Examples of Prop Type in a sentence
Specifically, it contains a full Pure Type System (PTS) with sorts S = Prop, Type , axioms A = Prop : Type , and product formation rules R = (s1, s2) s1, s2 S as formulated by Barendregt [2].
Specifically, it contains a full Pure Type System (PTS) with sorts S = Prop, Type , axioms A = Prop : Type , andproduct formation rules R = (s1, s2) s1, s2 S as formulated€by Barendregt [2].
The operation in question is that of deciding a proposition:Class Decision (P: Prop): Type := decide: sumbool P (¬ P).Here, sumbool is just the (informative) sum of proofs.Decision is a very general-purpose type class that also works for predicates.
The operation in question is that of deciding a proposition:Class Decision (P: Prop): Type := decide: sumbool P (¬ P).Here, sumbool is just the (informative) sum of proofs.{ }Decision is a very general-purpose type class that also works for predicates.
As a corollary, we obtain that for a function where the return type is a first-order inductive type, its erasure can be obtained separately, and will still evaluate to the correct value once applied to enough arguments.Note that, like in the extraction implemented currently in Coq, the rule Prop Type has to be disabled for type-checking (using the flag structure) to ensure erasability is stable by expansion.