APL was a notation before it was a program. Iverson used it on paper to describe algorithms, and the 1962 book A Programming Language had no running implementation behind it. APL\360 came later in the decade.
That order explains a lot. Right-to-left evaluation, no precedence table. One rule, because a notation for people can't ask readers to memorize a table. Symbols instead of keywords, because the page was the medium.
+/⍳10 is 55 with the default index origin. Read it the way it was meant. Plus reduction over the integers one to ten. No loop. No index variable. Nothing to be off by one.
The Turing lecture title says the rest. Notation as a Tool of Thought.
