symantic

This is an experimental library for composing, parsing, typing, compiling, transforming and interpreting a custom DSL (Domain-Specific Language).

Features

Those custom DSL can express a subset of GHC's Haskell type system:

• first class functions (aka. lambdas),
• chosen monomorphic types (like Bool or Maybe),
• chosen rank-1 polymorphic types (like (Maybe a)),
• chosen type class instances,
• chosen type family instances,
• and chosen type constraints;

where "chosen X" means declared in Haskell and selected when composing the DSL.

In particular, this library is currently not able to:

• do type inferencing for the argument of lambdas (they must all be explicitely annotated, aka. Church-style),
• do pattern matching (aka. case) (but Church-encoding functions are often enough),
• do rank-N polymorphic types (aka. non-prenex forall, like (forall s. ST s a) -> a).

And by itself, the DSL is only able to define new terms to be interpreted, no new types, or other type-level structures.

Warning

Please be aware that despite its using of powerful ideas from clever people, this remains a FUND-LESS SINGLE-PERSON EXPERIMENTAL LIBRARY. Meaning that it IS NOT heavily tested and documented, DOES NOT have a strong commitment to preserving backward compatibility, MAY FAIL to comply with the PVP, and CAN die without notice. You've been warned.

Use cases

The main goal of this library is to enable the runtime interpretation of terms, type-checked according to some types defined at composing-time (ie. GHC's compile-time).

Using a DSL enables to limit expressiveness in order to ease analysis. Here the idea is that the more complex logic shall remain written in Haskell, and then this library used to project an interface into a DSL (using GHC's Haskell as a FFI (Foreign Function Interface)). This in order to give runtime users the flexibility to write programs not requiring a full-blown Haskell compiler, yet enabling enough flexibility to let them express complex needs with a reasonably advanced type-safe way and a controlled environment of primitives.

Typical use cases

• Enabling runtime users to enter some Haskell-like expressions (maybe with a more convenient syntax wrt. the domain problem) without using at runtime all the heavy machinery and ecosystem of GHC (eg. by using hint), but still leaning on primitive functions coded in GHC's Haskell.
• Limiting those expressions to be built from well-controlled expressions only.
• Run some analyzes/optimizations on those well-controlled expressions.
• Report errors specific to the domain problem.

Usage

Please learn how to use this library by reading example source files in test/ in symantic-lib in Git repository.

These test files use megaparsec as parser (see test/Testing/Megaparsec.hs) and a default grammar somehow sticking to Haskell's, but staying context-free (so in particular: insensitive to the indentation), and supporting prefix and postfix operators. This grammar — itself written as a symantic embedded DSL with symantic-grammar — can be reused to build other ones, is not bound to a specific parser, and can produce its own EBNF rendition.

Acknowledgements

This library would probably be much worse than it is without the following seminal works:

• Finally Tagless by Jacques Carette, Oleg Kiselyov, and Chung-chieh Shan.
• Dependent Types in Haskell by Richard A. Eisenberg.
• A reflection on types by Simon Peyton Jones, Stephanie Weirich, Richard A. Eisenberg and Dimitrios Vytiniotis.
• Typeable by Ben Gamari and others.

Main ideas

• Symantic DSL. Terms are encoded in the Tagless-Final way (aka. the symantic way) which leverages the type class system of Haskell — instead of using data types — to form an embedded DSL. More specifically, a class encodes the syntax of terms (eg. Sym_Bool) and its class instances on a dedicated type encodes their semantics (eg. (Sym_Bool Eval) interprets a term as a value of its type in the host language (Bool in Haskell here), or (Sym_Bool View) interprets a term as a textual rendition, etc.).

  DSL are then composed/extended by selecting those symantic classes (and in an embedded DSL those could even be automatically inferred, when NoMonomorphismRestriction is on). Otherwise, when using symantics for a non-embedded DSL — the whole point of this library — the classes composing the DSL are selected manually at GHC's compile-time, through the type-level list ss given to readTerm.

  Moreover, those symantic terms are parameterized by the type of the value they encode, in order to get the same type safety as with plain Haskell values. Hence the symantic classes have the higher kind: ((* -> *) -> Constraint) instead of just (* -> Constraint).

  Amongst those symantics, Sym_Lambda introduces lambda abstractions by an higher-order approach, meaning that they directly reuse GHC's internal machinery to abstract or instantiate variables, which I think is by far the most efficient and simplest way of doing it (no (generalized or not) DeBruijn encoding like in bound's Monads).

• Singleton for any type. To typecheck terms using a (Type src vs t) which acts as a singleton type for any Haskell type index t of any kind, which is made possible with the dependant Haskell extensions: especially TypeFamilies, GADTs and TypeInType.

• Type constants using Typeable. Type constant could be introduced by indexing them amongst a type-level list, but since they are monomorphic types, using Typeable simplifies the machinery, and is likely more space/time efficient, including at GHC-compile-time.

• Type variables using a type-level list. Handling type variables is done by indexing them amongst a vs type-level list, where each type variable is wrapped inside a Proxy to handle different kinds. Performing a substitution (in substVar) preserves the type index t, which is key for preserving any associated Term. Unifying type variables is done with unsafeCoerce (in unifyType), which I think is necessary and likely safe.

Main extensions

• AllowAmbiguousTypes for avoiding a lot of uses of Proxy.
• ConstraintKinds for type lists to contain Constraints, or reifying any Constraint as an explicit dictionary Dict, or defining type synonym of type classes, or merging type constraints.
• DataKinds for type-level data structures (eg. type-level lists).
• DefaultSignatures for providing identity transformations of terms, and thus avoid boilerplate code when a transformation does not need to alter all semantics. Almost as explained in Reducing boilerplate in finally tagless style.
• GADTs for knowing types by pattern-matching terms, or building terms by using type classes.
• PolyKinds for avoiding a lot of uses of Proxy.
• Rank2Types or ExistentialQuantification for parsing GADTs.
• TypeApplications for having a more concise syntax to build Type (eg. tyConst @Bool).
• TypeFamilies for type-level programming.
• TypeInType (introduced in GHC 8.0.1) for Type to also bind a kind equality for the type t it encodes. Which makes the type application (TyApp) give us an arrow kind for the Haskell type constructor it applies an Haskell type to, releaving me from tricky workarounds.
• UndecidableInstances to relax the checks that the type-level programming does terminate.

Bugs

There are some of them hidding in there, and the whole thing is far from being perfect… Your comments, problem reports, or questions, are welcome! You have my email address, so… just send me some emails :]

To do

• Study to which point type inferencing is doable, now that Type is powerful enough to contain TyVars.
• Study to which point error messages can be improved, now that there is a Source carried through all Kinds or Types, it should enable some nice reports. Still, a lot of work and testing remain to be done, and likely some ideas to find too…
• Add more terms in symantic-lib.
• Add more transformations.
• Study how to list class instances.
• Study where to put INLINE, INLINEABLE or SPECIALIZE pragmas.
• Study how to support rank-N polymorphic types, special cases can likely use the boxed polymorphism workaround, but even if GHC were supporting impredicative types, I'm currently clueless about how to do this.