Re: Evaluation details

*To*: mathgroup at smc.vnet.net*Subject*: [mg86790] Re: Evaluation details*From*: Szabolcs Horvát <szhorvat at gmail.com>*Date*: Fri, 21 Mar 2008 01:52:49 -0500 (EST)*Organization*: University of Bergen*References*: <200803191026.FAA05164@smc.vnet.net> <frt57r$sjs$1@smc.vnet.net>

Andrzej Kozlowski wrote: > On 19 Mar 2008, at 11:26, Mumbo Jumbo wrote: >> Hello, >> >> I am quite puzzled why a Mathematica statement >> x=x+1; >> causes infinite recursion. Since the ducumentation states that the >> lhs of >> this statement is not evaluated, it seems to me that the evaluation >> of the >> rhs should not lead to recursive evaluation. >> TIA, Yuri. >> >> > > The left hand side is not "pre-evaluated" but an OwnValue for x is > created: > > In[3]:= Block[{$RecursionLimit = 20}, x = x + 1] > "reclim" : "Recursion depth of 20 exceeded." > Out[3]= Hold[x + 1] + 19 > > In[4]:= OwnValues[x] > Out[4]= {HoldPattern[x] :> Hold[x + 1] + 19} > > and then the rhs is evaluated, this OwnValue applied, a new OwnValue > for x created etc. [note: message CCd to MathGroup] I believe that there is a little mistake here. The rhs is evaluated first, and the OwnValue is only created afterwards. However, the return value of Set[] is the same as the result of the evaluation of the rhs. Mathematica keeps evaluating expressions (including the return value of Set[]) until it reaches a fixed point. Now the OwnValue has already been defined, so a fixed point is never reached: Mathematica goes into infinite recursion. So, if the input Block[{$RecursionLimit = 20}, x = x + 1] is evaluated only once, the OwnValue will be simply x + 1 and not Hold[x + 1] + 19 In[1]:= Block[{$RecursionLimit = 20}, x = x + 1] During evaluation of In[1]:= $RecursionLimit::reclim: Recursion depth \ of 20 exceeded. >> Out[1]= 18 + Hold[1 + x] In[2]:= OwnValues[x] Out[2]= {HoldPattern[x] :> 1 + x} Evaluating the same input again creates the OwnValue cited above: In[3]:= Block[{$RecursionLimit = 20}, x = x + 1] During evaluation of In[3]:= $RecursionLimit::reclim: Recursion depth \ of 20 exceeded. >> Out[3]= 19 + Hold[1 + x] In[4]:= OwnValues[x] Out[4]= {HoldPattern[x] :> 19 + Hold[1 + x]} Szabolcs Horvát

**References**:**Evaluation details***From:*"Mumbo Jumbo" <mjumbo@gmail.com>