Boolean expressions.
A blang is a boolean expression built up by applying the usual boolean operations to properties that evaluate to true or false in some context.
Usage
For example, imagine writing a config file for an application that filters a stream of integers. Your goal is to keep only those integers that are multiples of either -3 or 5. Using Blang for this task, the code might look like:
module Property = struct
type t =
| Multiple_of of int
| Positive
| Negative
[@@deriving sexp]
let eval t num =
match t with
| Multiple_of n -> num % n = 0
| Positive -> num > 0
| Negative -> num < 0
end
type config = {
keep : Property.t Blang.t;
} [@@deriving sexp]
let config = {
keep =
Blang.t_of_sexp
Property.t_of_sexp
(Sexp.of_string
"(or (and negative (multiple_of 3)) (and positive (multiple_of 5)))";
}
let keep config num : bool =
Blang.eval config.keep (fun p -> Property.eval p num)
Note how positive and negative and multiple_of become operators in a small, newly-defined boolean expression language that allows you to write statements like (and negative (multiple_of 3)).
Blang sexp syntax
The blang sexp syntax is almost exactly the derived one, except that:
1. Base properties are not marked explicitly. Thus, if your base property type has elements FOO, BAR, etc., then you could write the following Blang s-expressions:
FOO
(and FOO BAR)
(if FOO BAR BAZ)and so on. Note that this gets in the way of using the blang "keywords" in your value language.
2. And and Or take a variable number of arguments, so that one can (and probably should) write
(and FOO BAR BAZ QUX)
instead of
(and FOO (and BAR (and BAZ QUX)))
If you want to see the derived sexp, use Raw.sexp_of_t.
type +'a t = private | True| False| And of 'a t * 'a t| Or of 'a t * 'a t| Not of 'a t| If of 'a t * 'a t * 'a t| Base of 'a
Note that the sexps are not directly inferred from the type below -- there are lots of fancy shortcuts. Also, the sexps for 'a must not look anything like blang sexps. Otherwise t_of_sexp will fail. The directly inferred sexps are available via Raw.sexp_of_t.
Raw provides the automatically derived sexp_of_t, useful in debugging the actual structure of the blang.
Smart constructors that simplify away constants whenever possible
include Constructors
function true -> true_ | false -> false_
val if_ : 'a t -> 'a t -> 'a t -> 'a tconstant_value t = Some b iff t = constant b
The following two functions are useful when one wants to pretend that 'a t has constructors And and Or of type 'a t list -> 'a t. The pattern of use is
match t with
| And (_, _) as t -> let ts = gather_conjuncts t in ...
| Or (_, _) as t -> let ts = gather_disjuncts t in ...
| ...
or, in case you also want to handle True (resp. False) as a special case of conjunction (disjunction)
match t with
| True | And (_, _) as t -> let ts = gather_conjuncts t in ...
| False | Or (_, _) as t -> let ts = gather_disjuncts t in ...
| ...
gather_conjuncts t gathers up all toplevel conjuncts in t. For example,
gather_conjuncts (and_ ts) = tsgather_conjuncts (And (t1, t2)) = gather_conjuncts t1 @ gather_conjuncts t2gather_conjuncts True = [] gather_conjuncts t = [t] when t matches neither And (_, _) nor True
gather_disjuncts t gathers up all toplevel disjuncts in t. For example,
gather_disjuncts (or_ ts) = tsgather_disjuncts (Or (t1, t2)) = gather_disjuncts t1 @ gather_disjuncts t2gather_disjuncts False = [] gather_disjuncts t = [t] when t matches neither Or (_, _) nor False
include Container.S1 with type 'a t := 'a t
val mem : 'a t -> 'a -> equal:('a -> 'a -> bool) -> boolChecks whether the provided element is there, using equal.
val is_empty : 'a t -> boolval iter : 'a t -> f:('a -> unit) -> unitval fold : 'a t -> init:'accum -> f:('accum -> 'a -> 'accum) -> 'accumfold t ~init ~f returns f (... f (f (f init e1) e2) e3 ...) en, where e1..en are the elements of t
fold_result t ~init ~f is a short-circuiting version of fold that runs in the Result monad. If f returns an Error _, that value is returned without any additional invocations of f.
fold_until t ~init ~f ~finish is a short-circuiting version of fold. If f returns Stop _ the computation ceases and results in that value. If f returns Continue _, the fold will proceed. If f never returns Stop _, the final result is computed by finish.
Example:
type maybe_negative =
| Found_negative of int
| All_nonnegative of { sum : int }
(** [first_neg_or_sum list] returns the first negative number in [list], if any,
otherwise returns the sum of the list. *)
let first_neg_or_sum =
List.fold_until ~init:0
~f:(fun sum x ->
if x < 0
then Stop (Found_negative x)
else Continue (sum + x))
~finish:(fun sum -> All_nonnegative { sum })
;;
let x = first_neg_or_sum [1; 2; 3; 4; 5]
val x : maybe_negative = All_nonnegative {sum = 15}
let y = first_neg_or_sum [1; 2; -3; 4; 5]
val y : maybe_negative = Found_negative -3
val exists : 'a t -> f:('a -> bool) -> boolReturns true if and only if there exists an element for which the provided function evaluates to true. This is a short-circuiting operation.
val for_all : 'a t -> f:('a -> bool) -> boolReturns true if and only if the provided function evaluates to true for all elements. This is a short-circuiting operation.
val count : 'a t -> f:('a -> bool) -> intReturns the number of elements for which the provided function evaluates to true.
Returns the sum of f i for all i in the container.
val find : 'a t -> f:('a -> bool) -> 'a optionReturns as an option the first element for which f evaluates to true.
val find_map : 'a t -> f:('a -> 'b option) -> 'b optionReturns the first evaluation of f that returns Some, and returns None if there is no such element.
val to_list : 'a t -> 'a listval to_array : 'a t -> 'a arrayval min_elt : 'a t -> compare:('a -> 'a -> int) -> 'a optionReturns a minimum (resp maximum) element from the collection using the provided compare function, or None if the collection is empty. In case of a tie, the first element encountered while traversing the collection is returned. The implementation uses fold so it has the same complexity as fold.
val max_elt : 'a t -> compare:('a -> 'a -> int) -> 'a optionBlang.t sports a substitution monad:
return v is Base v (think of v as a variable)bind t f replaces every Base v in t with f v (think of v as a variable and f as specifying the term to substitute for each variable)
Note: bind t f does short-circuiting, so f may not be called on every variable in t.
include Interfaces.Monad with type 'a t := 'a t
val (>>=) : 'a t -> ('a -> 'b t) -> 'b tt >>= f returns a computation that sequences the computations represented by two monad elements. The resulting computation first does t to yield a value v, and then runs the computation returned by f v.
val (>>|) : 'a t -> ('a -> 'b) -> 'b tt >>| f is t >>= (fun a -> return (f a)).
val bind : 'a t -> f:('a -> 'b t) -> 'b treturn v returns the (trivial) computation that returns v.
val map : 'a t -> f:('a -> 'b) -> 'b tval join : 'a t t -> 'a tjoin t is t >>= (fun t' -> t').
val ignore_m : 'a t -> unit tignore_m t is map t ~f:(fun _ -> ()). ignore_m used to be called ignore, but we decided that was a bad name, because it shadowed the widely used Caml.ignore. Some monads still do let ignore = ignore_m for historical reasons.
val all : 'a t list -> 'a list tval all_unit : unit t list -> unit tLike all, but ensures that every monadic value in the list produces a unit value, all of which are discarded rather than being collected into a list.
These are convenient to have in scope when programming with a monad:
values t forms the list containing every v for which Base v is a subexpression of t
eval t f evaluates the proposition t relative to an environment f that assigns truth values to base propositions.
val eval_set :
universe:('elt, 'comparator) Set.t Lazy.t ->
('a -> ('elt, 'comparator) Set.t) ->
'a t ->
('elt, 'comparator) Set.teval_set ~universe set_of_base expression returns the subset of elements e in universe that satisfy eval expression (fun base -> Set.mem (set_of_base base) e).
eval_set assumes, but does not verify, that set_of_base always returns a subset of universe. If this doesn't hold, then eval_set's result may contain elements not in universe.
And set1 set2 represents the elements that are both in set1 and set2, thus in the intersection of the two sets. Symmetrically, Or set1 set2 represents the union of set1 and set2.
val specialize : 'a t -> ('a -> [ `Known of Base.Bool.t | `Unknown ]) -> 'a tspecialize t f partially evaluates t according to a perhaps-incomplete assignment f of the values of base propositions. The following laws (at least partially) characterize its behavior.
specialize t (fun _ -> `Unknown) = t
specialize t (fun x -> `Known (f x)) = constant (eval t f)
List.for_all (values (specialize t g)) ~f:(fun x -> g x = `Unknown)
Generalizes some of the blang operations above to work in a monad.