Definition of a Structured Verification in Maple

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Description

•

A structured verification is a Maple expression other than a symbol which can be interpreted as a verification. A typical example would be . This specifies that the two objects must be lists with two operands, and that each pair of operands must have the property that their difference when simplified, equals zero.

•	This help page first gives a formal grammatical description of the valid structured verifications, then notes on some of the special verifications, and lastly, examples.

•	In the formal definition below, read "::=" to mean "is defined to be", "\|" to mean "or", and "*" to mean "zero or more occurrences of".

	Syntax	Matches

verification ::=	{ verification* }	alternation; any of the verifications
	\| [ verification* ]	a list of the given verifications
	\| complex(numeric)	match complex numerical constants exactly
	\| string	match strings exactly
	\| verification = verification	an equation of the corresponding verifications
	\| verification <> verification	an inequality compared with given verifications
	\| verification < verification	a relation compared with given verifications
	\| verification <= verification	a relation compared with given verifications
	\| verification > verification	a relation compared with given verifications
	\| verification >= verification	a relation compared with given verifications
	\| verification .. verification	a range compared with given verifications
	\| verification and verification	an AND of the corresponding verifications
	\| verification or verification	an OR of the corresponding verifications
	\| not verification	a NOT of the corresponding verification
	\| verification &+ verification ...	a sum of the corresponding verifications
	\| verification &* verification ...	a product of the corresponding verifications
	\| verification &. verification ...	a dot product of the corresponding verifications
	\| verification ^ verification	a power compared with the given verifications
	\| fcnverification	a function or special verification

fcnverification ::=	set(verification)	sets of elements compared with the given verification
	\| list(verification)	lists of elements compared with the given verification
	\| `&+`(verification)	a sum of terms of the given verifications
	\| `&*`(verification)	a product of factors of the given verifications
	\| specfunc(verification,foo)	the function foo with arguments compared with the given verification
	\| anyfunc(verification*)	any functions with arguments compared with the given verifications
	\| function(verification)	any function with arguments compared with given verification
	\| name(verification)	any name with a value of the given verification
	\| foo(verification*)	a verification defined by a procedure addverify(foo::name, bar::procedure)
	\| foo(verification*)	the function foo with arguments compared with the given verifications

•	The square brackets [ and ] are used to check for a fixed argument sequence. The verification checks the equality of two lists, each with exactly 2 arguments, the first checked with simple equality and the second with simplify.

•	The set brackets { and } are used for alternation. The verification {set(float(10)),list(float(10))} matches either lists or sets of floating-point numbers which are considered equal if they are within 10 units in the last place.

•	The verification does a simple comparison.

•	The verifications compares two objects, complex(numeric) or string, to the expression expr.

•	The verification matches any two functions with arguments where the arguments agree according to the appropriate verifications.

•	The verification specfunc(ver, n) matches functions with 0 or more arguments where the arguments agree according to the verification ver. Thus verify(f, g, specfunc(ver, n)) is equivalent to all five of the forms, type(f, function), type(g, function), , , and verify([op(f)], [op(g)], list(ver)).