E. Palmgren. A categorical version of the BHK-interpretation. Technical report, Institut Mittag-Leer, The Royal Swedish Academy of Sciences, 2001. Home/Search Document Not in Database Summary Related Articles Check |
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Propositions as [Types] - Awodey, Bauer (2001) (1 citation) (Correct)
.... Q n:N P m:N Eq(2m; n) P m:N Eq(2m 1; n) does not carry any computational content at all it just witnesses the fact that every number is even or odd. The bracket types which we consider are essentially the same as the mono types of Maietti [Mai98] in a suitable setting. Palmgren [Pal01] formulated a BHK interpretation of intuitionistic logic and used image factorizations, which are used in the semantics of our bracket types, to relate the BHK interpretation to the standard category theoretic interpretation of propositions as subobjects. Aczel and Gambino [AG01] have promoted ....
....rules (a) A] A and (b) Q A B] Q A [B] In toposes (a) is Excluded Middle and (b) is the Axiom of Choice, which is strictly stronger. In type theory, therefore, b) cannot be proved from (a) consider a permutation model) while the converse inference is plausible, but unveri ed. See [Awo95, Pal01] for related results. 5. Alternate formulations. We can also consider a formulation of bracket types in which we have a new judgment P prop , expressing the fact that P is a proposition. The rules would then be as follows: A type [A] prop P prop P type a : A [a] A] q : ....
E. Palmgren. A categorical version of the BHK-interpretation. Technical report, Institut Mittag-Leer, The Royal Swedish Academy of Sciences, 2001.
Propositions as [Types] - Awodey, Bauer (2001) (1 citation) (Correct)
No context found.
E. Palmgren. A categorical version of the BHK-interpretation. Technical report, Institut Mittag-Leer, The Royal Swedish Academy of Sciences, 2001.
Propositions as [Types] - Awodey, Bauer (2001) (1 citation) (Correct)
No context found.
E. Palmgren. A categorical version of the BHK-interpretation. Technical report, Institut Mittag-Leer, The Royal Swedish Academy of Sciences, 2001.
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