mafm

Keybase proof

I hereby claim:

• I am mafm on github.
• I am mafm (https://keybase.io/mafm) on keybase.
• I have a public key whose fingerprint is E400 C3AC EC79 56C3 D6FE 927A FA3B 8B70 4B38 F927

To claim this, I am signing this object:

mafm

mafm

(* This is a demonstration of the use of the SML module system to
   encode (Generalized Algebraic Datatypes) GADTs via Church
   encodings. The basic idea is to use the Church encoding of GADTs in
   System Fomega and translate the System Fomega type into the module
   system. As I demonstrate below, this allows things like the
   singleton type of booleans, and the equality type, to be
   represented.

   This was inspired by Jon Sterling's blog post about encoding proofs
   in the SML module system:

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from __future__ import unicode_literals
import sys

# We only use unicode in our parser, except for __repr__, which must return str.
if sys.version_info.major == 2:
    repr_str = lambda s: s.encode("utf-8")
    str = unicode
else:
    repr_str = lambda s: s

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#!/usr/bin/env python2
#-*- coding: utf-8 -*-

# NOTE FOR WINDOWS USERS:
# You can download a "exefied" version of this game at:
# http://hi-im.laria.me/progs/tetris_py_exefied.zip
# If a DLL is missing or something like this, write an E-Mail (me@laria.me)
# or leave a comment on this gist.

# Very simple tetris implementation

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(*
 * An OCaml implementation of final tagless, inspired from this article by Oleksandr Manzyuk:
 * https://oleksandrmanzyuk.wordpress.com/2014/06/18/from-object-algebras-to-finally-tagless-interpreters-2/
 *)

module FinalTagless = struct
  type eval = { eval : int }
  type view = { view : string }

  module type ExpT = sig

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#!/usr/local/Gambit-C/bin/gsi

; Copyright (C) 2004 by Marc Feeley, All Rights Reserved.

; This is the "90 minute Scheme to C compiler" presented at the
; Montreal Scheme/Lisp User Group on October 20, 2004.

; Usage with Gambit-C 4.0:
;
;    % ./90-min-scc.scm test.scm

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Require Import List.
Require Import FunctionalExtensionality.
Require Import ZArith.
Require Import Zcompare.

(* c.f. https://twitter.com/Hillelogram/status/987432184217731073 *)

Set Implicit Arguments.

Lemma map_combine : forall A B C (f : A -> B) (g : A -> C) xs,

mafm

import static java.lang.System.*;

import java.util.function.BiFunction;
import java.util.function.Function;

// Implementation of a pseudo-GADT in Java, translating the examples from
// http://www.cs.ox.ac.uk/ralf.hinze/publications/With.pdf
// The technique presented below is, in fact, just an encoding of a normal Algebraic Data Type
// using a variation of the visitor pattern + the application of the Yoneda lemma to make it
// isomorphic to the targeted 'GADT'.

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--Roughly based on https://github.com/Gabriel439/Haskell-Morte-Library/blob/master/src/Morte/Core.hs by Gabriel Gonzalez et al.

data Expr = Star | Box | Var Int | Lam Int Expr Expr | Pi Int Expr Expr | App Expr Expr deriving (Show, Eq)

subst v e (Var v')       | v == v' = e
subst v e (Lam v' ta b ) | v == v' = Lam v' (subst v e ta)            b
subst v e (Lam v' ta b )           = Lam v' (subst v e ta) (subst v e b )
subst v e (Pi  v' ta tb) | v == v' = Pi  v' (subst v e ta)            tb
subst v e (Pi  v' ta tb)           = Pi  v' (subst v e ta) (subst v e tb)
subst v e (App f a     )           = App    (subst v e f ) (subst v e a )