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Just unfolds #34

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just-left-unfold-Nth
h0nzZik Dec 20, 2019
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just-right-unfold-Nth
h0nzZik Jan 12, 2020
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2 changes: 2 additions & 0 deletions prover/prover.md
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Original file line number Diff line number Diff line change
Expand Up @@ -31,6 +31,8 @@ module STRATEGIES-EXPORTED-SYNTAX
| "direct-proof"
| "check-lhs-constraint-unsat"
| "smt" | "smt-z3" | "smt-cvc4" | "smt-debug"
| "just-left-unfold-Nth" "(" Int ")"
| "just-right-unfold-Nth" "(" Int ")"
| "left-unfold" | "left-unfold-Nth" "(" Int ")"
| "right-unfold" | "right-unfold-Nth" "(" Int "," Int ")" | "right-unfold" "(" Symbol ")"
| "right-unfold-all" "(" "bound" ":" Int ")"
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57 changes: 57 additions & 0 deletions prover/strategies/unfolding.md
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Expand Up @@ -62,6 +62,63 @@ module STRATEGY-UNFOLDING
=> getUnfoldables(P) ++Patterns getUnfoldables(REST)
```

### Just Right Unfold

```k

rule <strategy> just-right-unfold-Nth(M)
=> just-right-unfold-Nth-#1(M, getUnfoldables(RHS))
...
</strategy>
<claim> \implies(\and(LHS), RHS) </claim>

syntax Strategy ::= "just-right-unfold-Nth-#1" "(" Int "," Patterns ")"
| "just-right-unfold-Nth-#2" "(" Pattern "," Pattern ")"


rule <strategy> just-right-unfold-Nth-#1(M, PS)
=> just-right-unfold-Nth-#2(getMember(M, PS), unfold(getMember(M, PS)))
...
</strategy>
requires 0 <=Int M andBool M <Int getLength(PS)

rule <claim> \implies(LHS, RHS => subst(RHS, PATTERN, BODY)) </claim>
<strategy> just-right-unfold-Nth-#2(PATTERN, BODY)
=> noop
...
</strategy>
```


### Just Left Unfold Nth

Just unfolds the Nth predicate on the LHS.

```k
rule <strategy> just-left-unfold-Nth(M)
=> just-left-unfold-Nth-#1(M, getUnfoldables(LHS))
...
</strategy>
<claim> \implies(\and(LHS), RHS) </claim>

syntax Strategy ::= "just-left-unfold-Nth-#1" "(" Int "," Patterns ")"
| "just-left-unfold-Nth-#2" "(" Pattern "," Pattern ")"


rule <strategy> just-left-unfold-Nth-#1(M, PS)
=> just-left-unfold-Nth-#2(getMember(M, PS), unfold(getMember(M, PS)))
...
</strategy>
requires 0 <=Int M andBool M <Int getLength(PS)

rule <claim> \implies(LHS => subst(LHS, PATTERN, BODY), RHS) </claim>
<strategy> just-left-unfold-Nth-#2(PATTERN, BODY)
=> noop
...
</strategy>

```

### Left Unfold (incomplete)

```k
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