I would like to broaden my knowledge of programming. (…) I thought I would pose the question here, along with several stipulations about the type of language I am looking for. Some are subjective, some are intended to ease the transition from Haskell.
Strong type system. (…) It also makes informally reasoning about the correctness of my program easier. I’m concerned with correctness, not efficiency.
Emphasis on recursion rather than iteration. (…)
You may be easing the transition a bit too much here, I’m afraid. The very strict type system and purely functional style are characteristic of Haskell and pretty much anything resembling a mainstream programming language will require compromising at least somewhat on one of these. So, with that in mind, here are a few broad suggestions aimed at retaining most of what you seem to like about Haskell, but with some major shift.
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Disregard practicality and go for “more Haskell than Haskell”: Haskell’s type system is full of holes, due to nontermination and other messy compromises. Clean up the mess and add more powerful features and you get languages like Coq and Agda, where a function’s type contains a proof of its correctness (you can even read the function arrow
->as logical implication!). These languages have been used for mathematical proofs and for programs with extremely high correctness requirements. Coq is probably the most prominent language of the style, but Agda has a more Haskell-y feel (as well as being written in Haskell itself). -
Disregard types, add more magic: If Haskell is sorcery, Lisp is the raw, primal magic of creation. Lisp-family languages (also including Scheme and Clojure) have nearly unparalleled flexibility combined with extreme minimalism. The languages have essentially no syntax, writing code directly in the form of a tree data structure; metaprogramming in a Lisp is easier than non-meta programming in some languages.
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Compromise a bit and move closer to the mainstream: Haskell falls into the broad family of languages influenced heavily by ML, any of which you could probably shift to without too much difficulty. Haskell is one of the strictest when it comes to correctness guarantees from types and use of functional style, where others are often either hybrid styles and/or make pragmatic compromises for various reasons. If you want some exposure to OOP and access to lots of mainstream technology platforms, either Scala on the JVM or F# on .NET have a lot in common with Haskell while providing easy interoperability with the Java and .NET platforms. F# is supported directly by Microsoft, but has some annoying limitations compared to Haskell and portability issues on non-Windows platforms. Scala has direct counterparts to more of Haskell’s type system and Java’s cross-platform potential, but has a more heavyweight syntax and lacks the powerful first-party support that F# enjoys.
Most of those recommendations are also mentioned in other answers, but hopefully my rationale for them offers some enlightenment.