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Line 40: A ''position'' is defined by a sequence of natural numbers. The empty sequence is denoted by ε and the sequence constructor by ‘.’. ''Example.'' — Position 2.1 in the expression {{math\|(+ (&lowast; ''e''<sub>1</sub> ''e''<sub>1</sub>) (&lowast; ''e''<sub>2</sub> ''e''<sub>2</sub>))}} is the place occupied by the first occurrence of {{math\|{{var\|e}}<sub>2</sub>}}. Expression {{mvar\|e}} ''with'' expression {{mvar\|e′}} ''inserted at'' position {{mvar\|p}} is denoted by {{math\|''e''[''e′''/''p'']}} and defined by Line 46: : {{math\|''e''[''e′''/''i''.''p''] ≡ <Ω ''e''<sub>1</sub> … ''e''<sub>''i''</sub>[''e′''/''p''] … ''e''<sub>''n''</sub>>}} if {{math\|''e'' ≡ <Ω ''e''<sub>1</sub> … ''e''<sub>''i''</sub> … ''e''<sub>''n''</sub>>}} else undefined, for all operators {{math\|Ω}} and expressions {{math\|{{var\|e}}<sub>1</sub>, …, {{var\|e}}<sub>{{var\|n}}</sub>}}. ''Example.'' — If {{math\|''e'' ≡ (+ (&lowast; ''e''<sub>1</sub> ''e''<sub>1</sub>) (&lowast; ''e''<sub>2</sub> ''e''<sub>2</sub>))}} then {{math\|''e''[''e''<sub>3</sub>/2.1] ≡ (+ (&lowast; ''e''<sub>1</sub> ''e''<sub>1</sub>) (&lowast; ''e''<sub>3</sub> ''e''<sub>2</sub>))}}. Position {{mvar\|p}} is ''purely referential'' in expression {{mvar\|e}} is defined by

Referential transparency: Difference between revisions