term* normalize_no_unfold(typing_context* Delta, term* t) {
if (t == NULL) return NULL;
switch (t->tag) {
case VAR:
{
return term_dup(t);
}
case APP:
{
term* l = normalize_no_unfold(Delta, t->left);
term* r = normalize_no_unfold(Delta, t->right);
if (l->tag == LAM) {
term* subs = substitute(l->var, r, l->right);
free_term(l);
free_term(r);
return normalize_no_unfold_and_free(Delta, subs);
}
return make_app(l, r);
}
case IMPLICIT:
case HOLE:
case TYPE:
case LAM:
case PI:
return term_dup(t);
default:
sentinel("unexpected tag %d");
}
error:
return NULL;
}
static term* elim_over_intro(typing_context* Delta, term* t) {
check(t && t->args && t->args[t->num_args - 1], "ill formed term");
check(t->tag == ELIM && t->args[t->num_args - 1]->tag == INTRO,
"elim_over_intro must be called on an eliminator applied to a constructor");
term* last = t->args[t->num_args - 1];
datatype* T = elim_to_datatype(t->var, Delta);
int index = datatype_intro_index(last->var, T);
check(index != -1, "bad intro index while evaluating %W", t, print_term);
term *app = term_dup(t->args[index + 1]);
int i;
for (i = 0; i < last->num_args; i++) {
app = make_app(app, term_dup(last->args[i]));
if (constructor_arg_is_inductive(T, last->var, i)) {
term *inductive = term_dup(t);
free_term(inductive->args[inductive->num_args - 1]);
inductive->args[inductive->num_args - 1] = term_dup(last->args[i]);
app = make_app(app, inductive);
}
}
free_term(t);
t = NULL;
return app;
error:
return NULL;
}
term* normalize_fuel(context *Sigma, typing_context* Delta, term* t, int fuel) {
if (t == NULL) return NULL;
check(term_locally_well_formed(t), "%W must be locally well formed", t, print_term);
check(fuel >= 0, "Stack depth exceeded")
switch (t->tag) {
case VAR:
return normalize_fuel_var(Sigma, Delta, t, fuel);
case APP:
return normalize_fuel_app(Sigma, Delta, t, fuel);
case LAM:
return normalize_fuel_lambda(Sigma, Delta, t, fuel);
case PI:
return normalize_fuel_pi(Sigma, Delta, t, fuel);
case ELIM:
return normalize_fuel_elim(Sigma, Delta, t, fuel);
case INTRO:
return normalize_fuel_intro(Sigma, Delta, t, fuel);
case DATATYPE:
return normalize_fuel_datatype(Sigma, Delta, t, fuel);
default:
return term_dup(t);
}
error:
return NULL;
}
term* normalize_fuel_var(context *Sigma, typing_context* Delta, term* t, int fuel) {
term* defn = context_lookup(t->var, Sigma);
if (defn == NULL) {
return term_dup(t);
}
return normalize_fuel(Sigma, Delta, defn, fuel-1);
}
term* normalize_fuel_elim(context *Sigma, typing_context* Delta, term* t, int fuel) {
term* ans = NULL;
term* last = normalize_fuel(Sigma, Delta, t->args[t->num_args - 1], fuel-1);
if (!last) goto error;
if (last->tag == INTRO) {
term* c = term_dup(t);
free_term(c->args[c->num_args - 1]);
c->args[c->num_args - 1] = last;
return normalize_and_free_fuel(Sigma, Delta, elim_over_intro(Delta, c), fuel-1);
} else {
ans = make_elim(variable_dup(t->var), t->num_args, t->num_params, t->num_indices);
int i;
for (i = 0; i < t->num_indices; i++) {
ans->indices[i] = normalize_fuel(Sigma, Delta, t->indices[i], fuel-1);
if (!ans->indices[i]) goto error;
}
for (i = 0; i < t->num_params; i++) {
ans->params[i] = normalize_fuel(Sigma, Delta, t->params[i], fuel-1);
if (!ans->params[i]) goto error;
}
for (i = 0; i < t->num_args - 1; i++) {
ans->args[i] = normalize_fuel(Sigma, Delta, t->args[i], fuel-1);
if (!ans->args[i]) goto error;
}
ans->args[t->num_args-1] = last;
return ans;
}
error:
free_term(last);
free_term(ans);
return NULL;
}
term* whnf(context *Sigma, typing_context* Delta, term* t) {
if (t == NULL) return NULL;
switch (t->tag) {
case VAR:
{
term* defn = context_lookup(t->var, Sigma);
if (defn == NULL) {
return term_dup(t);
}
return whnf(Sigma, Delta, defn);
}
case APP:
{
term* l = whnf(Sigma, Delta, t->left);
if (l->tag == LAM) {
term* subs = substitute(l->var, t->right, l->right);
free_term(l);
return whnf_and_free(Sigma, Delta, subs);
}
return make_app(l, term_dup(t->right));
}
case ELIM:
{
term* last = t->args[t->num_args - 1];
term* nlast = whnf(Sigma, Delta, last);
term* c = term_dup(t);
free_term(c->args[c->num_args - 1]);
c->args[c->num_args - 1] = nlast;
if (nlast->tag == INTRO) {
return whnf_and_free(Sigma, Delta, elim_over_intro(Delta, c));
} else {
return c;
}
}
case HOLE:
case DATATYPE:
case TYPE:
case LAM:
case INTRO:
case PI:
case IMPLICIT:
return term_dup(t);
}
}
static term* elim_over_intro(typing_context* Delta, term* t) {
check(t && t->args && t->args[t->num_args - 1], "ill formed term");
term* last = t->args[t->num_args - 1];
datatype* T = elim_to_datatype(t->var, Delta);
int index = datatype_intro_index(last->var, T);
term *app = term_dup(t->args[index + 1]);
int i;
for (i = 0; i < last->num_args; i++) {
app = make_app(app, term_dup(last->args[i]));
if (constructor_arg_is_inductive(T, last->var, i)) {
term *inductive = term_dup(t);
free_term(inductive->args[inductive->num_args - 1]);
inductive->args[inductive->num_args - 1] = term_dup(last->args[i]);
app = make_app(app, inductive);
}
}
free_term(t);
t = NULL;
return app;
error:
return NULL;
}
term* term_dup(term* t) {
if (t == NULL) return NULL;
term* ans = make_term();
ans->tag = t->tag;
ans->var = variable_dup(t->var);
ans->left = term_dup(t->left);
ans->right = term_dup(t->right);
DUP_VEC(ans->num_args, ans->args,
t->num_args, t->args,
term_dup, struct term*);
DUP_VEC(ans->num_params, ans->params,
t->num_params, t->params,
term_dup, struct term*);
DUP_VEC(ans->num_indices, ans->indices,
t->num_indices, t->indices,
term_dup, struct term*);
return ans;
}
term* normalize_fuel_intro(context *Sigma, typing_context* Delta, term* t, int fuel) {
term* ans = make_intro(variable_dup(t->var), term_dup(t->left), t->num_args, t->num_params);
int i;
for (i = 0; i < t->num_params; i++) {
ans->params[i] = normalize_fuel(Sigma, Delta, t->params[i], fuel-1);
}
for (i = 0; i < t->num_args; i++) {
// FIXME: this leaks on error --jrw
ans->args[i] = normalize_fuel(Sigma, Delta, t->args[i], fuel-1);
if (!ans->args[i]) goto error;
}
return ans;
error:
free_term(ans);
return NULL;
}
/*
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;
}