blessing - Why are there two different forms of the mitzvah brachot ("l-" and "al")?

Some mitzvah brachot are of the form ...vitzivanu "l'X" ("to X", infinitive verb), and others are of the form "al X" ("upon X", gerundive verb). I particularly noticed this during Sukkot with two similar ones in proximity; it's "likro et hahallel" but "al mikra megillah" (which led me in a roundabout way to ask this question). Why the difference?

I first thought that it might be the difference between something we do actively (we all say hallel) and something we experience more passively (most of us don't personally read the megillah; someone does on our behalf), but that doesn't work -- "al netilat (yadayim, lulav)" and "al achilat (matzah, maror)" are counter-examples. The difference also doesn't seem to be d'oraita versus d'rabbanan; both forms show up in both categories.

Is there significance, or in each case did the rabbis just choose between two equally-appropriate formulations and it doesn't mean anything more than that?

Answer

The Avudraham discusses this at length. He brings several different classification methods offered by different people. It seems that each classification method covers a large percentage of the cases, but there are some exceptions. The Abudraham then discusses some of the exceptions.

1. 
   

   First he brings the opinion of Rabbeinu Tam (brought in yydl's answer):

   
   
   
   
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     If the mitzvah is (completely) done right away, we say "Al". Some examples:

     
     
     
     
     • על אכילת מ צ ה .
     
     
     • על אכילת מ ר ו ר
     
     
     • על מקרא מגלה.
     
     
     
     
     
   
   
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     If the mitzvah requires some waiting before it is done (i.e. the single action does not complete the mitzvah), you say "L'". Some examples:

     
     
     
     
     • ‫‫לישב בסוכה‬
     
     
     • ‫ לשמוע קול שופר‬(There are pauses before it's done)
     
     
     • Hallel (You need to wait for people to respond)
     
     
     
     
   
   
   
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     Furthermore, Rabbeinu Tam offers another reason why Hallel is "L'Kro" and not "Al Mikrat Hallel" (or some variation). Any Mitzvah that is not a constant obligation you do not say "Al". Since we are commanded to say Hallel after surviving any calamity (as opposed to specific times) it is not considered a constant obligation.

     
     
     
     
     • The Abudraham does not like this answer, saying that this classification doesn't seem to have any logic behind it, and most of the reasons given for the exceptions seem a little weak. He also brings cases that contradict Rebbeinu Tam's classification system.
     
     
     
     
   
   
   
   


2. 
   

   Then he brings the Rambam (Berachot 11:15), who makes the following distinctions. The Rambam holds that the blessing may change depending on who is saying it:

   
   
   
   
   
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     If you (a) do the mitzvah for yourself and (b) it is an obligation, you say "L'", otherwise you say "Al". For example:

     
     
     
     
     • Circumcision
     
     
     • Making a fence around a roof
     
     
     
     
   
   
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     If you do those same Mitzvot as an emissary for someone else, you would say "Al

     
     
     
   
   
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     If you are doing a mitzvah for yourself and others:

     
     
     
     
     • If it is an optional Mitzvah, you say "Al" - e.g. Eiruv
     
     
     • If it is an obligatory mitzvah, you say "L'" - e.g. Shofar
     
     
     
     
   
   
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     If it is an optional mitzvah, you say "Al", whether you are doing it yourself or not. For example: Shechita

     
     
     
   
   
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     If the blessing precedes the action, you say "L'". The the action precedes the blessing you say "Al". For Example:

     
     
     
     
     • Since just picking up the Arba Minim fulfills your obligation, you say "Al Netilat Lulav". If you say the blessing before you pick up the Minim, you say "Litol Lulav"
     
     
     
     
   
   
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     (The Ra'avad questions the Rambam's classification. Among the distinctions he offers and ultimately rejects is the distinction between Rabinical and Biblical commandments. The Raavad also brings cases that don't conform to the Rambam's classification system)

     
     
   
   
   
   
   


3. 
   

   Abudraham the brings another opinion he does not name. It appears to be the Riva mentioned in @msh10's answer.

   
   
   
   
   • If the Mitzvah (a) can be done by proxy (shliach), and (b) will be done in the future (L'Habah) you say "Al"
   
   
   • If the Mitzvah (a) can not be done by proxy (shliach), and (b) will be done in the future (L'Habah) you say "L'"
   
   
   • If the Mitzvah (a) can be done by proxy (shliach), and (b) was done in the past (L'She'avar) you say "L'"
   
   
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     If the Mitzvah (a) can not be done by proxy (shliach), and (b) was done in the past (L'She'avar) you say "Al"

     
     
     
   
   
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     The exceptions are then discussed.

     
     
   
   
   
   

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So, with regards to the Sukkot we say "Al Netilat Lulav", but say "Leisheiv BaSukkah":

• According to Rabbienu Tam, the mitzvah of Lulav is over as soon as you pick up the lulav, but the mitzvah of sitting in a Sukkah extends.


• According to the Rambam, both Sukkah and Lulav are Mitzvot you are personally obligated to do, but as soon as you pick up the Lulav you've fulfilled your obligation, so you say "Al Netilat Lulav", but if you say the blessing before you pick it up you say "LiTol Lulav"


• According to the third opinion, you say "Leishev BaSukah" since the mitzvah can't be done by proxy and the main mitzvah is eating and drinking in the Sukkah, which is done after the blessing. The blessing on the Lulav on the other hand, is only done after you've already picked it up (thus fulfilling your obligation), and thus you say "Al Netilat Lulav"

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