Agda.TypeChecking.Forcing

A constructor argument is forced if it appears as pattern variable in an index of the target.

For instance x is forced in sing and n is forced in zero and suc:

  data Sing {a}{A : Set a} : A -> Set where
    sing : (x : A) -> Sing x

  data Fin : Nat -> Set where
    zero : (n : Nat) -> Fin (suc n)
    suc  : (n : Nat) (i : Fin n) -> Fin (suc n)

At runtime, forced constructor arguments may be erased as they can be recovered from dot patterns. For instance, unsing : {A : Set} (x : A) -> Sing x -> A unsing .x (sing x) = x can become unsing x sing = x and proj : (n : Nat) (i : Fin n) -> Nat proj .(suc n) (zero n) = n proj .(suc n) (suc n i) = n becomes proj (suc n) zero = n proj (suc n) (suc i) = n

This module implements the analysis of which constructor arguments are forced. The process of moving the binding site of forced arguments is implemented in the unifier (see the Solution step of Agda.TypeChecking.Rules.LHS.Unify.unifyStep).

Forcing is a concept from pattern matching and thus builds on the concept of equality (I) used there (closed terms, extensional) which is different from the equality (II) used in conversion checking and the constraint solver (open terms, intensional).

Up to issue 1441 (Feb 2015), the forcing analysis here relied on the wrong equality (II), considering type constructors as injective. This is unsound for program extraction, but ok if forcing is only used to decide which arguments to skip during conversion checking.

From now on, forcing uses equality (I) and does not search for forced variables under type constructors. This may lose some savings during conversion checking. If this turns out to be a problem, the old forcing could be brought back, using a new modality Skip to indicate that this is a relevant argument but still can be skipped during conversion checking as it is forced by equality (II).

Documentation

computeForcingAnnotations :: QName -> Type -> TCM [IsForced]

Given the type of a constructor (excluding the parameters), decide which arguments are forced. Precondition: the type is of the form Γ → D vs and the vs are in normal form.

isForced :: IsForced -> Bool

nextIsForced :: [IsForced] -> (IsForced, [IsForced])