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Concept Parameters for Generic Programming

Concept Parameters in STLC

Coq formalization of "concept parameters" for "generic" programming in STLC.

The first step is to add simple concepts and models into STLC: look at cpSTLCa* files in cpSTLC.
Concepts contain function signatures only, models define those functions. A program in cpSTLCa consists of concepts' and models' definitions and a term in STLC extended with concept parametrization and model application.

Here is an example of well-typed cpSTLCa program:

concept MonoidNat
  ident : Nat
  op    : Nat -> Nat -> Nat
endc

model MNPlus of MonoidNat
  ident = 0
  op    = \x:Nat.\y:Nat. x + y
endm

model MNMult of MonoidNat
  ident = 1
  op    = \x:Nat.\y:Nat. x * y
endm

(* accOrTwice takes MonoidNat concept parameter 
     and two nats, x and y, 
   and either accumulates x and y using monoid binary operation
     (if x is not equal to identity element)
     or accumulates y and y (if x is equal to identity element) 
*)
let 
  accOrTwice = \m#MonoidNat. \x:Nat.\y:Nat. if x == m.ident 
                 then m.op y y
                 else m.op x y
                          
in
  (* sum of 3 5*)
  accOrTwice # MNSum 3 5