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• Semantics

Nat-match-insensitive-char-p

Semantics of characters in case-insensitive character value notations.

Signature

(nat-match-insensitive-char-p nat char) → yes/no

Arguments

nat — Guard (natp nat).

char — Guard (characterp char).

Returns

yes/no — Type (booleanp yes/no).

A natural number matches a character in a case-insensitive character value notation iff the natural number is the code of the character or of the uppercase or lowercase counterpart of the character.

Definitions and Theorems

Function: nat-match-insensitive-char-p

(defun nat-match-insensitive-char-p (nat char)
  (declare (xargs :guard (and (natp nat) (characterp char))))
  (b* ((nat (mbe :logic (nfix nat) :exec nat)))
    (or (equal nat (char-code char))
        (equal nat (char-code (upcase-char char)))
        (equal nat (char-code (downcase-char char))))))

Theorem: booleanp-of-nat-match-insensitive-char-p

(defthm booleanp-of-nat-match-insensitive-char-p
  (b* ((yes/no (nat-match-insensitive-char-p nat char)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: nat-match-insensitive-char-p-of-char-fix

(defthm nat-match-insensitive-char-p-of-char-fix
  (equal (nat-match-insensitive-char-p nat (char-fix char))
         (nat-match-insensitive-char-p nat char)))

Theorem: nat-match-insensitive-char-p-of-nfix-nat

(defthm nat-match-insensitive-char-p-of-nfix-nat
  (equal (nat-match-insensitive-char-p (nfix nat)
                                       char)
         (nat-match-insensitive-char-p nat char)))

Theorem: nat-match-insensitive-char-p-nat-equiv-congruence-on-nat

(defthm nat-match-insensitive-char-p-nat-equiv-congruence-on-nat
  (implies (acl2::nat-equiv nat nat-equiv)
           (equal (nat-match-insensitive-char-p nat char)
                  (nat-match-insensitive-char-p nat-equiv char)))
  :rule-classes :congruence)

Theorem: nat-match-insensitive-char-p-of-char-fix-char

(defthm nat-match-insensitive-char-p-of-char-fix-char
  (equal (nat-match-insensitive-char-p nat (char-fix char))
         (nat-match-insensitive-char-p nat char)))

Theorem: nat-match-insensitive-char-p-chareqv-congruence-on-char

(defthm nat-match-insensitive-char-p-chareqv-congruence-on-char
  (implies (acl2::chareqv char char-equiv)
           (equal (nat-match-insensitive-char-p nat char)
                  (nat-match-insensitive-char-p nat char-equiv)))
  :rule-classes :congruence)