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PTS: Pure Type System for Erlang

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An intermediate Om language is based on Henk languages described first by Erik Meijer and Simon Peyton Jones in 1997. Later on in 2015 a new implementation of the ideas in Haskell appeared, called Morte. It used Boehm-Berarducci encoding of recursive data types into non-recursive terms. Morte has constants, variables, and kinds, is based only on pi, lambda and apply constructions, one axiom and four deduction rules. The Om language resembles Henk and Morte both in design and in implementation. This language indended to be small, concise, easily provable, clean and be able to produce verifiable programs that can be distributed over the networks and compiled at target with safe linkage.

$ curl -fsSL > mad
$ chmod +x mad"
$ ./mad dep com pla bun om

The PTS Systax is the following:

   <> ::= #option

    I ::= #identifier

    U ::= * < #number >

    O ::= U | I | ( O ) | O O
            | λ ( I : O ) → O
            | ∀ ( I : O ) → O

OM is an implementation of PTS with Infinite Number of Universes, the pure lambda calculus with dependent types. It can be compiled (code extraction) to bytecode of Erlang virtual machines BEAM and LING.

Trusted PTS with Infinite Universes

In repository OM you may found following parts of core:

PTS ships with different "modes" (spaces of types with own encodings), or "preludes", which you may find in priv directory. They are selectable with om:mode("normal").


This is a minimal practical prelude similar to Morte's base library of Gabriel Gonzalez. It contains common inductive constructions encoded using plain Church (or Boehm-Berarducci if you wish) encoding, and two basic (co)monadic effect systems: IO (free monad, for finite I/O) and IOI (free comonad, for infinitary I/O, long-term processes). The generated code is being sewed with Erlang effects that are passed as parameters to pure functions.

Note: all these folders (modules) are encoded in plain CoC in OM repository to demonstrate you the basic principles how things work. Later all these should be written in EXE languages and translated to OM automatically. You may think of OM as the low-level typed assembler of type theory.


  • Maxim Sokhatsky