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; Flatten function and lemmas
; Copyright (C) 2005-2013 Kookamara LLC
;
; Contact:
;
; Kookamara LLC
; 11410 Windermere Meadows
; Austin, TX 78759, USA
; http://www.kookamara.com/
;
; License: (An MIT/X11-style license)
;
; Permission is hereby granted, free of charge, to any person obtaining a
; copy of this software and associated documentation files (the "Software"),
; to deal in the Software without restriction, including without limitation
; the rights to use, copy, modify, merge, publish, distribute, sublicense,
; and/or sell copies of the Software, and to permit persons to whom the
; Software is furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in
; all copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
; DEALINGS IN THE SOFTWARE.
;
; Original author: Jared Davis <jared@kookamara.com>
;
; flatten.lisp
; This file was originally part of the Unicode library.
(in-package "ACL2")
(include-book "equiv")
(defun binary-append-without-guard (x y)
(declare (xargs :guard t))
(mbe :logic
(append x y)
:exec
(if (consp x)
(cons (car x)
(binary-append-without-guard (cdr x) y))
y)))
(defmacro append-without-guard (x y &rest rst)
(xxxjoin 'binary-append-without-guard (list* x y rst)))
(add-macro-alias append-without-guard binary-append-without-guard)
(defxdoc append-without-guard
:parents (std/lists append)
:short "Version of @(see append) that has a guard of @('t')"
:long "See @(see std::strict-list-recognizers) for a discussion of whether
requring lists to be @('nil')-terminated is right for you.")
(defsection flatten
:parents (std/lists)
:short "@(call flatten) appends together the elements of @('x')."
:long "<p>Typically @('x') is a list of lists that you want to
merge together. For example:</p>
@({
(flatten '((a b c) (1 2 3) (x y z)))
-->
(a b c 1 2 3 x y z)
})
<p>This is a \"one-level\" flatten that does not necessarily produce
an @(see atom-listp). For instance,</p>
@({
(flatten '(((a . 1) (b . 2))
((x . 3) (y . 4)))
-->
((a . 1) (b . 2) (x . 3) (y . 4))
})"
(defund flatten (x)
(declare (xargs :guard t))
(if (consp x)
(append-without-guard (car x)
(flatten (cdr x)))
nil))
(local (in-theory (enable flatten)))
;; The inferred type prescription isn't strong enough, it just says
;; (TS-UNION *TS-CONS* *TS-NIL*), so add a proper replacement.
(in-theory (disable (:type-prescription flatten)))
(defthm true-listp-of-flatten
(true-listp (flatten x))
:rule-classes :type-prescription)
(defthm flatten-when-not-consp
(implies (not (consp x))
(equal (flatten x)
nil)))
(defthm flatten-of-cons
(equal (flatten (cons a x))
(append a (flatten x))))
(defthm flatten-of-list-fix
(equal (flatten (list-fix x))
(flatten x)))
(defcong list-equiv equal (flatten x) 1
:hints(("Goal"
:in-theory (disable flatten-of-list-fix)
:use ((:instance flatten-of-list-fix (x x))
(:instance flatten-of-list-fix (x x-equiv))))))
(defthm flattenp-of-append
(equal (flatten (append x y))
(append (flatten x)
(flatten y)))))
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