sidekick/TODO.md

# Goals

## TODO

- functor for mapping equiv classes to values of some monoid, code to be
  used in 99% of the theories
  * [ ] also allow to register to "joins" between distinct classes
    (useful for injectivity or array reduction or selector reduction)
    → in a way this must become a (backtracking) query API for making theories
      easy to write
  * [ ] use it in th-data
  * [ ] use it in th-array
  * [ ] use it in th-define-subsort

- write theory of datatypes (without acyclicity) with local case splits + injectivity + selectors
- datatype acyclicity check

- provide a notion of smtlib theory, with `smtlib.ast --> Term.t option`
  and typing rule (extensible parsing+typing)
  * use if for th-bool
  * use if for th-distinct

- cleanup of CC/optims
  * store lits directly in (boolean) classes

- add terms of input goals pre-emptively to the CC/theories

- use funarith for basic Q arith
  * as a smtlib theory, too

- add `CC.add_rw_step t u` work, where `t-->u`
  (keep `t` in sig table, but flag is so it's inert and will not
   be pushed into `cc.pending` ever, should have almost 0 overhead after that)
  * use it for local simplifications
  * use it for function evaluation (i.e. rewrite rules)

- design evaluation system (guards + `eval:(term -> value) option` in custom TC)
- compilation of rec functions to defined constants
- theory of defined constants relying on congruence closure + evaluation
  of guards of each case

- abstract domain propagation in CC
- domain propagation (intervals) for ℚ arith
- full ℚ theory: shostak + domains + if-sat simplex

## Main goals

- Add a backend to send proofs to dedukti
    * First, pure resolution proofs
    * Then, require theories to output lemma proofs for dedukti (in some format yet to be decided)
- Allow to plug one's code into boolean propagation
    * react upon propagation (possibly by propagating more, or side-effect)
    * more advanced/specific propagation (2-clauses)?
    * implement 'constraints' (see https://www.lri.fr/~conchon/TER/2013/3/minisat.pdf )

## Long term goals

- max-sat/max-smt
- coq proofs ?

## Done

- make CC work on QF_UF
  * [x] public `add` function should push_pending then call main CC loop
    (internal one is called within the loop so no need)
  * [x] internalize terms on the fly (backtrackable) OR: at the beginning, backtrack to 0 to add a new term and then add trail again
  * ~~[ ] basic notion of activity (of subterms) for `ite` (and recfuns, later)?~~
- use `stmlib-utils`
- parser for cstors  (`declare-cstor`, same as `declare-fun`)
- refactor:
 1. have sidekick.env with only the signature that is instance-dependent + notion of theory (as module sig); 
 2. solver takes this env and SAT solver with compatible lits 
 3. move concrete terms, etc. into smtlib lib
 4. update theories
- fix: have normal theories `on_new_term` work properly (callback in the CC?)
- proper statistics
- make the core library entirely functorized
  * current term/cst/lit/… would become an implementation library to
    be used in the binary
- theory for `ite`
- theory for constructors
- do a `th-distinct` package
  * in CC, use payload to store set of distinct tags (if non empty)
  * if `¬distinct(t1…tn)` asserted, make big disjunction of cases (split on demand)
- in CC, store literal associated with term, for bool propagation
- in CC, propagation of boolean terms
- in CC, merge classes eagerly
- when CC merging two classes, if one is a value then pick it as representative
  (i.e. values are always representatives)
- large refactoring of CC
- simplify CC by separating cleanly public/internal API, remove excess batching
- notion of `value` (V_true,V_false,V_custom, + maybe undefined some day)
- checking models (for each clause, at least one true lit also evals to true in model)
  * have a `function` section in the model with `(id*value list) -> value`,
    extracted from congruence closure
- simplify terms a lot, remove solving/semantic terms
- remove `detach_clause`. never detach a clause until it's really dead;
  instead, do (and re-do) `internalize_clause` for its atoms.
- remove push/pop
- merge Solver_types.ml with Internal.ml
- theory of boolean constructs (on the fly Tseitin using local clauses)
  * test `Sat_solver.add_clause` and `new_atom` behavior upon backtracking
    → when we backtrack an atom, its Tseitin encoding should be removed
  * NOTE: clauses should never be added twice
    (or else: what if a clause is added, removed (but not filtered from watched lits) then re-added? duplicate?)
- backtrackable addition of clauses/atoms in Sat solver
- remove tseitin lib
- typing and translation Ast -> Term (from mc2?)
- main executable for SMT solver
- base types (Term, Lit, …)
- theory combination
- basic design of theories