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JavaScript Program Verification

The JavaScript program verifier combines the K verification infrastructure with the JavaScript semantics. The verification is enabled by the --prove option of the krun command:

$ krun --prove <specification.k> <program.js>

The specification <specification.k> essentially describes a set of pre-/post-conditions, and it should be given as a reachability rule written in K.

Use the Makefile to quickly run all of the verification examples:

$ make

The output of the make command is available in verification.out. For each program, the verifier simply outputs true when it succeeds in verifying the program. Note that the verifier may crash or fail to terminate when the program is not correct. We will improve usability of the verifier in the future.

List of Programs and Specifications

We have the following example programs and specifications to be verified:

Programs Source Codes Specifications
List reverse list/reverse.js list/reverse_spec.k
List append list/append.js list/append_spec.k
BST find bst/find.js bst/string_find_spec.k , bst/float_find_spec.k
BST insert bst/insert.js bst/string_insert_spec.k , bst/float_insert_spec.k
BST delete bst/delete.js bst/string_delete_spec.k , bst/float_delete_spec.k
BST find (in OOP style) bst-oop/bst.js:find bst-oop/bst_find_spec.k
BST insert (in OOP style) bst-oop/bst.js:insert bst-oop/bst_insert_spec.k
AVL find avl/avl.js:find avl/avl_find_spec.k
AVL insert avl/avl.js:insert avl/avl_insert_spec.k
AVL delete avl/avl.js:delete avl/avl_delete_spec.k

We have three different data structures of list, binary search tree, and AVL tree. For the binary search tree, we have two different implementations; one is written in C-like style (e.g., bst/insert.js) and another is written in OOP style (e.g., bst-oop/bst.js).

Specifications

The specifications are given as reachability rules using the K syntax and are located in *_spec.k files. For example, the rule below from the avl_insert_spec.k file captures the behavior of the avl insert routine:

rule
  <envs>...
    ENVS:Bag
    (.Bag => ?_:Bag)
  ...</envs>
  <objs>...
    (htree(O1)(T1:StringTree) => htree(?O2)(?T2:StringTree))
    OBJS:Bag
    (.Bag => ?_:Bag)
  ...</objs>
  <k>
    Call(
      // %var("insert"),
      @o(19),
      Undefined,
      @Cons(V:String, @Cons(O1:NullableObject, @Nil)))
  =>
    ?O2:NullableObject
  ...</k>
  requires avl(T1) andBool tree_height(T1) <Int (4294967296 -Int 1)
  ensures avl(?T2) andBool tree_keys(?T2) ==K { V } U tree_keys(T1)
    andBool tree_height(T1) <=Int  tree_height(?T2)
    andBool tree_height(?T2) <=Int tree_height(T1) +Int 1

While the rule is fairly verbose (due to operating on the configuration used to give semantics to JavaScript), most of it can be automatically generated. Specifically

  • the variables with the same names as cells but with capital letters (e.g. ENVS:Bag and OBJS:Bag) are placeholders for the parts of the configuration that are statically computed by running the semantics on the functions being verified (e.g. OBJS:Bags stands for all the builtin objects and the objects associated to the functions being verified).
  • the parts that captures general JavaScript behavior; e.g. the line (.Bag => ?_:Bag) in the <objs> cell that says that after a function call there may be some dead objects left over, since the semantics does not garbage collect (?_ is a existentially quantified anonymous variable)
  • the internal reference to the insert function, @o(19) (which can be automatically generated).

The parts of this rule specific to the avl insert routine are

  • the <k> cell, which says that the call to insert takes a string V and an object reference O1 and returns another object reference ?O2
  • the line (htree(O1)(T1:StringTree) => htree(?O2)(?T2:StringTree)) in the <objs> cell which says that before the call to insert, there is a tree rooted at O1 which represent the algebraic tree T1 in the heap, and after the call there is another tree rooted at ?O2 which represents the tree ?T2
  • the requires clause, which i) states that T1 is an avl, and ii) bounds the height of T1 to ensure there is no precision loss when computing the height of ?T2 (the tree after the insertion)
  • the ensures clause, which states that i) ?T2 is an avl, ii) the keys of ?T2 are the union of the keys of T1 and { V }, and iii) the height of ?T2 increases by at most one

With that in mind, we could generate the rule above from a more compact annotation

function insert(v, t)
//@requires htree(t)(T1) /\ avl(T1)
         /\ tree_height(T1) < 4294967295
//@ensures htree(t)(?T2) /\ avl(?T2)
        /\ tree_keys(?T2) == { V } U tree_keys(T1)
        /\ | tree_height(?T2) - tree_height(T1) | <  1

We did not implement this transformation yet. However a similar transformation (albeit for a simpler language) is implemented in the MatchC tool, which is available online at http://fsl.cs.illinois.edu/index.php/Special:MatchCOnline

Wrapper Module for Verification

The K verifier requires a wrapper module that combines the original language semantics with several verification specific libraries. A wrapper module can be written by simply importing several sub-modules such as the JavaScript semantics JS, verification lemmas VERIFICATION_LEMMAS, and a data type abstraction <PATTERN>, as follows:

require "js.k"
require "modules/verification_lemmas.k"
require "<pattern.k>"

module JS-VERIFIER

  imports JS
  imports VERIFICATION_LEMMAS
  imports <PATTERN>

endmodule

Directory Structure

  • patterns - definitions of the abstractions used in the specifications (list, tree, etc) given in K syntax
  • list - the source code and specifications for the list examples
  • bst - the source code and specifications for the binary search tree (written in C-like style) example
  • bst-oop - the source code and specifications for the binary search tree (written in OOP style) example
  • avl - the source code and specifications for the AVL tree example