catala/compiler/dcalc/vc_z3encoding.ml

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(* This file is part of the Catala compiler, a specification language for tax and social benefits
computation rules. Copyright (C) 2022 Inria, contributor: Aymeric Fromherz
<aymeric.fromherz@inria.fr>
Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
in compliance with the License. You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed under the License
is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
or implied. See the License for the specific language governing permissions and limitations under
the License. *)
open Utils
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open Ast
open Z3
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(** [translate_lit] returns the Z3 expression as a literal corresponding to [lit] **)
let translate_lit (ctx : context) (l : lit) : Expr.expr =
match l with
| LBool b ->
if b then Boolean.mk_true ctx else Boolean.mk_false ctx
| LEmptyError -> failwith "[Z3 encoding] LEmptyError literals not supported"
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| LInt n -> Arithmetic.Integer.mk_numeral_i ctx (Runtime.integer_to_int n)
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| LRat _ -> failwith "[Z3 encoding] LRat literals not supported"
| LMoney _ -> failwith "[Z3 encoding] LMoney literals not supported"
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| LUnit -> failwith "[Z3 encoding] LUnit literals not supported"
| LDate _ -> failwith "[Z3 encoding] LDate literals not supported"
| LDuration _ -> failwith "[Z3 encoding] LDuration literals not supported"
(** [translate_op] returns the Z3 expression corresponding to the
application of [op] to the arguments [args] **)
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let rec translate_op (ctx : context) (op : operator) (args : expr Pos.marked list) : Expr.expr =
match op with
| Ternop _top ->
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let _e1, _e2, _e3 = match args with
| [e1; e2; e3] -> e1, e2, e3
(* TODO: Print term for error message *)
| _ -> failwith "[Z3 encoding] Ill-formed ternary operator application"
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in
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failwith "[Z3 encoding] ternary operator application not supported"
| Binop bop ->
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let e1, e2 = match args with
| [e1 ; e2] -> e1, e2
(* TODO: Print term for error message *)
| _ -> failwith "[Z3 encoding] Ill-formed binary operator application"
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in
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(match bop with
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| And -> Boolean.mk_and ctx [translate_expr ctx e1; translate_expr ctx e2]
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| Or -> Boolean.mk_or ctx [translate_expr ctx e1; translate_expr ctx e2]
| Xor -> failwith "[Z3 encoding] application of binary operator Xor not supported"
| Add _ -> failwith "[Z3 encoding] application of binary operator Add not supported"
| Sub _ -> failwith "[Z3 encoding] application of binary operator Sub not supported"
| Mult _ -> failwith "[Z3 encoding] application of binary operator Mult not supported"
| Div _ -> failwith "[Z3 encoding] application of binary operator Div not supported"
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| Lt op_kind ->
(match op_kind with
| KInt -> Arithmetic.mk_lt ctx (translate_expr ctx e1) (translate_expr ctx e2)
| _ -> failwith "[Z3 encoding] application of binary operator Lt for non-integers not supported"
)
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| Lte _ -> failwith "[Z3 encoding] application of binary operator Lte not supported"
| Gt _ -> failwith "[Z3 encoding] application of binary operator Gt not supported"
| Gte _ -> failwith "[Z3 encoding] application of binary operator Gte not supported"
| Eq -> failwith "[Z3 encoding] application of binary operator Eq not supported"
| Neq -> failwith "[Z3 encoding] application of binary operator New not supported"
| Map -> failwith "[Z3 encoding] application of binary operator Map not supported"
| Concat -> failwith "[Z3 encoding] application of binary operator Concat not supported"
| Filter -> failwith "[Z3 encoding] application of binary operator Filter not supported"
)
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| Unop uop ->
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let e1 = match args with
| [e1] -> e1
(* TODO: Print term for error message *)
| _ -> failwith "[Z3 encoding] Ill-formed unary operator application"
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in
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(match uop with
| Not -> failwith "[Z3 encoding] application of unary operator Not not supported"
| Minus _ -> failwith "[Z3 encoding] application of unary operator Minus not supported"
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(* Omitting the log from the VC *)
| Log _ -> translate_expr ctx e1
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| Length -> failwith "[Z3 encoding] application of unary operator Length not supported"
| IntToRat -> failwith "[Z3 encoding] application of unary operator IntToRat not supported"
| GetDay -> failwith "[Z3 encoding] application of unary operator GetDay not supported"
| GetMonth -> failwith "[Z3 encoding] application of unary operator GetMonth not supported"
| GetYear -> failwith "[Z3 encoding] application of unary operator GetYear not supported"
)
(** [translate_expr] translate the expression [vc] to its corresponding Z3 expression **)
and translate_expr (ctx:context) (vc : expr Pos.marked) : Expr.expr =
match Pos.unmark vc with
| EVar _ -> failwith "[Z3 encoding] EVar unsupported"
| ETuple _ -> failwith "[Z3 encoding] ETuple unsupported"
| ETupleAccess _ -> failwith "[Z3 encoding] ETupleAccess unsupported"
| EInj _ -> failwith "[Z3 encoding] EInj unsupported"
| EMatch _ -> failwith "[Z3 encoding] EMatch unsupported"
| EArray _ -> failwith "[Z3 encoding] EArray unsupported"
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| ELit l -> translate_lit ctx l
| EAbs _ -> failwith "[Z3 encoding] EAbs unsupported"
| EApp (head, args) -> (match Pos.unmark head with
| EOp op -> translate_op ctx op args
| _ -> failwith "[Z3 encoding] EApp of a non-operator unsupported"
)
| EAssert _ -> failwith "[Z3 encoding] EAssert unsupported"
| EOp _ -> failwith "[Z3 encoding] EOp unsupported"
| EDefault _ -> failwith "[Z3 encoding] EDefault unsupported"
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| EIfThenElse (e_if, e_then, e_else) ->
(* Encode this as (e_if ==> e_then) /\ (not e_if ==> e_else) *)
let z3_if = translate_expr ctx e_if in
Boolean.mk_and ctx [
Boolean.mk_implies ctx z3_if (translate_expr ctx e_then);
Boolean.mk_implies ctx (Boolean.mk_not ctx z3_if) (translate_expr ctx e_else)
]
| ErrorOnEmpty _ -> failwith "[Z3 encoding] ErrorOnEmpty unsupported"
(** [solve_vc] is the main entry point of this module.
It takes a list of expressions [vcs] corresponding to verification conditions
that must be discharged by Z3, and attempts to solve them **)
let solve_vc (vcs : expr Pos.marked list) : unit =
Printf.printf "Running Z3 version %s\n" Version.to_string ;
let cfg = [("model", "true"); ("proof", "false")] in
let ctx = (mk_context cfg) in
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let solver = Solver.mk_solver ctx None in
let z3_vcs = List.map (translate_expr ctx) vcs in
List.iter (fun vc -> Printf.printf "Generated VC: %s\n" (Expr.to_string vc)) z3_vcs;
Solver.add solver z3_vcs;
if (Solver.check solver []) = SATISFIABLE then
Printf.printf "Success: Empty unreachable\n"
else
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(* TODO: Print model as error message for Catala debugging purposes *)
Printf.printf "Failure: Empty reachable\n"