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Ln

See the documentation for the target language syntax and semantics.

The shape analyzer determines which paths are "shape-safe", and the value analyzer checks if each path can indeed yield the provided output value. The shape analysis uses a non-deterministic Damas-Milner type inference, since the target language is not statically typed. The value analysis utilizes the Z3 theorem prover to prune branches as early as possible, as well as to unify with the output value.

Usage

To run, execute

./_build/default/bin/main.exe -all test.l

after dune build.

When the flag -all is omitted, only shape analysis is done.

Sample code

# lang 1
# (0, 0) 1
# (1, 1) 0
let h []
let a h.1
let b h.2
if (a + b)
  if (a + b) (a + a + 1) b
  if (a + b) b (a + a + 1)

should output

Shape & value analyzer. tests/test_7.l (L1)
Sample: ((0, 0), 1)
[let x = [([0 : β„“3], [0 : β„“4]) : β„“2] in [let h = [[] : β„“6] in [let a = [[h : β„“9].1 : β„“8] in [let b = [[h : β„“12].2 : β„“11] in [if [[a : β„“15] + [b : β„“16] : β„“14] [if [[a : β„“19] + [b : β„“20] : β„“18] [[[a : β„“23] + [a : β„“24] : β„“22] + [1 : β„“25] : β„“21] [b : β„“26] : β„“17] [if [[a : β„“29] + [b : β„“30] : β„“28] [b : β„“31] [[[a : β„“34] + [a : β„“35] : β„“33] + [1 : β„“36] : β„“32] : β„“27] : β„“13] : β„“10] : β„“7] : β„“5] : β„“1]
| []: (ΞΉ, ΞΉ), O: ΞΉ, Trace: let . = (.) in (let . = (.) in (let . = (.) in (if (. + .) β‰  0 if (. + .) β‰  0 . + . + .))); β„“1-β„“2-β„“3-β„“4-β„“5-β„“6-β„“7-β„“8-β„“9-β„“10-β„“11-β„“12-β„“13-β„“14-β„“15-β„“16-β„“17-β„“18-β„“19-β„“20-β„“21-β„“22-β„“23-β„“24-β„“25
| Eval: 1 + 2[2]
[let x = [([0 : β„“3], [0 : β„“4]) : β„“2] in [let h = [[] : β„“6] in [let a = [[h : β„“9].1 : β„“8] in [let b = [[h : β„“12].2 : β„“11] in [if [[a : β„“15] + [b : β„“16] : β„“14] [if [[a : β„“19] + [b : β„“20] : β„“18] [[[a : β„“23] + [a : β„“24] : β„“22] + [1 : β„“25] : β„“21] [b : β„“26] : β„“17] [if [[a : β„“29] + [b : β„“30] : β„“28] [b : β„“31] [[[a : β„“34] + [a : β„“35] : β„“33] + [1 : β„“36] : β„“32] : β„“27] : β„“13] : β„“10] : β„“7] : β„“5] : β„“1]
| []: (ΞΉ, ΞΉ), O: ΞΉ, Trace: let . = (.) in (let . = (.) in (let . = (.) in (if (. + .) β‰  0 if (. + .) = 0 .))); β„“1-β„“2-β„“3-β„“4-β„“5-β„“6-β„“7-β„“8-β„“9-β„“10-β„“11-β„“12-β„“13-β„“14-β„“15-β„“16-β„“17-β„“18-β„“19-β„“20-β„“26
| Falsy value found when guide_path expected a truthy value
[let x = [([0 : β„“3], [0 : β„“4]) : β„“2] in [let h = [[] : β„“6] in [let a = [[h : β„“9].1 : β„“8] in [let b = [[h : β„“12].2 : β„“11] in [if [[a : β„“15] + [b : β„“16] : β„“14] [if [[a : β„“19] + [b : β„“20] : β„“18] [[[a : β„“23] + [a : β„“24] : β„“22] + [1 : β„“25] : β„“21] [b : β„“26] : β„“17] [if [[a : β„“29] + [b : β„“30] : β„“28] [b : β„“31] [[[a : β„“34] + [a : β„“35] : β„“33] + [1 : β„“36] : β„“32] : β„“27] : β„“13] : β„“10] : β„“7] : β„“5] : β„“1]
| []: (ΞΉ, ΞΉ), O: ΞΉ, Trace: let . = (.) in (let . = (.) in (let . = (.) in (if (. + .) = 0 if (. + .) β‰  0 .))); β„“1-β„“2-β„“3-β„“4-β„“5-β„“6-β„“7-β„“8-β„“9-β„“10-β„“11-β„“12-β„“13-β„“14-β„“15-β„“16-β„“27-β„“28-β„“29-β„“30-β„“31
| Falsy value found when guide_path expected a truthy value
[let x = [([0 : β„“3], [0 : β„“4]) : β„“2] in [let h = [[] : β„“6] in [let a = [[h : β„“9].1 : β„“8] in [let b = [[h : β„“12].2 : β„“11] in [if [[a : β„“15] + [b : β„“16] : β„“14] [if [[a : β„“19] + [b : β„“20] : β„“18] [[[a : β„“23] + [a : β„“24] : β„“22] + [1 : β„“25] : β„“21] [b : β„“26] : β„“17] [if [[a : β„“29] + [b : β„“30] : β„“28] [b : β„“31] [[[a : β„“34] + [a : β„“35] : β„“33] + [1 : β„“36] : β„“32] : β„“27] : β„“13] : β„“10] : β„“7] : β„“5] : β„“1]
| []: (ΞΉ, ΞΉ), O: ΞΉ, Trace: let . = (.) in (let . = (.) in (let . = (.) in (if (. + .) = 0 if (. + .) = 0 . + . + .))); β„“1-β„“2-β„“3-β„“4-β„“5-β„“6-β„“7-β„“8-β„“9-β„“10-β„“11-β„“12-β„“13-β„“14-β„“15-β„“16-β„“27-β„“28-β„“29-β„“30-β„“32-β„“33-β„“34-β„“35-β„“36
| Eval: 1 + 2[2]
Sample: ((1, 1), 0)
[let x = [([1 : β„“3], [1 : β„“4]) : β„“2] in [let h = [[] : β„“6] in [let a = [[h : β„“9].1 : β„“8] in [let b = [[h : β„“12].2 : β„“11] in [if [[a : β„“15] + [b : β„“16] : β„“14] [if [[a : β„“19] + [b : β„“20] : β„“18] [[[a : β„“23] + [a : β„“24] : β„“22] + [1 : β„“25] : β„“21] [b : β„“26] : β„“17] [if [[a : β„“29] + [b : β„“30] : β„“28] [b : β„“31] [[[a : β„“34] + [a : β„“35] : β„“33] + [1 : β„“36] : β„“32] : β„“27] : β„“13] : β„“10] : β„“7] : β„“5] : β„“1]
| []: (ΞΉ, ΞΉ), O: ΞΉ, Trace: let . = (.) in (let . = (.) in (let . = (.) in (if (. + .) β‰  0 if (. + .) β‰  0 . + . + .))); β„“1-β„“2-β„“3-β„“4-β„“5-β„“6-β„“7-β„“8-β„“9-β„“10-β„“11-β„“12-β„“13-β„“14-β„“15-β„“16-β„“17-β„“18-β„“19-β„“20-β„“21-β„“22-β„“23-β„“24-β„“25
| Eval: 1 + 2[2] failed to unify with the output
[let x = [([1 : β„“3], [1 : β„“4]) : β„“2] in [let h = [[] : β„“6] in [let a = [[h : β„“9].1 : β„“8] in [let b = [[h : β„“12].2 : β„“11] in [if [[a : β„“15] + [b : β„“16] : β„“14] [if [[a : β„“19] + [b : β„“20] : β„“18] [[[a : β„“23] + [a : β„“24] : β„“22] + [1 : β„“25] : β„“21] [b : β„“26] : β„“17] [if [[a : β„“29] + [b : β„“30] : β„“28] [b : β„“31] [[[a : β„“34] + [a : β„“35] : β„“33] + [1 : β„“36] : β„“32] : β„“27] : β„“13] : β„“10] : β„“7] : β„“5] : β„“1]
| []: (ΞΉ, ΞΉ), O: ΞΉ, Trace: let . = (.) in (let . = (.) in (let . = (.) in (if (. + .) β‰  0 if (. + .) = 0 .))); β„“1-β„“2-β„“3-β„“4-β„“5-β„“6-β„“7-β„“8-β„“9-β„“10-β„“11-β„“12-β„“13-β„“14-β„“15-β„“16-β„“17-β„“18-β„“19-β„“20-β„“26
| Falsy value found when guide_path expected a truthy value
[let x = [([1 : β„“3], [1 : β„“4]) : β„“2] in [let h = [[] : β„“6] in [let a = [[h : β„“9].1 : β„“8] in [let b = [[h : β„“12].2 : β„“11] in [if [[a : β„“15] + [b : β„“16] : β„“14] [if [[a : β„“19] + [b : β„“20] : β„“18] [[[a : β„“23] + [a : β„“24] : β„“22] + [1 : β„“25] : β„“21] [b : β„“26] : β„“17] [if [[a : β„“29] + [b : β„“30] : β„“28] [b : β„“31] [[[a : β„“34] + [a : β„“35] : β„“33] + [1 : β„“36] : β„“32] : β„“27] : β„“13] : β„“10] : β„“7] : β„“5] : β„“1]
| []: (ΞΉ, ΞΉ), O: ΞΉ, Trace: let . = (.) in (let . = (.) in (let . = (.) in (if (. + .) = 0 if (. + .) β‰  0 .))); β„“1-β„“2-β„“3-β„“4-β„“5-β„“6-β„“7-β„“8-β„“9-β„“10-β„“11-β„“12-β„“13-β„“14-β„“15-β„“16-β„“27-β„“28-β„“29-β„“30-β„“31
| Falsy value found when guide_path expected a truthy value
[let x = [([1 : β„“3], [1 : β„“4]) : β„“2] in [let h = [[] : β„“6] in [let a = [[h : β„“9].1 : β„“8] in [let b = [[h : β„“12].2 : β„“11] in [if [[a : β„“15] + [b : β„“16] : β„“14] [if [[a : β„“19] + [b : β„“20] : β„“18] [[[a : β„“23] + [a : β„“24] : β„“22] + [1 : β„“25] : β„“21] [b : β„“26] : β„“17] [if [[a : β„“29] + [b : β„“30] : β„“28] [b : β„“31] [[[a : β„“34] + [a : β„“35] : β„“33] + [1 : β„“36] : β„“32] : β„“27] : β„“13] : β„“10] : β„“7] : β„“5] : β„“1]
| []: (ΞΉ, ΞΉ), O: ΞΉ, Trace: let . = (.) in (let . = (.) in (let . = (.) in (if (. + .) = 0 if (. + .) = 0 . + . + .))); β„“1-β„“2-β„“3-β„“4-β„“5-β„“6-β„“7-β„“8-β„“9-β„“10-β„“11-β„“12-β„“13-β„“14-β„“15-β„“16-β„“27-β„“28-β„“29-β„“30-β„“32-β„“33-β„“34-β„“35-β„“36
| Eval: 1 + 2[2] failed to unify with the output

The output is xterm-256 colorized: Capture

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