trace)->type != TYPE_APPL) {
fprintf(stderr, "not an apply\n");
break;
}
termtrace_go_arg(&term_top->trace);
} else if(strcmp(argv[i], "-up") == 0) {
if(term_top->trace->prev)
termtrace_go_prev(&term_top->trace);
} else if(strcmp(argv[i], "-top") == 0) {
while(term_top->trace->prev)
termtrace_go_prev(&term_top->trace);
} else if(strcmp(argv[i], "-swap") == 0) {
if(! termstack_get(term_top, 1)) {
fprintf(stderr, "stack underflow\n");
break;
}
struct termnode *next = term_top->next;
term_top->next = next->next;
next->next = term_top;
term_top = next;
} else if(strcmp(argv[i], "-dup") == 0) {
if(! termstack_get(term_top, 0)) {
fprintf(stderr, "stack underflow\n");
break;
}
termstack_push(&term_top,
term_duplicate(termtrace_current(term_top->trace)));
} else if(strcmp(argv[i], "-repl") == 0) {
if(! termstack_get(term_top, 1)) {
fprintf(stderr, "stack underflow\n");
break;
}
struct term *newterm = term_duplicate(termtrace_current(term_top->trace));
destroy_term(termstack_pop(&term_top));
destroy_term(termtrace_replace(term_top->trace, newterm));
} else {
FILE *stream = fmemopen(argv[i], strlen(argv[i]), "r");
if(! stream)
continue;
enum term_parse_res res;
struct term *term = term_parse(stream, &res);
fclose(stream);
if(term == NULL) {
long loc = ftell(stream);
if(! feof(stream))
loc--;
printf("parse error: %s at char %lu\n", term_parse_str(res), loc+1);
printf("%s\n", argv[i]);
for(long i = 0; i < loc; i++)
printf(" ");
printf("^\n");
break;
}
termstack_push(&term_top, term);
}
}
struct term *t;
while(NULL != (t = termstack_get(term_top, 0))) {
destroy_term(termstack_pop(&term_top));
}
destroy_term(church_true);
destroy_term(church_false);
return 0;
}
static pSlipObject let_to_application(pSlip gd, pSlipObject exp)
{
return make_application(gd, make_lambda(gd, let_parameters(gd, exp), let_body(exp)), let_arguments(gd, exp));
}