# Module Blang

    module Blang: sig .. end

A simple boolean domain-specific language

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`` | `(*` | 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. | `*)`

    val base : 'a -> 'a t

    val true_ : 'a t

    val false_ : 'a t

    val constant : bool -> 'a t

`function true -> true_ | false -> false_`

    val not_ : 'a t -> 'a t

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

n-ary `And`

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

n-ary `Or`

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

`if_ if then else`

    val constant_value : 'a t -> bool option

`constant_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 ...
          | ...

    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 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)

Note: `bind t f` does short-circuiting, so `f` may not be called on every variable in `t`.

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

-             if
                List.for_all (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

    val invariant : 'a t -> unit

    module Stable: sig .. end

    val t_of_sexp : (Sexplib.Sexp.t -> 'a) -> Sexplib.Sexp.t -> 'a t

    val sexp_of_t : ('a -> Sexplib.Sexp.t) -> 'a t -> Sexplib.Sexp.t

    val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int

    val bin_t : 'a Bin_prot.Type_class.t -> 'a t Bin_prot.Type_class.t

    val bin_read_t : 'a Bin_prot.Read.reader -> 'a t Bin_prot.Read.reader

    val __bin_read_t__ : 'a Bin_prot.Read.reader -> (int -> 'a t) Bin_prot.Read.reader

    val bin_reader_t : 'a Bin_prot.Type_class.reader -> 'a t Bin_prot.Type_class.reader

    val bin_size_t : 'a Bin_prot.Size.sizer -> 'a t Bin_prot.Size.sizer

    val bin_write_t : 'a Bin_prot.Write.writer -> 'a t Bin_prot.Write.writer

    val bin_writer_t : 'a Bin_prot.Type_class.writer -> 'a t Bin_prot.Type_class.writer

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.

###### smart constructors that simplify away constants whenever possible

`function true -> true_ | false -> false_`
n-ary `And`
n-ary `Or`
`if_ if then else`
`constant_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) = 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`

`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`

`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)

Note: `bind t f` does short-circuiting, so `f` may not be called on every variable in `t`.
`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.
`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.for_all (values (specialize t g)) ~f:(fun x -> g x = `Unknown)`

-             if
                List.for_all (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