W.A. Howard. Assignment of ordinals to terms for primitive recursive functionals of nite type. In Myhill J. Vesley R.E. Kino, A., editor, Intuitionism and Proof Theory: Bufallo N.Y. 1968. Home/Search Document Not in Database Summary Related Articles Check |
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A lambda-to-CL Translation for Strong Normalization - Akama (1997) (1 citation) (Correct)
....of sn and weakly normalizing (wn) to be separate (recall the conservation theorem (Corollary 11.3. 5 of [3] Our translation occurred to the author, when the author attempted to prove the sn of an annoying type theory by adapting Howard s sn proof by assigning ordinal numbers to typed terms [10]. Our translation can be regarded as his assignment to terms of not ordinal numbers but sn cl terms. To explain the first use of our translation, we first review Howard s proof, which is not wellknown but is an important work. The importance of his proof is that it relates two consistency proofs ....
....c , we have the reflection part of the Equivalence theorem. Remark 2.6 Someone may wonder whether A fi B implies A i iw B i . But this does not hold: take A j f: x: f)x; B j f: f . Remark 2. 7 The mapping J0K c is inspired by Howard s sn proof of typed calculus for prf(Section 4 of [10]) He introduced a mapping from terms to sets of vectors of ordinals based on a complicated application operator, a variable binder and a well founded partial order on ordinal vectors. His assignment system consists of axioms for redex constants, the (atom) axiom and (app) rule above, and the ....
W.A. Howard. Assignment of ordinals to terms for primitive recursive functionals of finite type. In A. Kino, J. Myhill, and R. Vesley, editors, Intuitionism and Proof Theory, pages 443--458. North-Holland, 1970.
The AMEN architecture. - Peter Hancock Abandoned (Correct)
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W.A. Howard. Assignment of ordinals to terms for primitive recursive functionals of nite type. In Myhill J. Vesley R.E. Kino, A., editor, Intuitionism and Proof Theory: Bufallo N.Y. 1968.
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