Here we give two examples of defining functions by mutual recursion in Axiom ## Recursion between Separate DomainsMutual recursion between domains is allowed. However, compiling such domains is a little tricky. Fist one need to compile files in "bootstrap mode". That is one needs to give: )boot $bootStrapMode := true Then compile domains first time using )boot $bootStrapMode := false and angain use Note, that goal of "bootstrap mode" compilation is to break cycles, so for example if there are two mutially dependent domains, then it is enough to compile in "bootstrap mode" just one. This process can not be used on the wiki, because wiki software automatically issues compilation commands. Instead one can use manual workaround which we describe below. First we show how to define two separate domains We must start with a "bootstrap" definition of spad )abbrev domain EVEN even even(): E == I where E == with parity: Integer -> Boolean I == add parity(n) == true spad Compiling FriCAS source code from file /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3342984326569348053-25px001.spad using old system compiler. EVEN abbreviates domain even ------------------------------------------------------------------------ initializing NRLIB EVEN for even compiling into NRLIB EVEN compiling exported parity : Integer -> Boolean EVEN;parity;IB;1 is replaced by QUOTET Time: 0.01 SEC. Now we can define spad )abbrev domain ODD odd odd(): E == I where E == with parity: Integer -> Boolean I == add parity(n:Integer) == -- output("ODD", spad Compiling FriCAS source code from file /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7392352806104595030-25px002.spad using old system compiler. ODD abbreviates domain odd ------------------------------------------------------------------------ initializing NRLIB ODD for odd compiling into NRLIB ODD compiling exported parity : Integer -> Boolean Time: 0.01 SEC. But the bootstrap definition of spad )abbrev domain EVEN even even(): E == I where E == with parity: Integer -> Boolean I == add parity(n) == -- output("EVEN", spad Compiling FriCAS source code from file /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/8584362905457126194-25px003.spad using old system compiler. Illegal NRLIB EVEN.NRLIB claims that its constructor name is the domain even but even is already known to be the for package EVEN . EVEN abbreviates domain even ------------------------------------------------------------------------ initializing NRLIB EVEN for even compiling into NRLIB EVEN compiling exported parity : Integer -> Boolean Time: 0.01 SEC. Now we can test the new function: fricas parity(10)$even
Type: Booleanfricas parity(8)$odd
Type: Booleanfricas parity(-1111)$odd
Type: Boolean## Recursion within a Single Domain It is possible to write this same recursion as a domain that
exports two functions spad )abbrev domain PARITY Parity Parity(): Exports == Implements where Exports == with Even: Integer -> Boolean Odd: Integer -> Boolean Implements == add Odd(n: Integer) == n>0 => Even(n-1) n<0 => Even(n+1) false Even(n: Integer) == n>0 => Odd(n-1) n<0 => Odd(n+1) true spad Compiling FriCAS source code from file /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/2188084076688500475-25px005.spad using old system compiler. PARITY abbreviates domain Parity ------------------------------------------------------------------------ initializing NRLIB PARITY for Parity compiling into NRLIB PARITY compiling exported Odd : Integer -> Boolean Time: 0 SEC. Test fricas Even(10)$Parity
Type: Booleanfricas Odd(8)$Parity
Type: Booleanfricas Odd(-1111)$Parity
Type: Boolean |