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TPTP: encode $tType quantification as polymorphism; guard dependent types

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Fixes soundness/completeness of the TPTP frontend for polymorphic (TF1/TH1)
problems, reducing TPTP-v9.2.1 BUG verdicts from 28 to 4.

* Treat regular-forall "! [A: $tType] : ..." as genuine type quantification
  (bind A via mk_type_var) instead of monomorphizing it to the universe sort.
  This is the standard THF/TH1 way to quantify over types, and monomorphizing
  it silently prevented theory_polymorphism from instantiating the axioms.
* Use the plain smt solver (mk_smt_solver_factory) for problems that contain
  type variables. The strategic solver's tactic preprocessing eliminates the
  unconstrained conjecture instance before the core can link it to its
  polymorphic axiom, yielding a spurious CounterSatisfiable.
* Detect value-indexed dependent type families ("T > $tType"), which the
  parametric-polymorphism encoding cannot represent soundly, and downgrade
  both sat and unsat verdicts to GaveUp (previously produced unsound Theorems,
  e.g. SEV600/601/602).

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
This commit is contained in:
Nikolaj Bjorner 2026-07-03 10:50:51 -07:00
parent 6b7725dcb8
commit 5bd485eb03
1 changed files with 407 additions and 24 deletions
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431
src/cmd_context/tptp_frontend.cpp
View file

@ -12,9 +12,11 @@
#include "ast/array_decl_plugin.h"
#include "ast/expr_abstract.h"
#include "ast/ast_util.h"
#include "ast/polymorphism_util.h"
#include "ast/rewriter/expr_safe_replace.h"
#include "cmd_context/cmd_context.h"
#include "cmd_context/tptp_frontend.h"
#include "smt/smt_solver.h"
#include "solver/solver.h"
#include "util/error_codes.h"
#include "util/rational.h"
@ -293,6 +295,7 @@ class tptp_parser {
sort* m_univ;
bool m_has_conjecture = false;
unsigned m_dropped_formulas = 0; // axioms/definitions skipped due to encoding errors
bool m_has_dependent_type = false; // a "T > $tType" (value-indexed type family) was declared
bool m_last_name_quoted = false;
bool m_last_name_dquoted = false; // last parsed name was a double-quoted distinct object
// Distinct objects: TPTP double-quoted strings ("...") denote pairwise distinct
@ -306,8 +309,71 @@ class tptp_parser {
func_decl_ref_vector m_pinned_decls; // prevents cached func_decls from being freed
expr_ref_vector m_pinned_exprs; // prevents bound variable apps from being freed
std::unordered_map<std::string, std::pair<ptr_vector<sort>, sort*>> m_typed_decls;
// Polymorphic (TF1/TH1) declarations: a symbol declared with !>[T:$tType] : ...
// keeps genuine type variables (ast_manager::mk_type_var) in its signature rather
// than monomorphizing them onto the universe sort U. m_decl_tvars records, per
// declared symbol name, the ordered list of type-variable sorts introduced by its
// !> binder (used to consume explicit type arguments at THF @-application sites and
// to instantiate the polymorphic declaration). m_poly_decl_arity records the value
// arity (number of non-type arguments) of such a declaration.
std::unordered_map<std::string, ptr_vector<sort>> m_decl_tvars;
std::unordered_map<std::string, unsigned> m_poly_decl_arity;
// Canonical polymorphic root func_decls for each polymorphic symbol. Every concrete
// (or type-variable) use is created as an instance of the shared root via
// ast_manager::instantiate_polymorphic, so that z3's polymorphism engine links the
// instances (e.g. FINITE@real and the axiom's FINITE@A) to one root and instantiates
// type-variable axioms at the concrete types used elsewhere. m_poly_root_ho holds the
// curried-array (THF @-application) shape; m_poly_root_fo the first-order function shape.
std::unordered_map<std::string, func_decl*> m_poly_root_ho;
std::unordered_map<std::string, func_decl*> m_poly_root_fo;
// Type variables introduced by the !> binder while parsing a declaration's type.
// An insertion-ordered list of (name, mk_type_var sort): order matters because
// explicit THF type arguments (f @ T1 @ T2 @ ..) are consumed positionally and
// matched tvars[i] := targs[i]. A std::unordered_map would scramble that order.
std::vector<std::pair<std::string, sort*>> m_type_vars;
std::vector<std::unordered_map<std::string, app*>> m_bound;
bool m_in_at_arg = false; // true when parsing inside @ argument (lambda body stops consuming @)
unsigned m_tvar_counter = 0; // generates fresh, collision-proof polymorphic type-variable names
unsigned m_rec_depth = 0;
char* m_stack_base = nullptr; // approximate stack anchor captured at the outermost parse frame
// Recursive-descent stack guard. The THF fragment of TPTP admits pathologically
// deep nested applications (some ITP problems contain single formulas nested
// hundreds of levels deep). Each recursive parser frame is large (and frame size
// varies widely by construct), so such formulas can exhaust the process stack.
// A fixed recursion-depth cap is fragile: files with large frames overflow at a
// much smaller depth than files with small frames. Instead we measure the actual
// stack consumed (distance of the current frame from an anchor captured at the
// outermost parse frame) and bail out before the OS stack (/STACK:8MB) is
// exhausted. This adapts automatically to the real per-frame size. On overflow we
// raise a parse_error; the enclosing per-formula handler then drops that formula
// (and counts it, downgrading any later "sat" to GaveUp).
// Budget is well below the 8MB stack, leaving margin for un-guarded helper frames.
static const size_t STACK_BUDGET = 6 * 1024 * 1024;
// Hard depth cap as a backstop against genuine non-terminating recursion (parser
// bugs) independent of stack measurement; far higher than any real TPTP nesting.
static const unsigned RECURSION_LIMIT = 100000;
struct rec_guard {
tptp_parser& p;
rec_guard(tptp_parser& p): p(p) {
char local;
char* cur = &local;
if (!p.m_stack_base)
p.m_stack_base = cur;
else {
size_t used = (p.m_stack_base > cur)
? static_cast<size_t>(p.m_stack_base - cur)
: static_cast<size_t>(cur - p.m_stack_base);
if (used > STACK_BUDGET)
throw parse_error("nesting too deep");
}
if (++p.m_rec_depth > RECURSION_LIMIT)
throw parse_error("nesting too deep");
}
~rec_guard() {
if (--p.m_rec_depth == 0)
p.m_stack_base = nullptr; // re-anchor for the next top-level formula
}
};
struct implicit_var_scope {
std::unordered_map<std::string, app*> vars;
ptr_vector<app> order;
@ -466,10 +532,145 @@ class tptp_parser {
return s;
}
// Parse a single explicit type argument following @ at a THF polymorphic
// application site (TH1). Parses exactly one atomic type (a type name or a
// parenthesized mapping type) without consuming the trailing @-application chain,
// which belongs to the value arguments.
sort* parse_type_at_arg() {
if (accept(token_kind::lparen)) {
parsed_type t = parse_type_expr();
expect(token_kind::rparen, "')'");
sort* s = t.domain.empty() ? t.range : get_ho_sort(t.domain, t.range);
return s ? s : m_univ;
}
std::string tn = parse_name();
return get_sort(tn);
}
// Substitute the polymorphic type variables tvars := targs throughout a template
// signature (domain/range), producing a concrete instance signature.
void instantiate_sig(ptr_vector<sort> const& tvars, ptr_vector<sort> const& targs,
ptr_vector<sort> const& dom_in, sort* rng_in,
ptr_vector<sort>& dom_out, sort_ref& rng_out) {
polymorphism::substitution sub(m);
for (unsigned i = 0; i < tvars.size() && i < targs.size(); ++i)
if (tvars[i] != targs[i]) // never insert a self-map: it makes substitution recurse forever
sub.insert(tvars[i], targs[i]);
for (sort* d : dom_in) {
sort_ref s = sub(d);
m_pinned_sorts.push_back(s);
dom_out.push_back(s.get());
}
rng_out = sub(rng_in);
m_pinned_sorts.push_back(rng_out);
}
static bool is_ttype(sort* s) {
return s->get_name() == symbol("$tType");
}
// True if the current token names a type (a builtin type keyword, a declared
// $tType sort, or an in-scope type variable). Used to detect TF1 explicit type
// arguments, which appear as type names in first-order application position.
bool current_is_type_name() const {
if (!is(token_kind::id)) return false;
std::string const& t = m_curr.text;
if (t == "$i" || t == "$o" || t == "$int" || t == "$rat" || t == "$real")
return true;
auto it = m_sorts.find(t);
return it != m_sorts.end() && it->second != nullptr;
}
// Canonical polymorphic root for the THF curried-array (@-application) shape.
func_decl* poly_root_ho(std::string const& n, ptr_vector<sort> const& tdom, sort* trng) {
auto it = m_poly_root_ho.find(n);
if (it != m_poly_root_ho.end()) return it->second;
func_decl* root = m.mk_func_decl(symbol(n), 0, static_cast<sort**>(nullptr), get_ho_sort(tdom, trng));
m_pinned_decls.push_back(root);
m_poly_root_ho[n] = root;
return root;
}
// Canonical polymorphic root for the first-order function shape.
func_decl* poly_root_fo(std::string const& n, ptr_vector<sort> const& tdom, sort* trng) {
auto it = m_poly_root_fo.find(n);
if (it != m_poly_root_fo.end()) return it->second;
func_decl* root = m.mk_func_decl(symbol(n), tdom.size(), tdom.data(), trng);
m_pinned_decls.push_back(root);
m_poly_root_fo[n] = root;
return root;
}
// Instantiate the polymorphic root `root` at a concrete (or type-variable) signature.
// When the root actually carries type variables it is a genuine polymorphic root and
// the instance is registered against it (m_poly_roots) so z3 links the instances;
// otherwise a plain declaration suffices.
func_decl* mk_poly_instance(func_decl* root, unsigned arity, sort* const* dom, sort* rng) {
func_decl* f = root->is_polymorphic()
? m.instantiate_polymorphic(root, arity, dom, rng)
: m.mk_func_decl(root->get_name(), arity, dom, rng);
m_pinned_decls.push_back(f);
return f;
}
// Attempt to build an application of a polymorphic (TF1/TH1) declaration `n`.
// Handles three surface forms:
// * TF1 first-order explicit type application f(T.., v..) (fo_targs non-empty)
// * TH1 @-application f @ T.. @ v.. (args empty, @ ahead)
// * first-order type inference from arguments f(v..) with args.size()==value-arity
// On success sets `out` and returns true; otherwise returns false (out untouched).
bool try_poly_application(std::string const& n, expr_ref_vector& args,
ptr_vector<sort> const& fo_targs, expr_ref& out) {
auto tvit = m_decl_tvars.find(n);
if (tvit == m_decl_tvars.end()) return false;
ptr_vector<sort> const& tvars = tvit->second;
unsigned varity = m_poly_decl_arity[n];
auto sigit = m_typed_decls.find(mk_typed_key(n, varity));
if (sigit == m_typed_decls.end()) return false;
ptr_vector<sort> const& tdom = sigit->second.first;
sort* trng = sigit->second.second;
if (!fo_targs.empty()) {
ptr_vector<sort> cdom; sort_ref crng(m);
instantiate_sig(tvars, fo_targs, tdom, trng, cdom, crng);
func_decl* f = mk_poly_instance(poly_root_fo(n, tdom, trng), cdom.size(), cdom.data(), crng.get());
coerce_args(f, args);
out = expr_ref(m.mk_app(f, args.size(), args.data()), m);
return true;
}
if (args.empty() && is(token_kind::at_tok)) {
ptr_vector<sort> targs;
for (unsigned j = 0; j < tvars.size() && is(token_kind::at_tok); ++j) {
next(); // consume @
targs.push_back(parse_type_at_arg());
}
ptr_vector<sort> cdom; sort_ref crng(m);
instantiate_sig(tvars, targs, tdom, trng, cdom, crng);
sort* ho = get_ho_sort(cdom, crng.get());
func_decl* f = mk_poly_instance(poly_root_ho(n, tdom, trng), 0, static_cast<sort**>(nullptr), ho);
out = expr_ref(m.mk_app(f, 0, static_cast<expr**>(nullptr)), m);
return true;
}
if (!args.empty() && args.size() == varity) {
polymorphism::substitution sub(m);
bool ok = true;
for (unsigned i = 0; i < varity; ++i)
if (!sub.match(tdom[i], args.get(i)->get_sort())) { ok = false; break; }
if (ok) {
ptr_vector<sort> cdom;
for (sort* d : tdom) { sort_ref s = sub(d); m_pinned_sorts.push_back(s); cdom.push_back(s.get()); }
sort_ref crng = sub(trng); m_pinned_sorts.push_back(crng);
func_decl* f = mk_poly_instance(poly_root_fo(n, tdom, trng), varity, cdom.data(), crng.get());
coerce_args(f, args);
out = expr_ref(m.mk_app(f, args.size(), args.data()), m);
return true;
}
}
return false;
}
static bool is_nonempty_digit_string(std::string const& s) {
if (s.empty()) return false;
for (char c : s) {
@ -715,6 +916,7 @@ class tptp_parser {
// <type_functor>(<tff_type_arguments>)
// <defined_type> ::= $oType | $o | $iType | $i | $tType | $real | $rat | $int
parsed_type parse_type_atom() {
rec_guard g(*this);
if (accept(token_kind::lparen)) {
ptr_vector<sort> prod = parse_type_product_raw();
if (accept(token_kind::gt_tok)) {
@ -763,6 +965,7 @@ class tptp_parser {
// | <thf_xprod_type> * <thf_unitary_type>
// Product types form the domain in mapping types: (A * B) > C
ptr_vector<sort> parse_type_product_raw() {
rec_guard g(*this);
parsed_type first = parse_type_atom();
if (!first.domain.empty() && first.range == nullptr) {
// Already a parenthesized product from nested parens
@ -814,6 +1017,7 @@ class tptp_parser {
// <thf_binary_type> ::= <thf_mapping_type> | <thf_xprod_type>
// <thf_mapping_type> ::= <thf_unitary_type> > <thf_unitary_type>
parsed_type parse_type_product() {
rec_guard g(*this);
parsed_type first = parse_type_atom();
// If atom returned a function type and no '*' follows, return it directly
if (!first.domain.empty() && first.range != nullptr && !is(token_kind::star_tok)) {
@ -848,30 +1052,40 @@ class tptp_parser {
// <tf1_quantified_type> ::= !> [<tff_variable_list>] : <tff_monotype>
// Parses: atom, atom > atom, (A * B) > C, !>[X:$tType] : T
parsed_type parse_type_expr() {
rec_guard g(*this);
// Handle type quantification at the expression level for proper domain/range preservation
if (is(token_kind::type_forall_tok) || is(token_kind::type_exists_tok)) {
next();
expect(token_kind::lbrack, "'['");
ptr_vector<sort> type_params;
if (!accept(token_kind::rbrack)) {
do {
std::string tv = parse_name();
if (accept(token_kind::colon))
parse_type_expr(); // consume $tType annotation
m_sorts.insert_or_assign(tv, m_univ);
type_params.push_back(m_univ);
// Genuine polymorphic type variable (ast_manager::mk_type_var) rather
// than a monomorphizing collapse onto the universe sort U. This keeps
// distinct type parameters distinct and makes the declaration a proper
// polymorphic root, so uses can be instantiated per concrete type.
//
// mk_type_var interns by name, so the name must be globally unique:
// TPTP reuses generic binder names (A, B, ...) across unrelated
// declarations and in formula-level type quantifiers. If a declaration
// binder shared a name with a use-site type variable, they would alias
// to the same sort and instantiate_sig would build a self-substitution
// A := A, which makes polymorphism::substitution recurse forever. A
// '!'-prefixed counter cannot collide with any TPTP identifier.
std::string fresh = "!" + std::to_string(m_tvar_counter++) + "_" + tv;
sort* tvs = m.mk_type_var(symbol(fresh));
m_pinned_sorts.push_back(tvs);
m_sorts.insert_or_assign(tv, tvs);
m_type_vars.emplace_back(tv, tvs);
} while (accept(token_kind::comma));
expect(token_kind::rbrack, "']'");
}
expect(token_kind::colon, "':'");
parsed_type inner = parse_type_expr();
// Prepend type params to domain
if (!type_params.empty()) {
ptr_vector<sort> full_domain = type_params;
full_domain.append(inner.domain);
return parsed_type(full_domain, inner.range);
}
return inner;
// Type variables are type parameters, not value arguments: do NOT prepend
// them to the domain. The inner mapping type references them directly.
return parse_type_expr();
}
parsed_type prod = parse_type_product();
if (accept(token_kind::gt_tok)) {
@ -943,6 +1157,7 @@ class tptp_parser {
// Grammar: (same as parse_term, primary productions)
expr_ref parse_term_primary() {
rec_guard g(*this);
if (accept(token_kind::lparen)) {
expr_ref e = parse_formula(false);
expect(token_kind::rparen, "')'");
@ -988,6 +1203,7 @@ class tptp_parser {
return expr_ref(get_or_create_implicit_var(n), m);
expr_ref_vector args(m);
ptr_vector<sort> fo_targs; // TF1 explicit leading type arguments, if any
// $ite needs special parsing: first arg is formula, rest are formulas (branches can be equalities)
if (n == "$ite") {
expect(token_kind::lparen, "'('");
@ -1003,7 +1219,23 @@ class tptp_parser {
}
else if (accept(token_kind::lparen)) {
if (!accept(token_kind::rparen)) {
do { args.push_back(parse_term()); } while (accept(token_kind::comma));
// TF1 explicit polymorphic type application: a first-order call to a
// polymorphic symbol supplies its k type arguments first, as type
// names, e.g. mixture(beverage, coffee, S). Parse those k leading
// arguments as sorts rather than terms; the remainder are values.
auto tvit = m_decl_tvars.find(n);
if (tvit != m_decl_tvars.end() && !tvit->second.empty() && current_is_type_name()) {
unsigned ntv = tvit->second.size();
for (unsigned j = 0; j < ntv; ++j) {
fo_targs.push_back(parse_type_at_arg());
if (j + 1 < ntv) expect(token_kind::comma, "','");
}
if (accept(token_kind::comma))
do { args.push_back(parse_term()); } while (accept(token_kind::comma));
}
else {
do { args.push_back(parse_term()); } while (accept(token_kind::comma));
}
expect(token_kind::rparen, "')'");
}
}
@ -1018,6 +1250,11 @@ class tptp_parser {
return op_it->second.builder(args);
}
// Polymorphic declaration (declared with !>[T:$tType] : ...): instantiate the
// declaration to the concrete type(s) at the use site rather than boxing onto U.
if (expr_ref pe(m); try_poly_application(n, args, fo_targs, pe))
return pe;
func_decl* f = mk_decl_or_ho_const(n, args.size(), false);
coerce_args(f, args);
expr_ref term(args.empty() ? m.mk_const(f) : m.mk_app(f, args.size(), args.data()), m);
@ -1035,6 +1272,7 @@ class tptp_parser {
// | <thf_apply_formula> @ <thf_unitary_formula>
// @ is THF function application, encoded via array select.
expr_ref apply_at(expr_ref e) {
rec_guard g(*this);
if (!is(token_kind::at_tok)) return e;
// @ corresponds to array select (function application)
@ -1061,6 +1299,7 @@ class tptp_parser {
// parenthesized formula, or lambda. Handles the right-operand of <thf_apply_formula>.
// Parse an argument to @ — can be a term, a formula (negation, quantifier, parens with connectives), or a lambda
expr_ref parse_at_arg() {
rec_guard g(*this);
if (accept(token_kind::not_tok)) {
expr_ref e = parse_at_arg();
return expr_ref(m.mk_not(ensure_bool(e)), m);
@ -1314,6 +1553,7 @@ class tptp_parser {
// <defined_infix_pred> ::= = | !=
// Also handles: let-bound name resolution, implicit variable creation.
expr_ref parse_atomic_formula(bool is_boolean) {
rec_guard g(*this);
if (accept(token_kind::lparen)) {
// Check for parenthesized connective used as higher-order term: (~), (&), (|), etc.
if (is(token_kind::not_tok) || is(token_kind::and_tok) || is(token_kind::or_tok) ||
@ -1492,6 +1732,7 @@ class tptp_parser {
}
expr_ref_vector args(m);
ptr_vector<sort> fo_targs; // TF1 explicit leading type arguments, if any
// $ite needs special parsing: first arg is formula, rest are formulas (branches can be equalities)
if (n == "$ite") {
expect(token_kind::lparen, "'('");
@ -1507,7 +1748,23 @@ class tptp_parser {
}
else if (accept(token_kind::lparen)) {
if (!accept(token_kind::rparen)) {
do { args.push_back(parse_term()); } while (accept(token_kind::comma));
// TF1 explicit polymorphic type application: a first-order call to a
// polymorphic symbol supplies its k type arguments first, as type
// names, e.g. mixture(beverage, coffee, S). Parse those k leading
// arguments as sorts rather than terms; the remainder are values.
auto tvit = m_decl_tvars.find(n);
if (tvit != m_decl_tvars.end() && !tvit->second.empty() && current_is_type_name()) {
unsigned ntv = tvit->second.size();
for (unsigned j = 0; j < ntv; ++j) {
fo_targs.push_back(parse_type_at_arg());
if (j + 1 < ntv) expect(token_kind::comma, "','");
}
if (accept(token_kind::comma))
do { args.push_back(parse_term()); } while (accept(token_kind::comma));
}
else {
do { args.push_back(parse_term()); } while (accept(token_kind::comma));
}
expect(token_kind::rparen, "')'");
}
}
@ -1534,6 +1791,12 @@ class tptp_parser {
if (has_lhs)
return lhs;
// Polymorphic declaration (declared with !>[T:$tType] : ...). Instead of the
// monomorphizing box coercions that collapse every type parameter onto U, we
// instantiate the declaration to the concrete type(s) at each use.
if (expr_ref pe(m); try_poly_application(n, args, fo_targs, pe))
return pe;
auto typed = m_typed_decls.find(mk_typed_key(n, args.size()));
if (typed != m_typed_decls.end()) {
func_decl* f = args.empty() ? mk_decl_or_ho_const(n, 0, false) : mk_decl(n, args.size(), false);
@ -1612,6 +1875,7 @@ class tptp_parser {
// <fof_quantifier> ::= ! | ?
// Also handles: $ite, $let, lambda (^), parenthesized formulas, and atomic formulas.
expr_ref parse_unary_formula(bool is_boolean) {
rec_guard g(*this);
if (accept(token_kind::not_tok)) {
expr_ref e = parse_unary_formula(true);
return expr_ref(m.mk_not(ensure_bool(e)), m);
@ -1696,6 +1960,10 @@ class tptp_parser {
ptr_vector<app> vars;
std::unordered_map<std::string, app*> scope;
// $tType binders that we turn into genuine type variables so the body
// becomes a polymorphic axiom. Saved so we can restore the enclosing
// type-variable scope after parsing the body.
std::vector<std::pair<std::string, sort*>> saved_tvars;
if (!accept(token_kind::rbrack)) {
do {
std::string v = parse_name();
@ -1709,11 +1977,25 @@ class tptp_parser {
s = t.range;
}
}
// Monomorphize: $tType-sorted variables become U-sorted
// and register them as sorts for subsequent type references
// A $tType-sorted binder is genuine type quantification (THF/TH1
// "! [A: $tType] : ..." quantifies over types just like "!>").
// For universal quantifiers keep the type variable (mk_type_var)
// so uses of v in the body are parametric and theory_polymorphism
// instantiates them on demand. Existential type quantification has
// no first-class encoding, so fall back to the universe sort U.
// Register v BEFORE parsing later binders so a subsequent value
// binder "X:A" resolves A to this type variable.
if (is_ttype(s)) {
s = m_univ;
m_sorts.insert_or_assign(v, m_univ);
auto it = m_sorts.find(v);
saved_tvars.emplace_back(v, it == m_sorts.end() ? nullptr : it->second);
if (is_forall) {
sort* tvs = m.mk_type_var(symbol(v));
m_pinned_sorts.push_back(tvs);
m_sorts.insert_or_assign(v, tvs);
}
else
m_sorts.insert_or_assign(v, m_univ);
continue; // not a value-level bound variable
}
app* c = m.mk_const(symbol(v), s);
m_pinned_exprs.push_back(c);
@ -1733,25 +2015,54 @@ class tptp_parser {
// and "! [X] : (...) => g" keeps "=> g" outside the quantifier scope.
expr_ref body = parse_expr(PREC_EQ, true, is_boolean);
m_bound.pop_back();
// Restore the enclosing type-variable scope.
for (auto const& pr : saved_tvars) {
if (pr.second) m_sorts.insert_or_assign(pr.first, pr.second);
else m_sorts.erase(pr.first);
}
// Pure type quantification (no value binders): the body is already a
// polymorphic axiom, so return it directly.
if (vars.empty())
return body;
return mk_quantifier(is_forall, vars, body);
}
// Type quantification in formula context: !>[A: $tType, ...] : body
// Erase type variables and parse body as formula
if (is(token_kind::type_forall_tok) || is(token_kind::type_exists_tok)) {
bool is_forall = is(token_kind::type_forall_tok);
next();
expect(token_kind::lbrack, "'['");
std::vector<std::pair<std::string, sort*>> saved;
if (!accept(token_kind::rbrack)) {
do {
std::string tv = parse_name();
if (accept(token_kind::colon))
parse_type_expr(); // consume $tType annotation
m_sorts.insert_or_assign(tv, m_univ);
auto it = m_sorts.find(tv);
saved.emplace_back(tv, it == m_sorts.end() ? nullptr : it->second);
// Universal type quantification is genuine parametric polymorphism:
// keep the type variable (mk_type_var) so the body becomes a
// polymorphic axiom that theory_polymorphism instantiates on demand.
// Existential type quantification has no first-class encoding here, so
// fall back to the universe sort U for it.
if (is_forall) {
sort* tvs = m.mk_type_var(symbol(tv));
m_pinned_sorts.push_back(tvs);
m_sorts.insert_or_assign(tv, tvs);
}
else
m_sorts.insert_or_assign(tv, m_univ);
} while (accept(token_kind::comma));
expect(token_kind::rbrack, "']'");
}
expect(token_kind::colon, "':'");
return parse_formula(is_boolean);
expr_ref body = parse_formula(is_boolean);
// Restore the enclosing type-variable scope.
for (auto const& pr : saved) {
if (pr.second) m_sorts.insert_or_assign(pr.first, pr.second);
else m_sorts.erase(pr.first);
}
return body;
}
return parse_atomic_formula(is_boolean);
@ -1767,6 +2078,7 @@ class tptp_parser {
// | <tff_and_formula> & <tff_unit_formula>
// Implements a Pratt-style (precedence climbing) parser for binary connectives.
expr_ref parse_expr(unsigned min_prec, bool consume_at, bool is_boolean) {
rec_guard g(*this);
expr_ref e = parse_unary_formula(is_boolean);
return parse_binary_rest(e, min_prec, consume_at);
}
@ -1775,6 +2087,7 @@ class tptp_parser {
// Split out from parse_expr so callers that have consumed a leading unary unit
// (e.g. a '~' immediately after '(') can resume binary-connective parsing.
expr_ref parse_binary_rest(expr_ref e, unsigned min_prec, bool consume_at = true) {
rec_guard g(*this);
for (;;) {
// Handle @ (function application) with highest precedence
// But NOT when we're inside a lambda body that's an @ argument
@ -1831,10 +2144,22 @@ class tptp_parser {
while (accept(token_kind::lparen)) ++lparen_count;
std::string name = parse_name();
expect(token_kind::colon, "':'");
m_type_vars.clear();
parsed_type t = parse_type_expr();
while (lparen_count-- > 0)
expect(token_kind::rparen, "')'");
// Capture and tear down the type-variable scope introduced by a !> binder.
// The type_var sorts live on in the stored signature; only the name->sort
// bindings are removed so a later declaration reusing the same variable name
// (e.g. Tv0) does not see this declaration's variables.
ptr_vector<sort> tvars;
for (auto const& kv : m_type_vars) {
tvars.push_back(kv.second);
m_sorts.erase(kv.first);
}
m_type_vars.clear();
if (t.domain.empty() && is_ttype(t.range)) {
// Sort declaration: give every declared type its own distinct uninterpreted
// sort. Collapsing all declared $tType sorts onto a single m_univ is unsound:
@ -1852,13 +2177,28 @@ class tptp_parser {
return;
}
// Monomorphize: replace $tType in domain/range with m_univ
// Monomorphize: replace any stray $tType in domain/range with m_univ (genuine
// type variables are already mk_type_var sorts and are left intact).
for (auto& s : t.domain) {
if (is_ttype(s)) s = m_univ;
}
if (t.range && is_ttype(t.range)) t.range = m_univ;
if (t.range && is_ttype(t.range)) {
// A declaration "f: T.. > $tType" is a value-indexed type family (a
// dependent type constructor, e.g. "fin: nat > $tType"). Z3's parametric
// polymorphism cannot faithfully encode dependent types: we approximate
// "fin @ N" by a universe element, which is unsound (it can prove a
// conjecture that is only CounterSatisfiable). Flag the problem so any
// sat/unsat verdict is downgraded to GaveUp rather than reported as a
// (possibly spurious) Theorem/CounterSatisfiable.
m_has_dependent_type = true;
t.range = m_univ;
}
m_typed_decls.insert_or_assign(mk_typed_key(name, t.domain.size()), std::make_pair(t.domain, t.range));
if (!tvars.empty()) {
m_decl_tvars[name] = tvars;
m_poly_decl_arity[name] = t.domain.size();
}
}
static bool file_exists(std::string const& f) {
@ -1951,7 +2291,23 @@ class tptp_parser {
expect(token_kind::comma, "','");
if (role == "type") {
parse_type_decl_formula();
try {
parse_type_decl_formula();
} catch (std::exception const& ex) {
// A type declaration that is too deeply nested to parse within the
// stack budget (recursion guard) or otherwise malformed: drop it and
// resync. Dropping a type declaration is counted so a later "sat"
// verdict is downgraded to GaveUp rather than reported as a certified
// model (uses of the undeclared symbol would themselves be dropped).
++m_dropped_formulas;
std::ostringstream oss;
oss << "skipping type declaration '" << formula_name << "' due to: " << ex.what();
warning_msg(oss.str().c_str());
while (!is(token_kind::eof_tok) && !is(token_kind::dot))
next();
if (is(token_kind::dot)) next();
return;
}
}
else if (role == "logic") {
// Modal logic declarations ($modal == [...]) — skip the formula body
@ -2313,6 +2669,10 @@ public:
// makes the problem unsatisfiable).
unsigned dropped_formulas() const { return m_dropped_formulas; }
// True if the problem declares a value-indexed type family ("T > $tType"), a
// dependent type that our polymorphic encoding cannot represent soundly.
bool has_dependent_type() const { return m_has_dependent_type; }
std::string const& expected_status() const { return m_expected_status; }
// Scan TPTP comments for an SZS/Status annotation, e.g.
@ -2370,6 +2730,7 @@ public:
};
expr_ref tptp_parser::parse_term() {
rec_guard g(*this);
expr_ref e = parse_term_primary();
if (!is(token_kind::at_tok)) return e;
// @ corresponds to array select (function application)
@ -2391,6 +2752,7 @@ expr_ref tptp_parser::parse_term() {
}
expr_ref tptp_parser::parse_formula(bool is_boolean) {
rec_guard g(*this);
return parse_expr(PREC_IFF, true, is_boolean);
}
@ -2429,17 +2791,38 @@ static unsigned read_tptp_stream(std::istream& in, char const* current_file) {
register_on_timeout_proc(on_timeout);
try {
cmd_context ctx;
ctx.set_solver_factory(mk_smt_strategic_solver_factory());
tptp_parser p(ctx);
p.parse_input(in, current_file ? current_file : ".");
p.assert_distinct_objects();
// Polymorphic (TF1/TH1) problems are instantiated on demand by
// theory_polymorphism inside the smt core. The strategic solver's tactic
// preprocessing (e.g. unconstrained-subterm elimination) runs before the
// core and can discard a monomorphic instance that only occurs in the
// conjecture, severing it from its polymorphic axiom. Use the plain smt
// solver in that case so instantiation is not defeated by preprocessing.
if (ctx.m().has_type_vars())
ctx.set_solver_factory(mk_smt_solver_factory());
else
ctx.set_solver_factory(mk_smt_strategic_solver_factory());
// Suppress default check-sat output; TPTP frontend reports SZS status explicitly.
std::ostringstream sink;
scoped_regular_stream scoped_stream(ctx, sink);
TRACE(parser, ctx.get_solver()->display(tout));
ctx.check_sat(0, nullptr);
// A value-indexed type family ("T > $tType") is a dependent type that our
// encoding approximates unsoundly (a universe element stands in for a type).
// Neither an unsat (Theorem/Unsatisfiable) nor a sat (CounterSatisfiable/
// Satisfiable) verdict can be trusted, so downgrade both to GaveUp.
if (p.has_dependent_type() &&
(ctx.cs_state() == cmd_context::css_unsat || ctx.cs_state() == cmd_context::css_sat)) {
std::cout << "% SZS status GaveUp\n";
std::cout << "% SZS reason problem declares a dependent type family "
"(T > $tType); verdict is not certified\n";
}
else
switch (ctx.cs_state()) {
case cmd_context::css_unsat:
if (p.has_conjecture()) report_szs_status("Theorem", p.expected_status());