add todo file

TODO.md

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+# Goals
+
+## TODO
+
+- SAT:
+  * merge all clause vectors into one
+  * remove all simplifications at level 0
+  * addition of clauses: should be much simpler
+
+- explicit lifecycle for SAT atoms  (dead/assigned/in-heap)
+- simplify addition of clauses:
+  * do not simplify at level 0
+  * steps on addition:
+    1. internalize all atoms (dead -> in-heap)
+    2. unit-propagate/do nothing/add clause
+    3. remove clause on backtracking if not at level 0
+
+- merge Solver_types.ml with Internal.ml
+- make CC work on QF_UF
+  * internalize terms on the fly (backtrackable)
+  * basic notion of activity (of subterms) for `ite` (and recfuns, later)?
+
+- redo_down_to_level_0 should actually redo down to `base_level`
+
+- add `CC.add_rw_step t u` work, where `t-->u`
+  (remove `t` from sig table, should have almost 0 overhead after that)
+  * use it for 
+
+- notion of `value` (V_true,V_false,V_custom, + maybe undefined some day)
+- write theory of datatypes (without acyclicity) with local case splits + `value` + injectivity
+- 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
+
+- datatype acyclicity check
+
+- Shostak theory of eq-ℚ
+
+- 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
+
+- 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