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Require Import Coq.Strings.String.
(** Require the monad definitions **)
Require Import ExtLib.Structures.Monads.
(** Use the instances for exceptions **)
Require Import ExtLib.Data.Monads.EitherMonad.
(** Strings will be used for error messages **)
Require Import ExtLib.Data.String.
Set Implicit Arguments.
Set Strict Implicit.
(** Syntax and values of a simple language **)
Inductive value : Type :=
| Int : nat -> value
| Bool : bool -> value.
Inductive exp : Type :=
| ConstI : nat -> exp
| ConstB : bool -> exp
| Plus : exp -> exp -> exp
| If : exp -> exp -> exp -> exp.
Section monadic.
(** Going to work over any monad [m] that is:
** 1) a Monad, i.e. [Monad m]
** 2) has string-valued exceptions, i.e. [MonadExc string m]
**)
Variable m : Type -> Type.
Context {Monad_m : Monad m}.
Context {MonadExc_m : MonadExc string m}.
(** Use the notation for monads **)
Import MonadNotation.
Local Open Scope monad_scope.
(** Functions that get [nat] or [bool] values from a [value] **)
Definition asInt (v : value) : m nat :=
match v with
| Int n => ret n
| _ =>
(** if we don't have an integer, signal an error using
** [raise] from the MoandExc instance
**)
raise ("expected integer got bool")%string
end.
Definition asBool (v : value) : m bool :=
match v with
| Bool b => ret b
| _ => raise ("expected bool got integer")%string
end.
(** The main evaluator routine returns a [value], but since we are
** working in the [m] monad, we return [m value]
**)
Fixpoint eval' (e : exp) : m value :=
match e with
(** when there is no error, we can just return (i.e. [ret])
** the answer
**)
| ConstI i => ret (Int i)
| ConstB b => ret (Bool b)
| Plus l r =>
(** evaluate the sub-terms to numbers **)
l <- eval' l ;;
l <- asInt l ;;
r <- eval' r ;;
r <- asInt r ;;
(** Combine the result **)
ret (Int (l + r))
| If t tr fa =>
(** evaluate the test condition to a boolean **)
t <- eval' t ;;
t <- asBool t ;;
(** case split and perform the appropriate recursion **)
if (t : bool) then
eval' tr
else
eval' fa
end.
End monadic.
(** Wrap the [eval] function up with the monad instance that we
** want to use
**)
Definition eval : exp -> string + value :=
eval' (m := sum string).
(** Some tests **)
Eval compute in eval (Plus (ConstI 1) (ConstI 2)).
Eval compute in eval (Plus (ConstI 1) (ConstB false)).
(** Other useful monads:
** * Reader - for handling lexicographic environments
** * State - for handling non-lexical state, like a heap
** * MonadFix - for handling unbounded recursion
**)
|
