feat(library/expr_lt): add expression comparison operator that ignores treat level parameters as wildcards

src/library/expr_lt.cpp

@@ -58,4 +58,114 @@ bool is_lt(expr const & a, expr const & b, bool use_hash) {
     }
     lean_unreachable(); // LCOV_EXCL_LINE
 }
+
+bool is_lt_no_level_params(level const & a, level const & b) {
+    if (is_eqp(a, b))              return false;
+    if (kind(a) != kind(b)) {
+        if (kind(a) == level_kind::Param || kind(b) == level_kind::Param)
+            return false;
+        return kind(a) < kind(b);
+    }
+    switch (kind(a)) {
+    case level_kind::Zero:
+        lean_unreachable(); // LCOV_EXCL_LINE
+    case level_kind::Param:
+        return false;
+    case level_kind::Global:
+        return global_id(a) < global_id(b);
+    case level_kind::Meta:
+        return meta_id(a) < meta_id(b);
+    case level_kind::Max:
+        if (is_lt_no_level_params(max_lhs(a), max_lhs(b)))
+            return true;
+        else if (is_lt_no_level_params(max_lhs(b), max_lhs(a)))
+            return false;
+        else
+            return is_lt_no_level_params(max_rhs(a), max_rhs(b));
+    case level_kind::IMax:
+        if (is_lt_no_level_params(imax_lhs(a), imax_lhs(b)))
+            return true;
+        else if (is_lt_no_level_params(imax_lhs(b), imax_lhs(a)))
+            return false;
+        else
+            return is_lt_no_level_params(imax_rhs(a), imax_rhs(b));
+    case level_kind::Succ:
+        return is_lt_no_level_params(succ_of(a), succ_of(b));
+    }
+    lean_unreachable();
+}
+
+bool is_lt_no_level_params(levels const & as, levels const & bs) {
+    if (is_nil(as))
+        return !is_nil(bs);
+    else if (is_nil(bs))
+        return false;
+    else if (is_lt_no_level_params(car(as), car(bs)))
+        return true;
+    else if (is_lt_no_level_params(car(bs), car(as)))
+        return false;
+    else
+        return is_lt_no_level_params(cdr(as), cdr(bs));
+}
+
+bool is_lt_no_level_params(expr const & a, expr const & b) {
+    if (is_eqp(a, b))                    return false;
+    unsigned wa = get_weight(a);
+    unsigned wb = get_weight(b);
+    if (wa < wb)                         return true;
+    if (wa > wb)                         return false;
+    if (a.kind() != b.kind())            return a.kind() < b.kind();
+    switch (a.kind()) {
+    case expr_kind::Var:
+        return var_idx(a) < var_idx(b);
+    case expr_kind::Constant:
+        if (const_name(a) != const_name(b))
+            return const_name(a) < const_name(b);
+        else
+            return is_lt_no_level_params(const_levels(a), const_levels(b));
+    case expr_kind::App:
+        if (is_lt_no_level_params(app_fn(a), app_fn(b)))
+            return true;
+        else if (is_lt_no_level_params(app_fn(b), app_fn(a)))
+            return false;
+        else
+            return is_lt_no_level_params(app_arg(a), app_arg(b));
+    case expr_kind::Lambda: case expr_kind::Pi:
+        if (is_lt_no_level_params(binding_domain(a), binding_domain(b)))
+            return true;
+        else if (is_lt_no_level_params(binding_domain(b), binding_domain(a)))
+            return false;
+        else
+            return is_lt_no_level_params(binding_body(a), binding_body(b));
+    case expr_kind::Sort:
+        return is_lt_no_level_params(sort_level(a), sort_level(b));
+    case expr_kind::Local: case expr_kind::Meta:
+        if (mlocal_name(a) != mlocal_name(b))
+            return mlocal_name(a) < mlocal_name(b);
+        else
+            return is_lt_no_level_params(mlocal_type(a), mlocal_type(b));
+    case expr_kind::Macro:
+        if (macro_def(a) != macro_def(b))
+            return macro_def(a) < macro_def(b);
+        if (macro_num_args(a) != macro_num_args(b))
+            return macro_num_args(a) < macro_num_args(b);
+        for (unsigned i = 0; i < macro_num_args(a); i++) {
+            if (is_lt_no_level_params(macro_arg(a, i), macro_arg(b, i)))
+                return true;
+            else if (is_lt_no_level_params(macro_arg(b, i), macro_arg(a, i)))
+                return false;
+        }
+        return false;
+    }
+    lean_unreachable();
+}
+
+int expr_cmp_no_level_params::operator()(expr const & e1, expr const & e2) const {
+    if (is_lt_no_level_params(e1, e2))
+        return -1;
+    else if (is_lt_no_level_params(e2, e1))
+        return 1;
+    else
+        return 0;
+}
 }

src/library/expr_lt.h

@@ -7,17 +7,19 @@ Author: Leonardo de Moura
 #pragma once
 #include "kernel/expr.h"
 namespace lean {
-/**
-    \brief Total order on expressions.
+/** \brief Total order on expressions.
 
     \remark If \c use_hash is true, then we use the hash_code to
     partially order expressions. Setting use_hash to false is useful
     for testing the code.
 */
 bool is_lt(expr const & a, expr const & b, bool use_hash);
+/** \brief Similar to is_lt, but universe level parameter names are ignored. */
+bool is_lt_no_level_params(expr const & a, expr const & b);
 inline bool operator<(expr const & a, expr const & b)  { return is_lt(a, b, true); }
 inline bool operator>(expr const & a, expr const & b)  { return is_lt(b, a, true); }
 inline bool operator<=(expr const & a, expr const & b) { return !is_lt(b, a, true); }
 inline bool operator>=(expr const & a, expr const & b) { return !is_lt(a, b, true); }
 struct expr_quick_cmp { int operator()(expr const & e1, expr const & e2) const { return is_lt(e1, e2, true) ? -1 : (e1 == e2 ? 0 : 1); } };
+struct expr_cmp_no_level_params { int operator()(expr const & e1, expr const & e2) const; };
 }