Designing IDP4
Matthias van der Hallen - Vigor Day (5/6/15)
Predicates and Functions:
Two sides of the same coin?
Predicate P:
Function P'::𝒟→ 𝔹
Function F:
Predicate F' ⊆𝒟⨯𝒟
Still, the difference is important from a KR perspective
I choose you
Language designers: Often 'Choose one and stick with it'!
Haskell: Functions
Prolog: Predicates
edge :: Vertex -> Vertex -> Bool
edge E1 E2 = True
edge E1 E3 = True
edge E2 E3 = True
edge _ _ = Falsesum(zero, M, M).
sum(s(N), M, s(R)):-
sum(N, M, R).It seems reasonable to want both
Problems arise:
Can we, in the backend, treat functions and predicates in an agnostic way?
min { x : even(x) }Representing predicates as functions to Bool:
Representing functions as predicates:
We suddenly want minimum over domain, not range.
∃c,h: Sum(a,b,c) ∧ Sum(f,g,h)
∧ Sum(c,h,x).We do not want to lose function application.