Importantly, theoretical sentences can only contain theoretical and logical terms; correspondence sentences involve all three kinds of terms; and observational sentences comprise only logical and observational terms.
The resulting view correspondence as isomorphism between properly analyzed truthbearers and facts avoids assigning strange objects to such phrases as "the average husband", "the sake of", and "the present king of France"; but the view remains committed to logically complex facts and to logical objects corresponding to the logical constants.
To see this, we need to outline the correspondence between logical operators and operations on types in CDTT obtained by implementing the "propositions-as-types" doctrine.
The bit sequence function is based on the logical operators, which is in correspondence with the bit sequence.
In the formulas-as-types analogy which is so popular and fruitful in theoretical computer science, a logical system is put in correspondence with a typed computational device (like typed lambda calculus), by associating to each proof of a formula a program having as type that very formula.
Summarised, the GM method resembles the idea of the BG algorithm (see Section 2.3.2), although no building of new logical integrities from previously found correspondences takes place here, and consequently no M N, M > 1 correspondences, i.e. no matches for complete routes are constructed.
This process also facilitates computing M 1 or M N, M > 1 correspondences (i.e., matching of complete routes): for this purpose, new logical integrities are built from previously found correspondences, which are then subject to new applications of BG in subsequent steps.
Versions of these views are defended by the logical atomists (see the entry on the correspondence theory of truth and section 2.4.2 below).
Theorem proving in Coq follows the ideas of the so-called BHK-correspondence,1 where types represent logical formulas and (lambda )-terms represent proofs [49].
