QEL: Fast Approximated Quantifier Elimination (#6820)

* qe_lite: cleanup and comment

no change to code

* mbp_arrays: refactor out partial equality (peq)

Partial array equality, PEQ, is used as an intermediate
expression during MBP for arrays. We need to factor it out
so that it can be shared between MBP-QEL and existing MBP.

Partial array equality (peq) is used in MBP for arrays.
Factoring this out to be used by multiple MBP implementations.

* rewriter: new rewrite rules

These rules are specializes for terms that are created in QEL.
QEL commit is comming later

* datatype_rw: new rewrite rule for ADTs

The rule handles this special case:

    (cons (head x) (tail x)) --> x

* array_rewriter rules for rewriting PEQs

Special rules to simplify PEQs

* th_rewriter: wire PEQ simplifications

* spacer_iuc: avoid terms with default in IUC

Spacer prfers to not have a term representing default value of an array.
This guides IUC from picking such terms in interpolation

* mbp_term_graph: replace root with repr

* mbp_term_graph: formatting

* mbp_term_graph: class_props, getters, setters

Class properties allow to keep information for an equivalence class.

Getters and setters for terms allow accessing information

* mbp_term_graph: auxiliary methods for qel

QEL commit is comming later in the history

* mbp_term_graph: bug fix

* mbp_term_graph: pick, refine repr, compute cgrnd

* mbp_term_graph: internalize deq

* mbp_term_graph: constructor

* mbp_term_graph: optionally internalize equalities

Reperesent equalities explicitly by nodes in the term_graph

* qel

* formatting

* comments on term_lt

* get terms and other api for mbp_qel

* plugins for mbp_qel

* mbp_qel_util: utilities for mbp_qel

* qe_mbp: QEL-based mbp

* qel: expose QEL API

* spacer: replace qe_lite in qe_project_spacer by qel

This changes the default projection engine that spacer uses.

* cmd_context: debug commands for qel and mbp_qel

New commands are

  mbp-qel -- MBP with term graphs
  qel     -- QEL with term graphs
  qe-lite -- older qelite

* qe_mbp: model-based rewriters for arrays

* qe_mbp: QEL-based projection functions

* qsat: wire in QEL-based mbp

* qsat: debug code

* qsat: maybe a bug fix

Changed the code to follow the paper by adding all predicates above a given
level, not just predicates of immediately preceding level.

* chore: use new api to create solver in qsat

* mbp_term_graph use all_of idiom

* feat: solver for integer multiplication

* array_peq: formatting, no change to code

* mbp_qel_util: block comment + format

* mbt_term_graph: clang-format

* bug fix. Move dt rewrite to qe_mbp

* array_peq: add header

* run clang format on mbp plugins

* clang format on mul solver

* format do-while

* format

* format do-while

* update release notes

---------

Co-authored-by: hgvk94 <hgvk94@gmail.com>
Co-authored-by: Isabel Garcia <igarciac@uwaterloo.ca>

src/smt/params/smt_params_helper.pyg

@@ -132,6 +132,7 @@ def_module_params(module_name='smt',
                           ('core.extend_patterns.max_distance', UINT, UINT_MAX, 'limits the distance of a pattern-extended unsat core'),
                           ('core.extend_nonlocal_patterns', BOOL, False, 'extend unsat cores with literals that have quantifiers with patterns that contain symbols which are not in the quantifier\'s body'),
                           ('lemma_gc_strategy', UINT, 0, 'lemma garbage collection strategy: 0 - fixed, 1 - geometric, 2 - at restart, 3 - none'),
-                          ('dt_lazy_splits', UINT, 1, 'How lazy datatype splits are performed: 0- eager, 1- lazy for infinite types, 2- lazy')
+                          ('dt_lazy_splits', UINT, 1, 'How lazy datatype splits are performed: 0- eager, 1- lazy for infinite types, 2- lazy'),
+                          ('qsat_use_qel', BOOL, True, 'Use QEL for lite quantifier elimination and model-based projection in QSAT')
                           ))