• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
    • Gl
    • Witness-cp
    • Ccg
    • Install-not-normalized
    • Rewrite$
    • Removable-runes
    • Fgl
      • Fgl-rewrite-rules
      • Fgl-function-mode
      • Fgl-object
      • Fgl-solving
      • Fgl-handling-if-then-elses
      • Fgl-getting-bits-from-objects
      • Fgl-primitive-and-meta-rules
      • Fgl-interpreter-overview
      • Fgl-counterexamples
      • Fgl-correctness-of-binding-free-variables
      • Fgl-debugging
      • Fgl-testbenches
      • Def-fgl-boolean-constraint
      • Fgl-stack
      • Fgl-rewrite-tracing
      • Def-fgl-param-thm
      • Def-fgl-thm
      • Fgl-fast-alist-support
      • Fgl-array-support
      • Advanced-equivalence-checking-with-fgl
      • Fgl-internals
        • Symbolic-arithmetic
        • Bfr
          • Bfr-eval
          • Bfrstate
          • Bfr->aignet-lit
          • Bfr-p
          • Bounded-lit-fix
          • Bfr-list-fix
          • Aignet-lit->bfr
          • Variable-g-bindings
          • Bfr-listp$
          • Bfrstate>=
          • Bfr-listp-witness
          • Fgl-object-bindings-bfrlist
          • Bfr-set-var
          • Bfr-negate
          • Bfr-fix
          • Fgl-bfr-object-bindings-p
          • Bfr-mode
          • Bfr-mode-is
          • Lbfr-case
          • Bfrstate-case
          • Bfrstate-mode-is
          • Lbfr-mode-is
          • Bfr-mode-p
        • Fgl-interpreter-state
    • Efficiency
    • Rewrite-bounds
    • Bash
    • Def-dag-measure
    • Bdd
    • Remove-hyps
    • Contextual-rewriting
    • Simp
    • Rewrite$-hyps
    • Bash-term-to-dnf
    • Use-trivial-ancestors-check
    • Minimal-runes
    • Clause-processor-tools
    • Fn-is-body
    • Without-subsumption
    • Rewrite-equiv-hint
    • Def-bounds
    • Rewrite$-context
    • Try-gl-concls
    • Hint-utils
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Bfr

Variable-g-bindings

Signature

(variable-g-bindings vars) → bindings

Arguments

vars — Guard (pseudo-var-list-p vars).

Returns

bindings — Type (fgl-object-bindings-p bindings).

Definitions and Theorems

Function: variable-g-bindings

(defun variable-g-bindings (vars)
  (declare (xargs :guard (pseudo-var-list-p vars)))
  (let ((__function__ 'variable-g-bindings))
    (declare (ignorable __function__))
    (if (atom vars)
        nil
      (cons (cons (pseudo-var-fix (car vars))
                  (g-var (car vars)))
            (variable-g-bindings (cdr vars))))))

Theorem: fgl-object-bindings-p-of-variable-g-bindings

(defthm fgl-object-bindings-p-of-variable-g-bindings
  (b* ((bindings (variable-g-bindings vars)))
    (fgl-object-bindings-p bindings))
  :rule-classes :rewrite)

Theorem: fgl-object-bindings-bfrlist-of-variable-g-bindings

(defthm fgl-object-bindings-bfrlist-of-variable-g-bindings
  (b* ((?bindings (variable-g-bindings vars)))
    (equal (fgl-object-bindings-bfrlist bindings)
           nil)))

Theorem: alist-keys-of-variable-g-bindings

(defthm alist-keys-of-variable-g-bindings
  (b* ((?bindings (variable-g-bindings vars)))
    (equal (alist-keys bindings)
           (pseudo-var-list-fix vars))))

Theorem: lookup-in-variable-g-bindings

(defthm lookup-in-variable-g-bindings
  (b* ((?bindings (variable-g-bindings vars)))
    (equal (hons-assoc-equal k bindings)
           (and (member k (pseudo-var-list-fix vars))
                (cons k (g-var k))))))

Theorem: variable-g-bindings-of-pseudo-var-list-fix-vars

(defthm variable-g-bindings-of-pseudo-var-list-fix-vars
  (equal (variable-g-bindings (pseudo-var-list-fix vars))
         (variable-g-bindings vars)))

Theorem: variable-g-bindings-pseudo-var-list-equiv-congruence-on-vars

(defthm variable-g-bindings-pseudo-var-list-equiv-congruence-on-vars
  (implies (pseudo-var-list-equiv vars vars-equiv)
           (equal (variable-g-bindings vars)
                  (variable-g-bindings vars-equiv)))
  :rule-classes :congruence)