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Program

Program->functions

Get the functions field from a program.

Signature
(program->functions x) → functions
Arguments: x — Guard (programp x).
Returns: functions — Type (function-setp functions).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: program->functions$inline

(defun program->functions$inline (x)
  (declare (xargs :guard (programp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'program->functions))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (function-set-fix (std::da-nth 1 x)))
         :exec (std::da-nth 1 x))))

Theorem: function-setp-of-program->functions

(defthm function-setp-of-program->functions
  (b* ((functions (program->functions$inline x)))
    (function-setp functions))
  :rule-classes :rewrite)

Theorem: program->functions$inline-of-program-fix-x

(defthm program->functions$inline-of-program-fix-x
  (equal (program->functions$inline (program-fix x))
         (program->functions$inline x)))

Theorem: program->functions$inline-program-equiv-congruence-on-x

(defthm program->functions$inline-program-equiv-congruence-on-x
  (implies (program-equiv x x-equiv)
           (equal (program->functions$inline x)
                  (program->functions$inline x-equiv)))
  :rule-classes :congruence)