Lectures onType Theory
Type formers and terms
appendix sectionnotation

Type formers and terms

In the Timpl entries below, (e) and (r) range over explicitness and relevance.

symbol meaning first
symbol meaning first
x:AB dependent product chapter 22
x:Ae,rB product with explicitness and relevance chapter 48
ΓA˙U suspended universe-formation guard chapter 50
x:AB dependent sum chapter 27
Wx:AB well-founded tree type chapter 28
EqA(a,b) extensional equality type chapter 35
IdA(a,b) identity type; extensional only in a declared source calculus chapter 28
a=Ab path-language form of identity chapter 62
1,0,2,N unit, empty, Boolean, and natural-number types chapter 27chapter 28
λ(x:A).b kernel abstraction with domain annotation chapter 22
λe,rx.b surface abstraction with binder metadata chapter 48
λe,r(x:A).b annotated abstraction with binder metadata chapter 48
fe,ra application with copied binder metadata chapter 48
λx.b ordinary unannotated abstraction where the fixed syntax permits it chapter 2
ΛX.b PTS spelling of explicit type abstraction chapter 22
λu::κ.A PTS spelling of constructor abstraction chapter 22
(a,b) dependent pair chapter 27
pr1,pr2 first and second projection chapter 27
the element of 1 chapter 27
tt,ff Boolean constructors chapter 28
0,suc natural-number constructors chapter 28
inl,inr coproduct constructors chapter 28
sup W-type constructor chapter 28
indA dependent eliminator for A chapter 28
recA nondependent recursor for A chapter 28
rec0 schematic recursor from 0; expected type fixes its target chapter 28
TD extensional source calculus for Dybjer’s theorem chapter 28
funext function extensionality map in TD chapter 28
νX natural container-normal-form isomorphism for Φ(X) chapter 28
ιΦ initial algebra structure transported to a W-type chapter 28
refl reflexivity constructor chapter 30
J identity eliminator chapter 30
K uniqueness-of-identity eliminator chapter 30

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