lambda-rti

THIS PROJECT IS ARCHIVED

A newer interpreter of the ITGL is available at ymyzk/lambda-dti.

lambda-rti is an interpreter of the implicitly typed gradual language (ITGL). This implementation consists of:

• Garcia and Cimini's type inference algorithm;
• a cast-inserting translator from the ITGL to the blame calculus; and
• an evaluator of the blame calculus with runtime type inference.

Requirements

• OCaml 4.03.0+
• Jbuiler (Dune)
• Menhir
• OUnit (for running unit tests)

Getting started

Global installation

$ dune build
$ dune install
$ lrti

Run $ lrti --help for command line options.

Local installation

$ dune build
$ ./_build/default/bin/main.exe

Run $ ./_build/default/bin/main.exe --help for command line options.

Docker

$ docker run -it --rm ymyzk/lambda-rti

Running tests

$ dune runtest

Syntax

Top-level

• Let declaration: let x ... = e;;
• Recursion declaration: let rec f x ... = e;;
• Expression: e;;

Expressions e

• Constants: integers, true, false, and ()
• Unary operators: + and -
• Binary operators: +, -, *, /, mod, =, <>, <, <=, >, >=, &&, and ||
• Abstraction:
  • Simple: fun x -> e
  • Multiple parameters: fun x y z ... -> e
  • With type annotations: fun (x: U1) y (z: U3) ... -> e
• Application: e1 e2
• Let expression:
  • Simple: let x = e1 in e2
  • Multiple parameters: let x y z ... = e1 in e2
  • With type annotations: let (x:U1) y (z: U3) ... : U ... = e1 in e2
• Recursion:
  • Simple: let rec f x = e1 in e2
  • Multiple parameters: let rec f x y z ... = e1 in e2
  • With type annotations: let rec f (x: U1) y (z: U3) ... : U = e1 in e2
• If-then-else Expression: if e1 then e2 else e3
• Sequence of expressions: e1; e2
• Type ascription: (e : U)

Types U

• Dynamic type: ?
• Base types: bool, int, and unit
• Function type: U -> U
• Type variables: 'a, 'b, ...

Comments

• Simple: (* comments *)
• Nested comments: (* leave comments here (* nested comments are also supported *) *)

Standard library

Some useful functions are available:

# is_bool;;
- : ? -> bool = <fun>
# is_int;;
- : ? -> bool = <fun>
# is_unit;;
- : ? -> bool = <fun>
# is_fun;;
- : ? -> bool = <fun>

# succ;;
- : int -> int = <fun>
# pred;;
- : int -> int = <fun>
# max;;
- : int -> int -> int = <fun>
# min;;
- : int -> int -> int = <fun>
# abs;;
- : int -> int = <fun>
# max_int;;
- : int = 4611686018427387903
# min_int;;
- : int = -4611686018427387904

# not;;
- : bool -> bool = <fun>

# print_bool;;
- : bool -> unit = <fun>
# print_int;;
- : int -> unit = <fun>
# print_newline;;
- : unit -> unit = <fun>

# ignore;;
- : 'a -> unit = <fun>

# exit;;
- : int -> unit = <fun>

Examples

# (fun (x:?) -> x + 2) 3;;
- : int = 5

# (fun (x:?) -> x + 2) true;;
Blame on the expression side:
line 2, character 14 -- line 2, character 15

# (fun (x:?) -> x 2) (fun y -> true);;
- : ? = true: bool => ?

# (fun (x:?) -> x) (fun y -> y);;
- : ? = <fun>: ? -> ? => ?

# (fun (x:?) -> x 2) (fun y -> y);;
- : ? = 2: int => ?

# (fun (f:?) -> f true) ((fun x -> x) ((fun (y:?) -> y) (fun z -> z + 1)));;
Blame on the environment side:
line 6, character 55 -- line 6, character 69

# (fun (f:?) -> f 2) ((fun x -> x) ((fun (y:?) -> y) (fun z -> z + 1)));;
- : ? = 3: int => ?

# let id x = x;;
id : 'a -> 'a = <fun>

# let dynid (x:?) = x;;
dynid : ? -> ? = <fun>

# succ;;
- : int -> int = <fun>

# (fun (f:?) -> f 2) (id (dynid succ));;
- : ? = 3: int => ?

# (fun (f:?) -> f true) (id (dynid succ));;
Blame on the environment side:
line 12, character 33 -- line 12, character 37

# let rec sum (n:?) = if n < 1 then 0 else n + sum (n - 1);;
sum : ? -> int = <fun>

# sum 100;;
- : int = 5050

# sum true;;
Blame on the expression side:
line 13, character 23 -- line 13, character 24

# exit 0;;

References

• Yusuke Miyazaki. Runtime Type Inference for Gradual Typing. Master's Thesis. Graduate School of Informatics, Kyoto University, 2018.
• Ronald Garcia and Matteo Cimini. Principal Type Schemes for Gradual Programs. In Proc. of ACM POPL, 2015.