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Iron Lambda

Iron Lambda is a collection of Coq formalizations for functional languages of increasing complexity. All proofs use straight deBruijn indices for binders.

  • The home page is on a separate site.
  • The absence of bugs has been mechanically verified, hence there is no bug tracker.
  • Comments on style, or requests for more information should go to iron [at]

Proofs that are "done" have at least Progress and Preservation theorems.

  • Simple

    Simply Typed Lambda Calculus (STLC). "Simple" here refers to the lack of polymorphism.

  • SimplePCF

    STLC with booleans, naturals and fixpoint.

  • SimpleRef

    STLC with mutable references. The typing judgement includes a store typing.

  • SimpleData

    STLC with algebraic data and case expressions. The definition of expressions uses indirect mutual recursion. Expressions contain a list of case-alternatives, and alternatives contain expressions, but the definition of the list type is not part of the same recursive group. The proof requires that we define our own induction scheme for expressions.

  • SystemF

    Compared to STLC, the proof for SystemF needs more lifting lemmas so it can deal with deBruijn indices at the type level.

  • SystemF2

    Very similar to SystemF, but with higher kinds.

  • SystemF2Data

    SystemF2 with algebraic data and case expressions. Requires that we define simultaneous substitutions, which are used when subsituting expressions bound by pattern variables into the body of an alternative. The language allows data constructors to be applied to general expressions rather than just values, which requires more work when defining evaluation contexts.

  • SystemF2Store

    SystemF2 with algebraic data, case expressions and a mutable store. All data is allocated into the store and can be updated with primitive polymorphic update operators.

  • SystemF2Effect

    SystemF2 with a region and effect system. Mutable references are allocated in regions in the store, and their lifetime follows the lexical structure of the code.