Logical relations

Logical relations are a proof method employed in programming language semantics to show that two denotational semantics are equivalent.

To describe the process, let us denote the two semantics by $[\![-]\!]_i$ , $i=1,2$ . For each type $A$ , we associate a particular relation $a\sim b$ between $[\![A]\!]_1$ and $[\![A]\!]_2$ . We define this relation such that for all program phrase $M$ , the two denotations are related: $[\![M]\!]_1 \sim [\![M]\!]_2$ . Another property of this relation is that related denotations for ground types are equivalent in some sense, usually equal. The conclusion is then that both denotations exhibit equivalent behavior on ground terms, hence are equivalent.

单词	Logical Relations
释义	Logical Relations 原声例句笑 How, indeed, should it come about that this particular logical relation, as soon as it is perceived, contracts, expands and shakes our limbs, whilst all other relations leave the body unaffected? 事实上，这种特殊的逻辑关系一旦被感知到，就会收缩、扩张和摇晃我们的四肢，而所有其他关系却不受影响，这是怎么回事呢？英语百科 Logical relations Logical relations are a proof method employed in programming language semantics to show that two denotational semantics are equivalent. To describe the process, let us denote the two semantics by $[\![-]\!]_i$ , $i=1,2$ . For each type $A$ , we associate a particular relation $a\sim b$ between $[\![A]\!]_1$ and $[\![A]\!]_2$ . We define this relation such that for all program phrase $M$ , the two denotations are related: $[\![M]\!]_1 \sim [\![M]\!]_2$ . Another property of this relation is that related denotations for ground types are equivalent in some sense, usually equal. The conclusion is then that both denotations exhibit equivalent behavior on ground terms, hence are equivalent.
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Logical Relations

Logical relations