File: clause.lisp

package info (click to toggle)
acl2 8.6%2Bdfsg-2
  • links: PTS
  • area: main
  • in suites: trixie
  • size: 1,111,420 kB
  • sloc: lisp: 17,818,294; java: 125,359; python: 28,122; javascript: 23,458; cpp: 18,851; ansic: 11,569; perl: 7,678; xml: 5,591; sh: 3,976; makefile: 3,833; ruby: 2,633; yacc: 1,126; ml: 763; awk: 295; csh: 233; lex: 197; php: 178; tcl: 49; asm: 23; haskell: 17
file content (73 lines) | stat: -rw-r--r-- 1,967 bytes parent folder | download | duplicates (5)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
(in-package "PROOF-CHECKER-ARRAY")

(include-book "literal")
(include-book "unique")

;; ===================================================================
;; ============================= CLAUSE ==============================

(defun clausep (clause)
  (declare (xargs :guard t))
  (and (literal-listp clause)
       (unique-literalsp clause)
       (no-conflicting-literalsp clause)))

(defthm clausep-true-listp
  (implies (clausep clause)
           (true-listp clause)))

(defthm clausep-member
  (implies (and (clausep clause)
                (member e clause))
           (literalp e)))

(defthm clausep-cdr
  (implies (and (clausep clause)
                (consp clause))
           (clausep (cdr clause))))


;; ===================================================================
;; ============================= FORMULA =============================

(defun formulap (formula)
  (declare (xargs :guard t))
  (if (atom formula)
      (null formula)
    (and (clausep (car formula))
         (formulap (cdr formula)))))


(defthm formulap-true-listp
  (implies (formulap formula)
           (true-listp formula)))

(defthm formulap-member
  (implies (and (formulap formula)
                (member e formula))
           (clausep e)))

(defthm formulap-cdr
  (implies (and (formulap formula)
                (consp formula))
           (formulap (cdr formula))))

(defthm formulap-implies-clausep-car
  (implies (and (formulap formula)
                (consp formula))
           (clausep (car formula))))


;; ===================================================================
;; ========================= FLATTEN-FORMULA =========================

(defun flatten-formula (formula)
  (declare (xargs :guard (formulap formula)))
  (if (atom formula)
      nil
    (append (car formula)
            (flatten-formula (cdr formula)))))

(defthm literal-listp-flatten-formula
  (implies (formulap formula)
           (literal-listp (flatten-formula formula))))