Presentation at Onward! 2023 on Programming Language design.

1. TowardProgrammingLanguagesforReasoning:
Humans,SymbolicSystems,andAIAgents
Mark Marron
University of Kentucky

4. ReasoningChallenges

10. Don’t need amazing new language construct or fancy analysis
Solving complexity by adding more complexity is not working
We have all the parts we need –
consider our preconceptions & design with reasoning as a
primary concern at each step!

11. Eliminate foundational sources of
complexity!
• No Loops
• Immutable & referentially
transparent values
• Let and ITE based logic
• Fully determinized semantics
Make implicit information explicit!
• Explicit asserts, data invariants
• Strongly (and explicitly) typed –
including typed primitives

13. function abs(x: Int): Int {
var sign = 1i;
if(x < 0i) {
sign = -1i;
}
return x * sign;
}
function allPos(...args: List<Int>): Bool {
return args.allOf(pred(x) => x >= 0i);
}
allPos(1i, 2i, 3i); //true

14. function abs(x: Int): Int
{
var sign = 1;
if(x < 0) {
sign = -1;
}
return x * sign;
}
function abs(x: Int): Int {
sign_0 = 1;
if(x < 0) {
sign_1 = -1;
}
sign_2 = φ(sign_0, sign_1);
return x * sign_2;
}

15. ref method intern(str: String): Int {
if(this.has(str)) { return this.get(str); } //use the ref this parameter
ref this.add(str, this.size()); //update the ref this parameter
return this.size(); //multi-return updated parameter
}
...
var env = Environment{};
let nameid1 = ref env.internString("hello");
let nameid2 = ref env.internString("goodbye");
_debug(env); //Environment{ "hello”=>0n, "goodbye”=>1n }

16. typedecl ZipcodeUS = /[0-9]{5}(-[0-9]{4})?/;
typedecl ZipcodeUS = /[0-9]{5}(-[0-9]{4})?/;
function isNYCode(s: StringOf<ZipcodeUS>): Bool {
return s.value().startsWith(/1[0-4]/);
}
isNYCode("10001"ZipcodeUS) //true
isNYCode("40506"ZipcodeUS) //false
typedecl ZipcodeUS = /[0-9]{5}(-[0-9]{4})?/;
function isNYCode(s: StringOf<ZipcodeUS>): Bool {
return s.value().startsWith(/1[0-4]/);
}
isNYCode("10001"ZipcodeUS) //true
isNYCode(“40506"ZipcodeUS) //false
isNYCode("12") //type error not a StringOf<ZipcodeUS>
isNYCode("WC1E"PostcodeUK) //type error not a StringOf<ZipcodeUS>

17. function gcd(x: Int, y: Int): Int
requires x > 0i && y > 0i; //check is always done
ensures test $return > 0i; //only in debug/test build
{
...
}
entity CalendarEvent {
field name: String;
field location: String;
field start: DateTime;
field duration: Minutes;
invariant $name !== "";
invariant $location !== "";
invariant $duration > 0n_Minutes;
...
}

19. (define-fun abs((x Int)) Int
(let ((sign 1))
(ite (x < 0)
(let ((@sign_1 -1))
(* x @sign_1)
)
(* x sign)
)
)
)
function abs(x: Int): Int
{
var sign = 1i;
if(x < 0i) {
sign = -1i;
}
return x * sign;
}

21. /*Find the largest pair of values from the lists.*/
function findMaxPair(x: List<Int>, y: List<Int>): [Int, Int]
{
defer;
}
//=> return [x.max(), y.max()];
ensures x.contains($return.0) && y.contains($return.1);
examples [
[List{3, 2}, List{3, 5} => [2, 5]]
];
//=> return List::zip(x, y).maxArg(fn(v) => v.0);
//=> return List::zip(x, y).maxArg(fn(v) => v.0 + v.1);
Fails on Input: [List{3, 2}, List{3, 5}]
Result - [3, 5]
Expected + [2, 5]
Can you debug this and fix the code?

24. https://github.com/BosqueLanguage/BosqueCore

26. typedecl Fahrenheit = Int;
typedecl Mph = Nat;
typedecl Percentage = Nat & {
invariant $value <= 100n;
}
let a = 100n_Percentage;
let b = 101n_Percentage; //Static Error
let p = a – 25n_Percentage;
let q = a + 25n_Percentage; //Runtime Error
let a = 100i_Fahrenheit;
let b = 99i_Fahrenheit;
check a < b;

27. (define-fun abs((x Int)) Int
(let ((sign 1))
(ite (x < 0)
(let ((@sign_1 -1))
(* x @sign_1)
)
(* x sign)
)
)
)
function abs(x: Int): Int {
var sign = 1i;
if(x < 0i) {
sign = -1i;
}
return x * sign;
}