Lambda Mountain

λ☶ (pronounced Lambda Mountain) is a typed macro assembler that provides a relatively clean implementation of System F<: with Specialization.

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Not Your Average Assembler

Despite being an assembler, LM provides

• algebraic data types
• parameterized code and data
• hygienic macros
• platform agnostic standard libraries

Why Such a Small Codebase?

LM is currenlty about 6000 lines of code. LM solves an N by M Problem with language frontends vs language backends. The LM project might interface with larger codebases that define frontends or backends, but the core LM Calculus can stay small.

What is a Fragment Assembler?

An assembler takes pieces of data and sticks them together. Assemblers don't always understand the meaning of what they do, they just do it.

A fragment is a Key-Value Map of Strings to S-Expressions. This data structure permits more detailed manipulation of code than a typical assembler.

What is Ad-Hoc Specialization?

If we have several overloaded functions then specialization lets us choose the best fit for any particular application.

f := λ(: x X). x;
f := λ(: y Y). y;

f (: x X)

In this example the function application does not “fit” the application that expects a Y type argument, so there is only one possible candidate function.

type X implies Y;

f := λ(: x X). x;
f := λ(: y Y). y;

f (: x X)

Now both candidate functions “fit”, however X is a narrower type than Y. All X are Y, but not all Y are X. In this case we say that X is a “better fit” than Y.

Why is Ad-Hoc Specialization so Important For an Assembler?

Specialization allows us to express high-level ideas at the level of a generic functional language AND compile the code down to machine code transparently. There are no hidden layers in the compiler. The programmer gets to inspect and verify every single transformation down to individual instructions.

More About The Type System

The type system is strongly normalizing and decidable as long as all overloaded functions are given acceptable explicit types.

Prominent Features include:

• Higher Order Functions (Functional Programming)
• Parametric Polymorphism (Generic Programming)
• Subtyping (Object Hierarchies)
• Ad-Hoc Polymorphism (Function Hierarchies)
• Plural Types (Types behave more like logical predicates)