:: a typeCtrl KGHC 9.10.3 · lts/ghc-9.10.x · c74966e · 2026-09-27
ModuleAgda-2.7.0.1Haskell2010
Solving size constraints under hypotheses.
The size solver proceeds as follows:
Get size constraints, cluster into connected components.
All size constraints that mention the same metas go into the same cluster. Each cluster can be solved by itself.
Constraints that do not fit our format are ignored. We check whether our computed solution fulfills them as well in the last step.
Find a joint context for each cluster.
Each constraint comes with its own typing context, which
contains size hypotheses j : Size< i. We need to find a
common super context in which all constraints of a cluster live,
and raise all constraints to this context.
There might not be a common super context. Then we are screwed, since our solver is not ready to deal with such a situation. We will blatantly refuse to solve this cluster and blame it on the user.
Convert the joint context into a hypothesis graph.
This is straightforward. Each de Bruijn index becomes a
rigid variable, each typing assumption j : Size< i becomes an
arc.
Convert the constraints into a constraint graph.
Here we need to convert MetaVs into flexible variables.
Run the solver
Convert the solution into meta instantiations.
Double-check whether the constraints are solved.
Flag to control the behavior of size solver.
DefaultToInftyInstantiate all unconstrained size variables to ∞.
DontDefaultToInftyLeave unconstrained size variables unsolved.
Eq DefaultToInftyDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.SolveOrd DefaultToInftyDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.SolveShow DefaultToInftyDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.SolveSolve size constraints involving hypotheses.
TODO: this does not actually work!
We would like to use a constraint c created in context Δ from module N
in the current context Γ and current module M.
Δ is module tel Δ₁ of N extended by some local bindings Δ₂.
Γ is the current context.
The module parameter substitution from current M to N be
Γ ⊢ σ : Δ₁.
If M == N, we do not need the parameter substitution. We try raising.
We first strengthen Δ ⊢ c to live in Δ₁ and obtain c₁ = strengthen Δ₂ c.
We then transport c₁ to Γ and obtain c₂ = applySubst σ c₁.
This works for different modules, but if M == N we should not strengthen
and then weaken, because strengthening is a partial operation.
We should rather lift the substitution σ by Δ₂ and then
raise by Γ₂ - Δ₂.
This "raising" might be a strengthening if Γ₂ is shorter than Δ₂.
(TODO: If the module substitution does not exist, because N is not
a parent of M, we cannot use the constraint, as it has been created
in an unrelated context.)
A hazardous hack, may the Gods have mercy on us.
To cast to the current context, we match the context of the
given constraint by CtxId, and as fallback, by variable name (douh!).
This hack lets issue 2046 go through.
Return the size metas occurring in the simplified constraints.
A constraint like ↑ _j =< ∞ : Size simplifies to nothing,
so _j would not be in this set.
Solve a cluster of constraints sharing some metas.
Collect constraints from a typing context, looking for SIZELT hypotheses.
Convert size constraint into form where each meta is applied
to indices n-1,...,1,0 where n is the arity of that meta.
X[σ] <= t becomes X[id] <= t[σ^-1]
X[σ] ≤ Y[τ] becomes X[id] ≤ Y[τ[σ^-1]] or X[σ[τ^1]] ≤ Y[id]
whichever is defined. If none is defined, we give up.
Cf. SizedTypes.oldCanonicalizeSizeConstraint.
Fixes (the rather artificial) issue 300. But it is unsound when pruned metas occur and triggers issue 1914. Thus we deactivate it. This needs to be properly implemented, possibly using the metaPermuatation of each meta variable.
Turn a constraint over de Bruijn indices into a size constraint.
Turn a term into a size expression.
Returns Nothing if the term isn't a proper size expression.