• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • C
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
      • Semantics
        • Step
        • Write-var
        • Outcome
        • Beval
        • Read-var
        • Config
        • Terminatingp
        • Aeval
        • Step*
        • Stepn
        • Env
          • Envp
          • Env-fix
          • Env-equiv
      • Abstract-syntax
      • Interpreter
    • Sidekick
    • Leftist-trees
    • Java
    • Taspi
    • Bitcoin
    • Riscv
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Axe
    • Bigmems
    • Builtins
    • Execloader
    • Aleo
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Env

Envp

Recognizer for env.

Signature

(envp x) → *

Definitions and Theorems

Function: envp

(defun envp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (stringp (caar x))
         (integerp (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (acl2::fast-<< (caar x) (caadr x))
                  (envp (cdr x)))))))

Theorem: booleanp-of-envp

(defthm booleanp-of-envp
  (booleanp (envp x)))

Theorem: mapp-when-envp

(defthm mapp-when-envp
  (implies (envp x) (omap::mapp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: envp-of-tail

(defthm envp-of-tail
  (implies (envp x)
           (envp (omap::tail x))))

Theorem: stringp-of-head-key-when-envp

(defthm stringp-of-head-key-when-envp
  (implies (and (envp x) (not (omap::emptyp x)))
           (stringp (mv-nth 0 (omap::head x)))))

Theorem: integerp-of-head-val-when-envp

(defthm integerp-of-head-val-when-envp
  (implies (and (envp x) (not (omap::emptyp x)))
           (integerp (mv-nth 1 (omap::head x)))))

Theorem: envp-of-update

(defthm envp-of-update
  (implies (and (envp x) (stringp k) (integerp v))
           (envp (omap::update k v x))))

Theorem: envp-of-update*

(defthm envp-of-update*
  (implies (and (envp x) (envp y))
           (envp (omap::update* x y))))

Theorem: envp-of-delete

(defthm envp-of-delete
  (implies (envp x)
           (envp (omap::delete k x))))

Theorem: envp-of-delete*

(defthm envp-of-delete*
  (implies (envp x)
           (envp (omap::delete* k x))))

Theorem: stringp-when-assoc-envp-binds-free-x

(defthm stringp-when-assoc-envp-binds-free-x
  (implies (and (omap::assoc k x) (envp x))
           (stringp k)))

Theorem: stringp-of-car-of-assoc-envp

(defthm stringp-of-car-of-assoc-envp
  (implies (and (envp x) (omap::assoc k x))
           (stringp (car (omap::assoc k x)))))

Theorem: integerp-of-cdr-of-assoc-envp

(defthm integerp-of-cdr-of-assoc-envp
  (implies (and (envp x) (omap::assoc k x))
           (integerp (cdr (omap::assoc k x)))))

Theorem: integerp-of-lookup-when-envp

(defthm integerp-of-lookup-when-envp
  (implies (and (envp x) (omap::assoc k x))
           (integerp (omap::lookup k x))))