 
Summary: Categorical Semantics for LogicEnriched Type Theories
Robin Adams
Royal Holloway, University of London
TYPES 2011, 8 September 2011
Robin Adams (RHUL) Categorical Semantics for LTTs TYPES 2011 1 / 21
The CurryHoward Isomorphism
There are two facts that are both sometimes referred to as the
CurryHoward isomorphism. One is trivial, one is not.
Robin Adams (RHUL) Categorical Semantics for LTTs TYPES 2011 2 / 21
The CurryHoward Isomorphism
There are two facts that are both sometimes referred to as the
CurryHoward isomorphism. One is trivial, one is not.
Trivial Fact
It is possible to write a linear syntax for natural deduction proofs, and then
write P : for `P is a proof of (that depends on the free variables
and hypotheses )'
Robin Adams (RHUL) Categorical Semantics for LTTs TYPES 2011 2 / 21
The CurryHoward Isomorphism
There are two facts that are both sometimes referred to as the
CurryHoward isomorphism. One is trivial, one is not.
