#curry-howard

[eka-mark]

Note that natural language agrees with the correspondence between proofs and programs: it is natural to use the sentence "to apply a theorem" in the same manner as one uses the sentence "to apply a function." In both cases, we actually use the same App rule.

Interactive Theorem Proving and Program Development

Yves Bertot & Pierre Castéran

[csquotes-blog]

There is a strong analogy between using a named operation in a program regardless of "how it works" and using a theorem regardless of how it has been proved.

E. W. Dijsktra, Structured Programming