Agda- A dependently typed functional programming language and proof assistant

Safe HaskellNone




match :: [Clause] -> [Arg Pattern] -> Permutation -> Match NatSource


  1. the function clauses cs 2. the patterns ps and permutation perm of a split clause

we want to compute a variable index of the split clause to split on next.

First, we find the set cs' of all the clauses that are instances (via substitutions rhos) of the split clause.

In these substitutions, we look for a column that has only constructor patterns. We try to split on this column first.

Match the given patterns against a list of clauses

data MPat Source

We use a special representation of the patterns we're trying to match against a clause. In particular we want to keep track of which variables are blocking a match.

data Match a Source

If matching is inconclusive (Block) we want to know which variables are blocking the match.


Yes a

Matches unconditionally.


Definitely does not match.

Block BlockingVars

Could match if non-empty list of blocking variables is instantiated properly.


Functor Match 
Monoid a => Monoid (Match a)

Combine results of checking whether function clause patterns covers split clause patterns.

No is dominant: if one function clause pattern is disjoint to the corresponding split clause pattern, then the whole clauses are disjoint.

Yes is neutral: for a match, all patterns have to match.

Block accumulates variables of the split clause that have to be instantiated to make the split clause an instance of the function clause.

type BlockingVar = (Nat, Maybe [QName])Source

Nothing means there is an overlapping match for this variable. Just cons means that it is an non-overlapping match and cons are the encountered constructors.

zipBlockingVars :: BlockingVars -> BlockingVars -> BlockingVarsSource

Left dominant merge of blocking vars.

choice :: Match a -> Match a -> Match aSource

choice m m' combines the match results m of a function clause with the (already combined) match results $m'$ of the later clauses. It is for skipping clauses that definitely do not match (No). It is left-strict, to be used with foldr. If one clause unconditionally matches (Yes) we do not look further.

matchLits :: Clause -> [Arg Pattern] -> Permutation -> BoolSource

Check if a clause could match given generously chosen literals

matchClause :: MatchLit -> [Arg MPat] -> Nat -> Clause -> Match NatSource

matchClause mlist qs i c checks whther clause c number i covers a split clause with patterns qs.

matchPats :: MatchLit -> [Arg Pattern] -> [Arg MPat] -> Match ()Source

matchPats mlist ps qs checks whether a function clause with patterns ps covers a split clause with patterns qs

matchPat :: MatchLit -> Pattern -> MPat -> Match ()Source

matchPat mlit p q checks whether a function clause pattern p covers a split clause pattern q. There are three results: Yes () means it covers, because p is a variable pattern or q is a wildcard. No means it does not cover. Block [x] means p is a proper instance of q and could become a cover if q was split on variable x.