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Program Transformation in MartinLöf's Type Theory
, 1994
"... ion This rule allows the introduction of a new equation from an existing one, by means of the introduction of a local definition in terms of a where clause. If e 1 ' e 2 is an equation with e 2 containing the subexpression a, then the following equation can be derived: e 1 ' e 2 [a / u] where u = a ..."
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ion This rule allows the introduction of a new equation from an existing one, by means of the introduction of a local definition in terms of a where clause. If e 1 ' e 2 is an equation with e 2 containing the subexpression a, then the following equation can be derived: e 1 ' e 2 [a / u] where u = a, where in e 2 the subexpression a has been replaced by the variable u and abstracted in a where clause. As MTS does not provide local definitions in expressions where clauses will be represented by the expressions they abbreviate. An expression of the form e where u = a is really an abbreviation for ((u:e) a). So, given an equation e 1 ' e 2 , if its rhs e 2 can be seen as a function e applied to an object a, then the corresponding abstraction of the subexpression a was found. Hence, Abstraction can be defined by the rule: e 2 A ! B a 2 A h 1 2 e 1 'B e 2 h 2 2 e 2 'B apply(e; a) abstr (h 1 ; h 2 ) 2 e 1 'B apply(e; a) that is a simple application of transitivity (trans) of equality: ...