Use substitutions for implementing defined functions (#6437)

This eliminates explicit tracking of defined functions, and instead makes define-fun add to preprocessing substitutions.
In other words, the effect of:

(define-fun f X t)
is to add f -> (lambda X t) to the set of substitutions known by the preprocessor. This is essentially the same as when
(= f (lambda X t)) was an equality solved by non-clausal simplification

The motivation for this change is both uniformity and for performance, as fewer traversals of the input formula.

In this PR:

define-fun are now conceptually higher-order equalities provided to smt::Assertions. These assertions are always added as substitutions instead of being pushed to AssertionPipeline.
Top-level substitutions are moved from PreprocessingContext to Env, since they must be accessed by Assertions. Proofs for this class are enabled dynamically during SmtEngine::finishInit.
The expandDefinitions preprocessing step is replaced by apply-substs. The process assertions module no longer needs access to expand definitions.
The proof manager does not require a special case of using the define-function maps.
Define-function maps are eliminated from SmtEngine.
Further work will reorganize the relationship between the expand definitions module and the rewriter, after which global calls to SmtEngine::expandDefinitions can be cleaned up. There is also further work necessary to better integrate theory expand definitions and top-level substitutions, which will be done on a followup PR.

1 files changed, 4 insertions, 4 deletions

diff --git a/src/smt/preprocessor.h b/src/smt/preprocessor.h
index c590b7164..e0ad2cc14 100644
--- a/src/smt/preprocessor.h
+++ b/src/smt/preprocessor.h
@@ -25,6 +25,7 @@
 #include "theory/booleans/circuit_propagator.h"
 
 namespace cvc5 {
+class Env;
 namespace preprocessing {
 class PreprocessingPassContext;
 }
@@ -46,7 +47,7 @@ class Preprocessor
 {
  public:
   Preprocessor(SmtEngine& smt,
-               context::UserContext* u,
+               Env& env,
                AbstractValues& abs,
                SmtEngineStatistics& stats);
   ~Preprocessor();
@@ -94,17 +95,16 @@ class Preprocessor
       const Node& n,
       std::unordered_map<Node, Node, NodeHashFunction>& cache,
       bool expandOnly = false);
-
   /**
    * Set proof node manager. Enables proofs in this preprocessor.
    */
   void setProofGenerator(PreprocessProofGenerator* pppg);
 
  private:
-  /** A copy of the current context */
-  context::Context* d_context;
   /** Reference to the parent SmtEngine */
   SmtEngine& d_smt;
+  /** Reference to the env */
+  Env& d_env;
   /** Reference to the abstract values utility */
   AbstractValues& d_absValues;
   /**