#       counters are automata
#      ______      ___________
# --->/ INIT \--->/ INCREMENT \---.
#     \______/    \_DECREMENT_/<--'
#

# tests automaton if it is initialized
# β₁
define([TEST_ATM], [

	ifelse([$#], [0], [

		ROOT_ERROR([$0(…) must be initialized])
	])
])

# β₁β₂
define([COUNT_UP], defn([TEST_ATM])[

	# the INIT node defines a unique symbol as the internal counter value
	define([$0_val], [$1])

	# transition to the INCREMENT node
	define([$0], [$0_val[]define([$0_val], incr($0_val))])
])

# β₁β₂
define([COUNT_DOWN], defn([TEST_ATM])[

	# the INIT node defines a unique symbol as the internal counter value
	define([$0_val], [$1])

	# transition to the DECREMENT node
	define([$0], [$0_val[]define([$0_val], decr($0_val))])
])