package alba

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package alba
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Library
Module
Module type
Parameter
Class
Class type
val bruijn_convert : int -> int -> int
module Lambda_info : sig ... end
module Pi_info : sig ... end
module Application_info : sig ... end
type t =
  1. | Sort of Sort.t
  2. | Value of Value.t
  3. | Variable of int
  4. | Typed of t * typ
  5. | Appl of t * t * Application_info.t
  6. | Lambda of typ * t * Lambda_info.t
  7. | Pi of typ * typ * Pi_info.t
  8. | Where of string * typ * t * t
    (*

    Where (name, tp, exp, def) is equivalent to the beta redex Appl ( Lambda (tp, exp, "name"), def)

    *)
and typ = t
and formal_argument = string * typ
and inductive
type t_n = t * int
type typ_n = typ * int
val proposition : t
val any : t
val any_uni : int -> t
val variable : int -> t
val application : t -> t -> t
val implicit_application : t -> t -> t
val binary : t -> t -> t -> t
val applications : t -> t list -> t
val lambda0 : string -> bool -> typ -> t -> t
val product0 : string -> bool -> typ -> typ -> typ
val make_product : string -> bool -> bool -> typ -> typ -> typ

make_product name typed kind arg_typ res_typ

val lambda : string -> typ -> t -> t
val product : string -> typ -> typ -> t
val arrow : typ -> typ -> typ
val lambda_untyped : string -> typ -> t -> t
val product_untyped : string -> typ -> typ -> t
val lambda_in : formal_argument list -> t -> t
val product_in : formal_argument list -> t -> t
val expand_where : string -> typ -> t -> t -> t

Rewrite a where block as an application with a lambda term.

val char : int -> t

char code character value.

val string : string -> t

string str string value.

val number_values : string -> t list
val type_of_sort : Sort.t -> typ
val is_sort : typ -> bool
val pi_sort : typ -> typ -> typ
val split_application : t -> t * (t * Application_info.t) list

split_application t

val map : (int -> int) -> t -> t

map f t

Map the free variables with f

val up_from : int -> int -> t -> t

up_from start delta t: increases all free variables >= start in t by delta

requires: 0 <= delta

val up : int -> t -> t

up delta t: increases all free variables in t by delta

requires: 0 <= delta

val up1 : t -> t

up1 t: increases all free variable in t by 1

val down_from : int -> int -> t -> t option

down_from start delta t: decreases all free variables >= start in t by delta if possible. Returns None it there is a free variable in t with index i < delta.

requires: 0 <= delta

val down : int -> t -> t option

down delta t: decreases all free variables in t by delta if possible. Returns None if there is a free variable in t with index i < delta.

requires: 0 <= delta

val substitute0 : (int -> t) -> bool -> t -> t

substitute0 f beta_reduce t

val substitute : (int -> t) -> t -> t

substitute f term substitutes each free variable i in term by the term f i.

val substitute_with_beta : (int -> t) -> t -> t

substitute f term substitutes each free variable i in term by the term f i and do beta reduction in case that f i appears in a function position and is a function abstraction.

val apply : t -> t -> t
val apply_nargs : t -> int -> Application_info.t -> t

apply_nargs f n mode returns

f (Var (n-1)) ... (Var 0)

where all applications are done with mode mode.

val fold_free : (int -> 'a -> 'a) -> t -> 'a -> 'a
val to_index : int -> t -> t
val to_level : int -> t -> t
val has : (int -> bool) -> t -> bool

has p term does the term have a free variable satisfying p?

val forall : (int -> bool) -> t -> bool

forall p term do all free variables in term satisfy p?

val has_variable : int -> t -> bool
module Monadic (M : Fmlib.Module_types.MONAD) : sig ... end

Monadic functions

module Inductive : sig ... end

Inductive types