Module Blang

module Blang: Blang

Blang provides infrastructure for writing simple boolean DSLs. All expressions in a Blang language evaluate to a bool. The language is parameterized over another language of base propositions.

The syntax is almost exactly the obvious s-expression syntax, except that:

1. Base elements are not marked explicitly. Thus, if your base language 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)))

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`

val base : 'a -> 'a t

val true_ : 'a t

val false_ : 'a t

val constant : bool -> 'a t

val not_ : 'a t -> 'a t

val andalso : 'a t -> 'a t -> 'a t

val orelse : 'a t -> 'a t -> 'a t

val and_ : 'a t list -> 'a t

val or_ : 'a t list -> 'a t

val if_ : 'a t -> 'a t -> 'a t -> 'a t

val is_constant : 'a t -> bool option

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)

val gather_conjuncts : 'a t -> 'a t list

gather_conjuncts t gathers up all toplevel conjuncts in t. For example,

gather_conjuncts (and_ ts) = ts
gather_conjuncts (And (t1, t2)) = gather_conjuncts t1 @ gather_conjuncts t2
gather_conjuncts True = []
gather_conjuncts t = [t] when t matches neither And (_, _) nor True

val gather_disjuncts : 'a t -> 'a t list

gather_disjuncts t gathers up all toplevel disjuncts in t. For example,

gather_disjuncts (or_ ts) = ts
gather_disjuncts (Or (t1, t2)) = gather_disjuncts t1 @ gather_disjuncts t2
gather_disjuncts False = []
gather_disjuncts t = [t] when t matches neither Or (_, _) nor False

include Sexpable.S1

Note that the sexps are not directly inferred from the type above -- there are lots of fancy shortcuts. Also, the sexps for 'a must not look anything like blang sexps. Otherwise t_of_sexp will fail.

include Binable.S1

include Container.S1

include Monad

Blang.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)

val values : 'a t -> 'a list

values t forms the list containing every v for which Base v is a subexpression of t

val eval : 'a t -> ('a -> bool) -> bool

eval t f evaluates the proposition t relative to an environment f that assigns truth values to base propositions.

val specialize : 'a t -> ('a -> [ `Known of bool | `Unknown ]) -> 'a t

specialize 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.forall (values (specialize t g)) ~f:(fun x -> g x = `Unknown)

if List.forall (values t) ~f:(fun x -> match g x with | `Known b -> b = f x | `Unknown -> true) then eval t f = eval (specialize t g) f