LiquidHaskell (LH) refines Haskell's types with logical predicates that let you enforce critical properties at compile time. (Hover on images to animate.)

Guarantee Functions are Total

LH warns you that head is not total as it is missing the case for [] and checks that it is total on NonEmpty lists. (more...)

The input contract propagates to uses of head which are verified by ensuring the arguments are NonEmpty.

Keep Pointers Within Bounds

LH lets you avoid off-by-one errors that can lead to crashes or buffer overflows. (more...)

Dependent contracts let you specify, e.g. that dotProduct requires equal-sized vectors.

Avoid Infinite Loops

LH checks that functions terminate and so warns about the infinite recursion due to the missing case in fib. (more...)

Metrics let you check that recursive functions over complex data types terminate.

Enforce Correctness Properties

Write correctness requirements, for example a list is ordered, as refinements. LH makes illegal values be unrepresentable. (more...)

LH automatically points out logic bugs, and proves that functions return correct outputs for all inputs.

Prove Laws by Writing Code

Specify laws, e.g. that the append function ++ is associative, as Haskell functions.

Verify laws via equational proofs that are plain Haskell functions. Induction is simply recursion, and case-splitting is just pattern-matching. (more...)