VSL - The data.free_monoid Structure

# Copyright 2011  Petter Urkedal
#
# This file is part of the Viz Standard Library <http://www.vizlang.org/>.
#
# The Viz Standard Library (VSL) is free software: you can redistribute it
# and/or modify it under the terms of the GNU Lesser General Public License as
# published by the Free Software Foundation, either version 3 of the License,
# or (at your option) any later version.
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# more details.
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open prelude.ubiquitous

type t α := option (free_semigroup.t α)

let empty be none

let singleton x be some (free_semigroup.singleton x)

let length at none% be 0
	   at some a be free_semigroup.length a

let cat
    at none% at b be b
    at a at none% be a
    at some a at some b be some (free_semigroup.cat a b)

let for_all f be option.for_all (free_semigroup.for_all f)
let for_some f be option.for_some (free_semigroup.for_some f)
let fold f be option.fold (free_semigroup.fold f)
let iter f be option.iter (free_semigroup.iter f)
let map f be option.map (free_semigroup.map f)

in tagged
    let for_all f be option.for_all (free_semigroup.tagged.for_all f)
    let for_some f be option.for_some (free_semigroup.tagged.for_some f)
    let fold f be option.fold (free_semigroup.tagged.fold f)
    let iter f be option.iter (free_semigroup.tagged.iter f)