Soundness of the Logical Framework for Its Typed Operational Semantic

Polarized Subtyping for Sized Types

“…al. (1999), bear strong resemblances to Goguen's typed operational semantics (Goguen, 1995(Goguen, , 1999.…”

Typed Operational Semantics for Dependent Record Types

“…For example, in TOS, the following judgement Γ |= M → N → P : A informally asserts that, among other things, N and P are the weak-head normal form and the normal form of the term M, respectively. 3 For the logical framework LF, for example, its corresponding TOS has been studied [Gog99] and its inference rules are given in Appendix B. Since many meta-theoretic properties Basic f orms: Abbreviated f orms: of a type theory are concerned with its computational behaviour, it is not a surprise that TOS provides an effective approach to the meta-theory of type theories.…”

“…By induction on derivations. For the cases of LF-rules, see [Gog99]. We consider the following two cases about record types.…”

“…H. Goguen [Gog94,Gog99] has developed a method called typed operational semantics (TOS for short) to prove meta-theoretic properties of type theories, including strong normalisation, Church-Rosser and subject reduction. In this paper, using the TOS approach, we study the meta-theoretic properties of a type system with dependent record types.…”

Untyped Algorithmic Equality for Martin-Löf’s Logical Framework with Surjective Pairs

“…Although a syntactical proof should be possible following Goguen [Gog99,Gog05], we prefer a model construction since it is more apt to extensions of the type theory.…”