►Dracula: Reference Manual
▼1 ACL2
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assert$
defaxiom
deflabel
defstub
deftheory
defthm
in-theory
include-book
mutual-recursion
theory-invariant
defconst
defun
declare
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1.3 Events and Definitions

ACL2 events are special terms which define new functions or logical rules. Defined names are in scope within their own definition and below; forward references are not allowed. Use the mutual-recursion event for mutually recursive functions.

(assert$ test form)
Raises an error if the given test fails.

Examples:

  > (assert$ (< 0 1) t)

  t

  > (assert$ (< 1 0) t)

  assert$: Assertion failed!

  (< 1 0)

(defaxiom name term :rule-classes rule-classes :doc doc-string)
Defines an axiom. Using defaxiom is not recommended.

Example:

  > (defaxiom sbar (equal t nil)
              :rule-classes nil
              :doc ":Doc-Section ...")

  rename-below: used outside of begin-below in: (rename-below

  (sbar19 sbar))

(deflabel name :doc doc-string)
Defines a label, for adding a landmark and/or adding a documentation topic.

Example:

  > (deflabel interp-section
              :doc ":Doc-Section ...")

(defstub name args-sig => output-sig :doc doc-string)

(deftheory name term :doc doc-string)
Defines a theory (to enable or disable a set of rules)

Example:

  > (deftheory interp-theory
               (set-difference-theories
                 (universal-theory :here)
                 (universal-theory 'interp-section)))

(defthm name term
:rule-classes rule-classes
:instructions instructions
:hints        hints
:otf-flg      otf-flg
:doc          doc-string)
Defines a theorem to be proved and named.

Example:

  > (defthm x+x=2x (= (+ x x) (* 2 x)))

  rename-below: used outside of begin-below in: (rename-below

  (x+x=2x20 x+x=2x))

(in-theory term :doc doc-string)

Example:

  > (in-theory (set-difference-theories
                 (universal-theory :here)
                 '(flatten (:executable-counterpart flatten))))

(include-book "<basename>")
(include-book "<basename>" :dir :system)
(include-book "<basename>" :dir :teachpacks)
The include-book form imports definitions from a file called a book. Dracula supports three variants.

  (include-book "my-path/my-book")
Without a :dir option, Dracula adds a ".lisp" extension to the base name and attempts to load a file relative to the current directory. In the case above, the program must reside in a directory with a "my-path" subdirectory containing a book named "my-book.lisp".

Books must be valid Dracula programs; they must start with (in-package "ACL2"); and they must contain only events, no top-level expressions.

  (include-book "my-path/my-book" :dir :system)
This variant loads a book from the system directory included with an ACL2 installation. Dracula simulates only a couple of the definitions from these books, but allows other books to be included for theorem proving purposes. See ACL2 Books for the list of books supported by Dracula.

  (include-book "my-path/my-book" :dir :teachpack)
The third variant loads one of the books provided with Dracula, called teachpacks. These books make use of DrScheme features such as interactive animations and other i/o, and are also reflected in the ACL2 logic. See Teachpacks for the list of provided teachpacks.

(mutual-recursion def1 ... defn)
For defining mutually-recursive functions.

Example:

  > (mutual-recursion
     (defun evenlp (x)
       (if (consp x) (oddlp (cdr x)) t))
     (defun oddlp (x)
       (if (consp x) (evenlp (cdr x)) nil)))

  rename-below: used outside of begin-below in: (rename-below

  (evenlp2123 evenlp21) (oddlp2224 oddlp22))

(theory-invariant term :key key :error t/nil)

(defconst name val)
Defines a constant value. The name must begin and end with asterisks.

Examples:

  > (defconst *PI* 22/7)

  rename-below: used outside of begin-below in: (rename-below

  (the-ref *PI*))

  > (* 2 *PI*)

  eval:600:0: *PI*: undefined in: *PI*

(defun name (args) (declare decl ...) ... body)
Defines a function.

Examples:

  > (defun absolute-value (x)
         (cond
           ((< x 0) (* -1 x))
           (t x)))

  rename-below: used outside of begin-below in: (rename-below

  (absolute-value2526 absolute-value25))

  > (absolute-value 5)

  compile: unbound identifier (and no #%top syntax

  transformer is bound) in: absolute-value25

  > (absolute-value -5)

  compile: unbound identifier (and no #%top syntax

  transformer is bound) in: absolute-value25

(declare d ...)
Used in defun to give ACL2 extra information about a function.

(defequiv pred)
Declares pred to be an equivalence predicate. It is equivalent to the following, with the supplied name substituted for pred in all identifiers:
  (defthm pred-is-an-equivalence
    (and (booleanp (pred x y))
         (pred x x)
         (implies (pred x y) (pred y x))
         (implies (and (pred x y)
                       (pred y z))
                  (pred x z)))
    :rule-classes (:equivalence))

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