Sentence examples for proof terms from inspiring English sources

Proofs (justifications) are represented by proof terms which do not contain individual variables.

Proof terms in \(\mathsf{LP}\) are nothing but BHK terms understood as classical proofs.

Hierarchy constructors are defined in the type system to construct proof terms capturing hierarchical structure.

Security policies are, in Aglet, proof terms that ensure some security policy.

In addition to \ \textsf{LP}\) operations there is one more series of operations on proof terms, \({\sf gen}_x t)\), corresponding to generalization over individual variable \(x\).

As part of a project to provide a constructive semantics for intuitionistic logic, a formal logic of explicit proof terms was presented in Artemov 2001.

In this respect, \ \Box\) cannot be replaced by any specific proof term depending on \(t\) only and (6) cannot be presented in an entirely explicit justification-style format.

However within the framework of Justification Logic, building on the proofs of \(X\) and of \(X\leftrightarrow Y\), we can construct a proof term \(f u,v)\) which represents the proof of \(Y\) and so \(f u,v Y\) is provable.

The proof normalization approach views the state of a computation as a proof term and the process of computing as normalization (known alternatively as β-reduction or cut-elimination).

However, writing a proof term whose type is that of a logical formula can be a hard task, even for very simple propositions.

The command Theorem allows us to state some formula that we want to prove and it starts the interactive proof mode, in which tactics can be used to produce the wanted proof term.